petrology of the basic granulites from kodaikanal south india abstract basic granulites occurring as small enclaves and pods within charnockites contain predominantly orthopyroxene clinopyroxene hornblende plagioclase feldspar and quartz chemical composition of coexisting orthopyroxene clinopyroxene plagioclase and hornblende has been represented in acf and afm diagrams the mineral assemblages and the textural relationships of the basic granulites have been described garnet is notably absent in the basic granulites and this is explained as due to lower

simulation of curved open channel flows by 3d hydrodynamic model a mathematical model of three dimensional 3d free surface flows has been applied to simulate the curved channel flows and mass transport in the horizontal plane a channel fitted curvilinear coordinate system is used whereas in the vertical plane the transformation is adopted to track the free surface and variable bed topography to reduce the numerical diffusion the second order upwind scheme of roe is incorporated to discretize the convection terms the standard k e model has been modified to take account of some anisotropic effects appearing in shallow curved channels i e streamline curvature and the damping effects of free surface and solid walls the governing equations are solved in a collocated grid system by a fractional three step implicit algorithm two test cases from curved flumes have been studied 1 a 270 channel bend with a sloped outer bank and 2 a meandering channel with mass transport the results are compared with the available data which shows generally good agreement

surface based transport model for mixed size sediment we present a transport model for mixed sand gravel sediments fractional transport rates are referenced to the size distribution of the bed surface rather than subsurface making the model completely explicit and capable of predicting transient conditions the model is developed using a new data set of 48 coupled observations of flow transport and bed surface grain size using five different sediments the model incorporates a hiding function that resolves discrepancies observed among earlier hiding functions the model uses the full size distribution of the bed surface including sand and incorporates a nonlinear effect of sand content on gravel transport rate not included in previous models the model shares some common elements with two previous surface based transport models but differs in using the full surface size distribution and in that it is directly developed from a relatively comprehensive data set with unambiguous measurement of surface grain size over a range of flow transport rate and sediments

composition and structure of the central aleutian island arc from arc parallel wide angle seismic data new results from wide angle seismic data collected parallel to the central aleutian island arc require an intermediate to mafic composition for the middle crust and a mafic to ultramafic composition for the lower crust and yield lateral velocity variations that correspond to arc segmentation and trends in major element geochemistry the 3 d ray tracing 2 5 d inversion of this sparse wide angle data set which incorporates independent phase interpretations and new constraints on shallow velocity structure produces a faster and smoother result than a previously published velocity model middle crustal velocities of 6 5 7 3 km s over depths of 10 20 km indicate an andesitic to basaltic composition high lower crustal velocities of 7 3 7 7 km s over depths of 20 35 km are interpreted as ultramafic mafic cumulates and or garnet granulites the total crustal thickness is 35 37 km this result indicates that the aleutian island arc has higher velocities and thus more mafic compositions than average continental crust implying that significant modifications would be required for this arc to be a suitable building block for continental crust lateral variations in average crustal velocity below 10 km roughly correspond to trends in major element geochemistry of primitive mg 0 6 lavas the highest lower crustal velocities and presumably most mafic material are detected in the center of an arc segment between unmak and unalaska islands implying that arc segmentation exerts control over crustal composition

predicting incipient motion including the effect of turbulent pressure fluctuations in the bed 1 incipient motion of particles on a river bed can in principle be understood and predicted from a balance of the forces acting on the particles on a natural river bed the exposure of particles to the flow is variable the effect of exposure on the initiation of motion including the case of deep embedding is studied in this paper so far the turbulence induced lifting force has been derived exclusively from examinations of the surface flow the understanding of destabilization processes of the riverbed is improved when turbulence induced vertical pressure gradients in the upper sediment layer are included this is particularly important for particles that lie in the lee of larger ones an analytical solution for the critical shields parameter of spherical particles is found including the effects of pressure fluctuations in the bed macroscale flow structures average bed slope and shallow flow existing laboratory data designed to test the effect of exposure and roughness conditions are in excellent agreement with the new model

spatially averaged open channel flow over rough bed in this paper it is suggested that the double averaged in temporal and in spatial domains momentum equations should be used as a natural basis for the hydraulics of rough bed open channel flows especially with small relative submergence the relationships for the vertical distribution of the total stress for the simplest case of 2d steady uniform spatially averaged flow over a rough bed with flat free surface are derived these relationships explicitly include the form induced stresses and form drag as components of the total stress using this approach we define three types of rough bed flows 1 flow with high relative submergence 2 flow with small relative submergence and 3 flow over a partially inundated rough bed the relationships for the double averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible the double averaged turbulent and form induced intensities and stresses for the case of regular spherical segment type roughness show the dominant role of the double averaged turbulence stresses and form drag in momentum transfer in the near bed region

effects of a pebble cluster on the turbulent structure of a depth limited flow in a gravel bed river pebble clusters are important morphological features of gravel bed rivers and have a significant effect on the spatial and temporal response of the flow this paper presents original results from measurements of velocity taken at a high spatial and temporal resolution in a turbulent flow upstream and downstream from a pebble cluster three electromagnetic current meters 0 013 m in diameter mounted on a wading rod were deployed upstream and downstream of an isolated pebble cluster along 31 vertical profiles that contained between 7 and 13 points in a 5 m long section the high sampling resolutions in a natural environment permitted characterization of the complex dynamics of the turbulent flow in the vicinity of the cluster the description of these dynamics is based on the interpretation of contour maps of several turbulence statistics including moments of velocity distributions reynolds shear stress quadrant analysis and autocorrelation function downstream from the cluster flow is decelerated the intensity of turbulence increases and zones of strong vertical motions are present the superimposition of the maps allowed us to decompose the field of turbulent flow around a pebble cluster into distinct regions in a downstream direction from the cluster we observed zones of flow acceleration recirculation vortex shedding flow reattachment fluid upwelling and flow recovering results indicate the existence of highly dynamic boundaries between zones where strong intermittent events are generated they also highlight the difference between shedding and upwelling motions of the flow

a mixing layer theory for flow resistance in shallow streams 1 a variety of surface roughness characterizations have emerged from nineteenth and twentieth century studies of channel hydraulics when the water depth h is much larger than the characteristic roughness height ks roughness formulations such as manning s n and the friction factor f can be explicitly related to the momentum roughness height zo in the log law formulation for turbulent boundary layers thereby unifying roughness definitions for a given surface however when h is comparable to or even smaller than ks the log law need not be valid using a newly proposed mixing layer analogy for the inflectional velocity profile within and just above the roughness layer a model for the flow resistance in shallow flows is developed the key model parameter is the characteristic length scale describing the depth of the kelvin helmholtz wave instability it is shown that the new theory originally developed for canopy turbulence recovers much of the earlier roughness results for flume experiments and shallow gravel streams this study is the first to provide such a unifying framework between canopy atmospheric turbulence and shallow gravel stream roughness characterization the broader implication of this study is to support the merger of a wealth of surface roughness characterizations independently developed in nineteenth and twentieth century hydraulics and atmospheric sciences and to establish a connection between roughness formulations across traditionally distinct boundary layer types

contamination of the marcy anorthosite massif adirondack mountains ny petrologic and isotopic evidence oxygen isotope analyses of 101 samples from the marcy anorthosite massif 61 from this study 40 from taylor 1969 indicate that two major and distinct processes of crustal contamination have affected the massif ninety percent of the 93 samples with over 65 plagioclase are enriched in 18o by 2 6 relative to normal anorthosites or gabbros the average 18o for 83 enriched samples is 9 5 depletions in 18o occur in 8 of the samples which have values ranging from 3 0 to 5 8 only 2 of the samples fall within the normal magmatic range for anorthosites low 18o values of 3 0 to 5 8 in the anorthosite occur only near contacts and a gradient in 18o occurs near the contact within the border zone of the massif low 18o values in both the anorthosite and adjacent wollastonite skarns with 18o down to 1 3 were probably caused by isotopic exchange with heated meteoric water when the anorthosite intruded at shallow levels prior to grenvilleage 1 1 by granulite facies metamorphism the 18o enrichment was ascribed to exchange between anorthosite and 18o rich marble by means of a pervasive h2o co2 fluid during the regional metamorphism by taylor 1969 however a number of lines of evidence argue against this hypothesis 1 the preservation of premetamorphic low 18o values in anorthosite from the border zone as well as preserved gradients in 18o from a number of localities 2 mass balance calculations of the amount of marble necessary to produce the 18o enrichment 3 metamorphic phase equilibria which buffer p text co text 2 and p text h text 2 text o to low values and 4 recent oxygen isotope analyses show homogeneity which indicates that magmatic oxygen isotope compositions have been preserved we evaluated the importance of magmatic assimilation of country rock at the present level of intrusion as an alternative cause of the 18oenrichment samples from 2 distinct lobes of the massif were analyzed the ne lobe where xenoliths of metasedimentary country rock are common and the nw lobe where xenoliths are scarce and the country rock is dominantly granitic the mean values of 18o for these two lobes are 9 6 in the ne and 9 3 in the nw thus magmatic assimilation at the present level of exposure probably had only localized and relatively minor effects on the oxygen isotope composition of the massif this conclusion is supported by rb sr data variations in rb content and 87sr 86sr i show that such crustal contamination is localized generally occurring only in samples near the border zone all of the available results suggest that the 18o enrichment is a magmatic feature acquired prior to intrusion at the present level of exposure

a gabbro to eclogite transition on flemsoy sunnmore western norway the migmatitic gneisses on the nordoyane islands western norway enclose abundant inclusions of coronitic gabbros and different types of country rock eclogites gabbros on flemsoy show a prograde step wise transition to eclogite via a transitional stage in which garnet and orthopyroxene form coronas between igneous olivine and sodic plagioclase relics after igneous plagioclase cumulates eclogitization proceeds by a complex set of continuous and discontinuous reactions opx and spinel form as transient phases but are consumed in various omphacite forming reactions during eclogite recrystallization relict igneous clinopyroxene shows a continuous increase in jd content while garnet becomes less calcic and more homogeneous from the corona stage to recrystallized eclogite the reactions are strongly diffusion controlled and have been enhanced locally by oxidation and the presence of a fluid phase and deformation while low strain areas of the gabbros remained coronitic whole rock chemistry mineral parageneses and calculated p t conditions are similar for the gabbroeclogites and two types of country rock eclogites some of the layered country rock eclogites appear to have been derived from the coronite bodies p estimates are in the order 15 20 kbar while kgarcpxd values suggest maximum t values of 750 60 c for the eclogite metamorphism in the area

geobarometers involving clinopyroxene garnet plagioclase ilmenite rutile sphene and quartz estimation of pressure in quartz absent assemblages enthalpy of formation and third law entropy for andradite ca3fe2si3o12 and hedenbergite cafesi2o6 at standard state have been retrieved from experimental p t f o2 data on the stability relations of these phases the data for hedenbergite were combined with the thermodynamic data for related phases berman 1988 to formulate the geobarometers based on the reactions cafesi2o6 2caal2si2o8 2fetio3 ca3al2si3o12 fe3al2si3o12 2tio2 cpg ir 3cafesi2o6 3caal2si2o8 3fetio3 ca3al2si3o12 2fe3al2si3o12 3catisio5 cpg is and 3cafesi2o6 3caal2si2o8 2ca3al2si3o12 fe3al2si3o12 3sio2 cpg o the geobarometers involving rutile and sphene are proposed for the first time in several granulite terranes pressures have been estimated from the three geobarometers for basic granulites and charnockitic suite of rocks containing the above assemblages in clinopyroxene garnet plagioclase quartz ilmenite rutile assemblages pressures obtained from cpg ir are within 500 bars of pressures calculated from the cpg q barometer however if rutile is absent the pressures computed from the cpg ir barometer are 300 to 1 200 bars higher than those calculated from the cpg q barometer for maximum differences in pressures obtained from the two equilibria tio2 activity a tio2 in the rocks is calculated to be 0 8 the sphene bearing geobarometer cpg is also registers pressures comparable 500 bars to those obtained from the cpg q barometer the close agreement in pressure values obtained from the cpg ir and the cpg is equilibria with those registered by the cpg q geobarometer in assemblages containing quartz implies that the rutile and sphene bearing geobarometers which do not involve quartz can also be applied to estimate pressures from quartz absent assemblages assemblages which are not amenable to quantitative geobarometry using existing formulations

macroroughness and variations in reach averaged flow resistance in steep mountain streams 1 steep mountain streams typically feature macroroughness elements like large immobile boulders or channel spanning bedforms such as step pool sequences the effects of macroroughness on resistance and flow velocity are not well understood and appropriate field parameters for representing macroroughness in flow velocity equations have not been identified the prediction of flow velocity in rough and steep streams therefore remains challenging we measured flow velocity and several macroroughness parameters i e boulder concentration boulder diameter and protrusion and roughness of longitudinal channel profiles in six reaches of steep mountain streams with plane bed riffle step pool and cascade channel morphologies the between site variations in flow resistance can be explained to a large degree by nondimensionalization of discharge and flow velocity using channel slope and a characteristic roughness length using any of our roughness parameters as the characteristic roughness length this nondimensionalization leads to a similarity collapse of the entire data set the remaining differences in flow resistance among the streams are related to dimensionless measures of macroroughness that describe the concentration of boulders or step density in a reach boulder concentration represents the measure best describing the data and is used in a simple regression equation for flow velocity the predictions were better than predictions by the variable power law equation proposed by ferguson although the regression might not be statistically significant the observed trends suggest that boulder concentration partly explains the residual variance of between site variation of flow resistance

velocity distribution and bed roughness in high gradient streams a model for the velocity field over a poorly sorted bed is derived herein and applied to flow in steep streams with coarse gravel beds in such streams large clasts often are comparable in size to stream depth and act as obstacles to the flow the effect of these obstacles on a flow is estimated by partitioning total stress proportional to the depth slope product into a purely fluid component and a form drag component associated with flow around the obstacles an eddy viscosity closure is used with a length scale dependent on both distance from the boundary and wake dimension resulting velocity profiles agree well with profiles measured by marchand et al 1984 in nine mountain streams in colorado model runs for a range of conditions reveal that the velocity distribution depends primarily on d84z and flow depth h d84z is the length of the vertically oriented axis of clasts at the 84th percentile of the grain size distribution calculated values of mean velocity normalized by shear velocity are well represented by a simple log linear relationship in terms of relative roughness d84 h

p t paths from high temperature shear zones beneath ophiolites mctamorphic rocks of the st anthony complex of north western newfoundland are best interpreted in terms of a high temperature shear zone formed between down going continental margin rocks and overriding oceanic lithosphere in a subduction zone high grade rocks immediately beneath the oceanic lithosphere peridotite display retrograde meta morphism in high strain zones whereas lower grade rocks near the base of the metamorphic complex display prograde metamorphism in high strain zones mylonite zones in meta basitcs at all levels in the complex contain the assemblage epidote hornblende albite sodic oligoclase these observations suggest that the inverted metamorphic gradient within the st anthony complex results from the fortuitous preservation of residual metamorphic assemblages from different crustal levels within an epidote amphibolite facies shear zone the degree of re equilibration is strongly dependent on the degree of strain and is best achieved in synmetamorphic mylonite zones this interpretation of the st anthony complex can be extended to other sub ophiolite metamorphic sheets which show very similar relationships it is proposed that most metamorphic sheets beneath ophiolites are high temperature shear zones the p t paths of which preserve records of burial and exhumation in subduction zones

comparing different methods of bed shear stress estimates in simple and complex flow fields bed shear stress is a fundamental variable in river studies to link ow conditions to sediment transport it is however dif cult to estimate this variable accurately particularly in complex ow elds this study compares shear stress estimated from the log pro le drag reynolds and turbulent kinetic energy tke approaches in a laboratory ume in a simple boundary layer over plexiglas and over sand and in a complex ow eld around de ectors results show that in a simple boundary layer the log pro le estimate is always the highest over plexiglas the tke estimate was the second largest with a value 30 per cent less than the log estimate however over sand the tke estimate did not show the expected increase in shear stress in a simple boundary layer the reynolds shear stress seems the most appropriate method particularly the extrapolated value at the bed obtained from a turbulent pro le in a complex ow eld around de ectors the tke method provided the best estimate of shear stress as it is not affected by local streamline variations and it takes into account the increased streamwise turbulent uctuations close to the de ectors it is suggested that when single point measurements are used to estimate shear stress the instrument should be positioned close to 0 1 of the ow depth which corresponds to the peak value height in pro les of reynolds and tke shear stress copyright 2004 john wiley sons ltd

the characteristics of turbulence in a shear zone downstream of a channel constriction in a coarse grained forced pool a field based project was initiated to characterize the influence of varying discharge and bed topography along a pool exit slope on the strength of turbulence generated by vortex shedding velocities were measured with an adv downstream of a boulder constriction within a shear zone of a large pool measurements were repeated for four flows that varied from 20 to 50 of bankfull discharge an additional longitudinal profile was conducted along the pool thalweg plots of velocity demonstrate high near bed velocities and turbulence levels in the pools turbulence levels were highest closer to the constriction in the shear zone turbulent kinetic energy decayed in the downstream direction in response to the bed topography and at lower discharges instantaneous velocities are large enough to temporarily lift pebbles at this depth it appears that instantaneous forces created by vortex shedding may play an important role in scouring pools downstream of constrictions the turbulence may also respond to changes in bed topography in a manner that encourages feedbacks among bed topography characteristics of turbulence and sediment transport

velocity distribution in compound channel flows by numerical modeling the paper examines the problem of prediction of uniform turbulent flow in a compound channel with the nonlinear k e model this model is capable of predicting the secondary currents caused by the anisotropy of normal turbulent stresses that are important features of the flow in compound channels as they determine the transverse momentum transfer the model is applied to reproduce experimental runs available in the literature the comparison shows that the model predicts with accuracy the distribution of the primary velocity component the secondary circulation and the discharge distribution the numerical results are used to search a subdivision surface between main channel and floodplain on the basis of the flow field and to compare different subdivision surfaces on the basis of the discharge distribution by a simple uniform flow formula the better subdivision surfaces as predicted by the model are the diagonal surface going from the corner between main channel and floodplain to the free surface on

the spatial characterization of turbulence around large roughness elements in a gravel bed river abstract this study characterizes the flow field above and around multiple instream submerged cobbles boulders and pebble clusters in order to obtain a better understanding of the hydrodynamics associated with large roughness elements lres in gravel bed rivers spatially distributed high frequency three dimensional velocity measurements were recorded in situ using acoustic doppler velocimeters at different flow stages the spatial distributions of turbulent kinetic energy ke longitudinal component integral timescales itsu and reynolds shear stresses were characterized and are presented for selected sites the longitudinal vertical reynolds shear stress increased with flow stage more strongly than the longitudinal lateral or lateral vertical reynolds shear stresses and dominate at the highest measured flows canonical redundancy analysis was used to relate lre morphometrics and mean flow conditions to the turbulence parameters estimated in the lre wakes i e ke itsu and reynolds shear stresses lre size and mean unobstructed velocity explained the highest proportion of the variance in the turbulent wake statistics multivariate regression models based on lre width mean unobstructed longitudinal velocity and flow depth are presented offering a tool to predict lre wake turbulence

flow resistance in steep streams an experimental study 1 frequently an assessment of the mean water velocity in a stream is necessary to estimate the discharge associated with a particular flow depth or conversely the mean depth associated with a particular discharge in the absence of a direct measurement of flow velocity a flow resistance approach which establishes the relation between depth and velocity can be applied two approaches have been used in the past traditional approaches based on the use of a resistance coefficient e g darcy weisbach or dimensionless hydraulic geometry approaches to examine if one approach is more appropriate for steep streams data from 31 flume experiments conducted to examine flow resistance in self formed cascade channels were analyzed a dimensionless hydraulic geometry approach developed using at a station data to characterize the q exponent and between site data to characterize the exponent on the channel slope term was more accurate than more traditional approaches the developed relation was similar to the established rational relation v g0 2q0 6s 0 4s0 2 suggesting that the rational relation has merit the approach does not utilize a flow partitioning approach since in steep streams with small relative depths the grains themselves generate form and spill resistance the observation that a single dimensionless hydraulic geometry flow resistance relation can describe measurements across a range of grain sizes and bed slopes 3 21 suggests that steep streams may follow a single scaling relation similar to the regime equations associated with lowland rivers

response of bed surface patchiness to reductions in sediment supply 1 river beds are often arranged into patches of similar grain size and sorting patches can be distinguished into free patches which are zones of sorted material that move freely such as bed load sheets forced patches which are areas of sorting forced by topographic controls and fixed patches of bed material rendered immobile through localized coarsening that remain fairly persistent through time two sets of flume experiments one using bimodal sand rich sediment and the other using unimodal sand free sediment are used to explore how fixed and free patches respond to stepwise reductions in sediment supply at high sediment supply migrating bed load sheets formed even in unimodal sand free sediment yet grain interactions visibly played a central role in their formation in both sets of experiments reductions in supply led to the development of fixed coarse patches which expanded at the expense of finer more mobile patches narrowing the zone of active bed load transport and leading to the eventual disappearance of migrating bed load sheets reductions in sediment supply decreased the migration rate of bed load sheets and increased the spacing between successive sheets one dimensional morphodynamic models of river channel beds generally are not designed to capture the observed variability but should be capable of capturing the time averaged character of the channel when applied to our experiments a 1 d morphodynamic model rte bookagdegnormgravmixpw xls predicted the bed load flux well but overpredicted slope changes and was unable to predict the substantial variability in bed load flux and load grain size because of the migration of mobile patches our results suggest that 1 the distribution of free and fixed patches is primarily a function of sediment supply 2 the dynamics of bed load sheets are primarily scaled by sediment supply 3 channels with reduced sediment supply may inherently be unable to transport sediment uniformly across their width and 4 cross stream variability in shear stress and grain size can produce potentially large errors in width averaged sediment flux calculations

linking spatial patterns of bed surface texture bed mobility and channel hydraulics in a mountain stream to potential spawning substrate for small resident trout abstract in this paper we examined spatial patterns of bed texture bed mobility and channel hydraulics in four reaches of a mountain stream with moderate gradient

flow resistance estimation in mountain rivers examination of the flow resistance of high gradient gravel and boulder bed rivers using data collected in british mountain rivers with slopes of 0 4 4 shows that there are differences in resistance variation between mountain and lowland rivers and that between site variations do not necessarily reflect at a site variations comparison of data with the familiar resistance equation relating the dracy weisbach friction factor to the logarithm of relative submergence shows that the equation tends to overestimate the resistance in uniform flow the equation also tends to underestimate the rate of change of resistance at a site as discharge varies with high gradients the influences of nonuniform channel profile sediment size distribution channel slope and sediment transport are reviewed but the data do not allow any quantification of these effects instead an empirical approach based on the available data is presented allowing the friction factor to be calculated from the relative submergence with an error of up to n25 to n35 a summary of the field data is included

numerical simulation of turbulence and sediment transport of medium sand a model of sand transport in water is produced by combining a turbulence resolving large eddy simulation les with a discrete element model dem prescribing the motion of individual grains of medium sand the momentum effect of each particle on the fluid is calculated at the les cell containing the particle and the fluid velocity and pressure interpolated to each particle center is used to derive fluid force on each particle in the dem eleven numerical experiments are conducted of an initially flat bed of particles the experiments span a range of motion from essentially no motion to vigorous suspension hydraulic roughness is found to increase abruptly at the transition from bed load to suspended load transport suspended sediment extracts momentum from the flow and decreases the rate of shear whereas slightly higher in the flow vertical drag by suspended grains damps turbulence and increases the rate of shear vertical sediment diffusivity and effective particle settling velocity are much smaller than is commonly assumed in suspended sediment models the bed load experiments suggest that saltation by itself is a poor model of bed load sand transport in contrast to expectations from saltation models the peak bed load flux occurs at essentially the same level as the bed and grains move slowly in frequent contact with other grains higher and faster moving bed load grains that can be considered to be in saltation represent a smaller portion of the total flux entrainment of bed load grains occurs in response to fluid penetration of the bed by high vorticity turbulence structures embedded within broader high speed fluid regions referred to as a sweeps or high speed wedges

flow turbulence over fixed and weakly mobile gravel beds characteristics of turbulence structure in quasi 2d flows with static and weakly mobile gravel beds are presented three sets of measurements with acoustic doppler velocimeters in an irrigation canal were used two with subcritical bed shear stress static beds and one with the bed shear stress o close to critical oc weakly mobile bed the analyses included vertical distributions of local mean velocities turbulence intensities turbulent shear stresses velocity auto and cross spectra the quadrant method and high order velocity moments a number of properties of turbulence intensities high order moments streamwise bursting parameters and velocity spectra appeared to be similar for all three flows but some properties were different the most important one was an observed reduction in the von karman constant for the flow with weakly mobile bed comparison of these results with other studies and analogies with drag reducing flows suggest that at o oc 1 the drag on the bed for a given granula

evaluation of flow resistance in gravel bed rivers through a large field data set 1 a data set of 2890 field measurements was used to test the ability of several conventional flow resistance equations to predict mean flow velocity in gravel bed rivers when used with no calibration the tests were performed using both flow depth and discharge as input since discharge may be a more reliable measure of flow conditions in shallow flows generally better predictions are obtained when using flow discharge as input the results indicate that the manning strickler and the keulegan equations show considerable disagreement with observed flow velocities for flow depths smaller than 10 times the characteristic grain diameter most equations show some systematic deviation for small relative flow depth the use of new definitions for dimensionless variables in terms of nondimensional hydraulic geometry equations allows the development of a new flow resistance equation the best overall performance is obtained by the ferguson approach which combines two power law flow resistance equations that are different for deep and shallow flows to use this approach with flow discharge as input a logarithmic matching equation in terms of the new dimensionless variables is proposed for the domains of intermediate and large scale roughness the field data indicate a considerable increase in flow resistance as compared with the domain of small scale roughness the ferguson approach is used to discuss the importance of flow resistance partitioning for bed load transport calculations at flow conditions with intermediate and large scale roughness in natural gravel cobble and boulder bed streams

theoretical development on the effects of changing flow hydraulics on incipient bed load motion 1 several decades of flume and field measurements have indicated that in rough turbulent flows the critical shields stress increases with increasing slope and associated decreasing relative depth this result contradicts the usual consideration of a decreased critical shields value on very steep slopes because of increased gravitational effects however recent studies have demonstrated that these experimental results could be reproduced with a force balance model if the classical logarithmic velocity profile was replaced with a velocity profile that was more compatible with available velocity measurements over gravel beds these measurements indicate the existence of a roughness layer that is a zone of almost constant velocity close to the bed whose properties mean velocity and turbulence depended on the flow s relative depth unfortunately velocity profile measurements for low relative depth associated with steep slopes are scarce and it is still difficult to include such flow properties in a force balance model flow resistance data on the basis of depth average velocity measurements are very common and cover a wide range of slopes and relative depths in this paper these data are used to fit a velocity profile including a roughness layer when used in a force balance model for incipient motion it adequately reproduced a data set composed of 270 critical shields values measured in a flume with near uniform sediments the relevance of this research to field problems is discussed using a data set composed of 92 critical shields stresses obtained from field measurements finally a model is proposed for field applications taking into account the slope effect

adv measurements around a cluster microform in a shallow mountain stream a field study was conducted to examine the turbulent properties of the flow around a naturally formed cluster bedform this was carried out on a mountain river using a 3d acoustic doppler velocimeter adv concurrent with this objective the ability of the adv to make measurements in a shallow flow over a cobble bed ho d84 1 75 was examined adv measurements in natural clear water shallow flows around obstacles are inherently difficult to obtain due to 1 signal interference between the acoustic reflections from the boundary and the adv sample volume 2 regions of high turbulent intensity such as in local detached shear layers and 3 low concentrations of suspended particles passing through the adv sampling volume these processes result in velocity time series that contain a significant amount of spikes lower than average signal to noise ratios and lower than average correlation values a filtering process that optimized the removal of bad points while retaining a sufficient number of poin

influence of relative submergence on spatial variance and form induced stress of gravel bed flows 1 spatial flow variance has a strong control on sediment transport sediment water interface exchange mechanisms and the distribution and behavior of aquatic organisms in rivers thus being able to quantify spatial flow variance and how it varies with different water levels is important for understanding how fluvial processes change during periods of time varying flow in this paper laboratory flume measurements of near bed flow velocity were used to quantify spatial flow variance and form induced stress and their variation with flow submergence within and above the surface of porous gravel beds with differing grain roughness the analysis revealed spatial flow variance was usually four or five times higher within the roughness layer than above a rise in relative submergence resulted typically in a decrease in spatial variance relative to bed shear velocity in streamwise form induced intensity streamwise turbulence intensity and form induced momentum flux both within and above the roughness layer flow submergence had no consistent influence on spatial variance in the vertical flow direction and in reynolds stress form induced stress was significant within the roughness layer more so at shallow depths the greater significance was driven primarily by higher spatial flow variance in time averaged streamwise velocity at these depths the implication is the relative role of momentum transfer mechanisms within the roughness layer and thus sediment water interface exchange processes in rivers will change during periods of time varying flows

a model for flow over two dimensional bed forms when non cohesive sediment is set in motion by a unidirectional flow waves of sand often result moreover these waves typically are asymmetrical with steep lee faces that produce flow separation behind each wave a wake region forms which grows in height and decays in strength with distance downstream producing a near bottom acceleration the no slip condition at the bed however requires an internal boundary layer to form beneath the wake region which retards the flow there the interaction of these flow processes produces a local maximum in the boundary shear stress downstream of a bump even over an otherwise flat bed because the erosion rate is proportional to the stress divergence for bed load and weak suspended load transport erosion will occur upstream of this point and desposition will occur downstream of it thus influencing the bottom shape herein the equations of motion are solved for the accelerating internal boundary layer beneath a wake the resulting velocity and boundary shear str

robust classification for the joint velocity intermittency structure of turbulent flow over fixed and mobile bedforms two datasets of turbulence velocities collected over different bedform types under contrasting experimental conditions show similarity in terms of velocity intermittency characteristics and suggest a universality to the velocity intermittency structure for flow over bedforms one dataset was obtained by sampling flow over static bedforms in different locations and the other was based on a static position but mobile bedforms a flow classification based on the velocity intermittency behaviour is shown to reveal some differences from that based on an analysis of reynolds stresses boundary layer correlation and turbulent kinetic energy this may be attributed to the intermittency variable which captures the local effect of individual turbulent flow structures locations in the wake region or the outer layer of the flow are both shown to have a velocity intermittency behaviour that departs from that for idealized wakes or outer layer flow because of the superposition of localized flow structures generated by bedforms the combined effect of this yields a velocity intermittency structure unique to bedform flow the use of a time series of a single velocity component highlights the potential power of our approach for field numerical and laboratory studies the further validation of the velocity intermittency method for non idealized flows undertaken here suggests that this technique can be used for flow classification purposes in geomorphology hydraulics meteorology and environmental fluid mechanics 2014 the authors earth surface processes and landforms published by john wiley sons ltd

submerged and unsubmerged natural hydraulic jumps in a bedrock step pool mountain channel high resolution digital elevation models dems for natural submerged and unsubmerged jump regions were tested against the classical hydraulic jump chj and engineering analogues that have dominated previous geomorphic and engineering research dems were compared for two discharge conditions the data showed bed and water surface features of the natural jump regions differ significantly from chj conditions and engineering analogues with respect to boundary conditions roughness elements were highly irregular in frequency spacing size and orientation and were comprised of form obliquity and bed scour in boulder bed and pure bedrock conditions the data also showed bed and water surface features of natural jump regions have similarities and deviations from chj conditions and engineering analogues with respect to hydraulic characteristics several variations were observed in the hydraulic characteristics between the ballistic and sloping jets revised conceptual models based on idealized corollaries were developed for the natural jump regions based on upstream energy head relative to the downstream tailwater depth and step geometry the dems highlight the importance of recognizing the interrelationship between spatial transcritical flow structures and localized topographic heterogeneities in bedrock channels

velocity characteristics along a small step pool channel this paper summarizes measurements of velocity along three reaches of a small mountain channel with step pool bedforms a one dimensional electromagnetic current meter was used to record velocity fluctuations at 37 fixed measurement points during five measurement intervals spanning the peak of the annual snowmelt hydrograph measurement cross sections were located upstream from a bed step at the step lip downstream from the step and in a uniform gradient run data analyses focused on characteristics of velocity profiles and on correlations between velocity characteristics and the potential control variables bedform type reach gradient and flow depth to test the hypothesis that velocity characteristics are related to channel bedform types anova and ancova tests were performed for the average velocity and coefficient of variation of point velocity data results indicate that high frequency velocity variations correlate to some degree with both channel characteristics and discharge velocity became more variable as stage increased particularly at low gradient reaches with less variable bed roughness velocity profiles suggest that locations immediately downstream from bed steps are dominated by wake turbulence from mid profile shear layers locations immediately upstream from steps at step lips and in runs are dominated by bed generated turbulence adverse pressure gradients upstream and downstream from steps may be enhancing turbulence generation whereas favourable pressure gradients at steps are suppressing turbulence the bed generated turbulence and skin friction of runs appear to be less effective energy dissipators than the wake generated turbulence and form drag of step pool bedforms copyright 2000 john wiley sons ltd

continuous reactions with amphibole garnet and plagioclase end member continuous and degenerate reactions are derived for the multisystem with the six components na2o cao mg fe o al2o3 sio2 h2o among the phases plagioclasess garnetss amphiboless cpx opx olivine spinel quartz and an aqueous fluid the chemography of this system is degenerate due to the co linearity 2opx ol qtz this co linearity has its implications both on reaction space and phase equilibria from a total of 28 reaction systems reaction space is derived for nine subsystems phases in parentheses are absent case a1 cpx ol cpx opx and cpx qtz case a2 spl ol spl opx and spl qtz case b ol opx ol qtz and opx qtz in the absence of either cpx or spl case a three reactions form an invariant point either cpx or spl where the co linear phases olivine opx and quartz coexist on the transformation line 2opx ol qtz changing mineral compositions force invariant points to move along the line with the different reaction curves changing their relative position according to schreinemakers rules zero contours i e the location where a phase s disappear s in reaction space correspond to singular points in phase diagrams two types are distinguished singular points of indispensable and of substitutable phases in the first case the phase disappears from the entire bundle while in the second it disappears from a single reaction in the specific case where the substitutable phases are also the co linear ones two of the three co linear phases disappear simultaneously two of the three reaction curves coincide in the system including cpx and spl case b three reactions ol opx ol qtz and opx qtz oppose three invariant points ol opx and qtz invariant points no longer move along the line 2opx ol qtz the coincidence of the zero contours of all three co linear phases in reaction space the result of the chemographic degeneracy causes the respective singular points to coincide in the phase diagrams this is the location where curves must be rearranged in a bundle to conform schreinemakers rules the reaction grs1prp2 2 ol an is fourth order degenerate and part of all nine subsystems cases a and b it can be used to relate the different phase diagrams to one another

structure of flow over alluvial bedforms an experiment on linking field and laboratory methods this paper presents results of a field study designed to examine the structure of flow over mobile and fixed bedforms in a natural stream and to compare the results with findings of previous laboratory studies within the framework of double time space averaging approach measurements of turbulence were obtained in a small river in illinois usa over a fine spatial grid of sampling points above a mobile sandy bedform and its artificially moulded replica flow structure over the artificial bedform is similar to that observed in laboratory studies but is markedly different from the flow structure over natural bedforms these differences are most pronounced in the roughness sublayer whereas flow in the logarithmic layer over natural and artificial sand waves is fairly similar and exhibits spatial uniformity the double time space averaged distributions of turbulence statistics conform to the multilayer model of flow structure over bedforms mean velocity distributions indicate neither classical flow recirculation nor substantial reduction of velocities in the lee of bedform crests however vertical patterns of turbulence statistics over depth suggest that stacked wakes similar to those observed in laboratory studies exist above the bedforms thus despite the absence of flow separation wake development seems to be induced by the systematic influence of upstream bedforms on the vertical structure of turbulence copyright 2006 john wiley sons ltd

the reaction garnet clinopyroxene quartz 2 orthopyroxene anorthite a potential geobarometer for granulites a mineralogic geobarometer based on the reaction garnet clinopyroxene quartz 2 orthopyroxene anorthite is proposed the geobarometric formulations for the fe and mg end member equilibria are begin gathered p text fe text text bars text 32 text 097 t text text 26385 text 22 text 79 t 848 t1 text n t 848 text hfill text 3 655 0 0138t text left frac text t 848 text text 2 t right hfill text text 3 text 123 t1 text n frac a a text n text plag a text fs text p ddot u text x 2 a text alm text gt a text hed text opx hfill p text mg text bars 9 text 270 t 4006 0 9305 text t 848 t1 text n t 848 text hfill text 1 1963 text text 6 0128 text x 10 text 3 t left frac t 848 2 t right hfill text 3 489 text t1 text n frac a an text plag text a text ens text opx text a text pyr text gt text a text diop text cpx text hfill end gathered the end member thermodynamic data have been taken from the data base of helgeson et al 1978 and saxena and erikson 1983 the activities of pyroxene components and anorthite in plagioclase have been modelled after wood and banno 1973 and newton 1983 respectively the activities of pyrope and almandine are calculated from the binary interaction parameters for garnet solid solutions proposed by saxena and erikson 1983

three dimensional flow structure around small scale bedforms in a simulated gravel bed environment pebble clusters are common small scale morphological features in gravel bed rivers occupying as much as 10 per cent of the bed surface important links exist between the presence of pebble clusters and the development of flow structures these links are poorly understood at the three dimensional level particularly neglected has been the effect of clusters on the lateral flow characteristics a laboratory study was conducted using a hydraulic flume within which simulated pebble clusters were superimposed onto a plane bed of gravel material high resolution three dimensional flow data were collected above the bed at two different flow depths using an acoustic doppler velocimeter the results present evidence of the importance of lateral flow in the development of turbulent flow structure narrow regions of high lateral and downstream turbulence intensity exist to both sides of clusters and in a three dimensional separation zone in their lee this may indicate the presence of horseshoe type vortical structures analogous to those identified in less hydraulically rough environments however it is likely that these structures are more complicated given the mutual interference of the surrounding medium the lateral flow was also identified as a key component in the upwelling identified by other authors in the lee of pebble clusters the results of the vertical flow analysis confirm the hypothesis that six regions with distinct vertical flow characteristics exist above clusters flow acceleration up the stoss side of the cluster recirculation behind the cluster in the wake region vortex shedding from the pebble crest and shear layer flow reattachment downstream of the cluster upwelling of flow downstream of the point of reattachment and recovery of flow copyright 2001 john wiley sons ltd

thermal history of alberta deep basin comparative study of fluid inclusion and vitrinite reflectance data the thermal history of the alberta deep basin the gas saturated westernmost part of the western canadian sedimentary basin has been studied by analyzing aqueous and hydrocarbon fluid inclusions in diagenetic cements and comparing the results with coal maturity data results indicate that most of the diagenetic quartz druse precipitated from low salinity fluids 2 3 wt at a temperature of 170 195 c calcite cement precipitated after quartz druse during uplift and cooling at temperatures of 108 169 c inclusions rich in larger hydrocarbon molecules occur in cements that precipitated at 150 c whereas methane rich inclusions occur in cements that precipitated at 165 c or at lower temperatures after significant uplift and cooling of the b sin maximum burial temperatures tmb calculated from vitrinite reflectance data using the lopatin waples tti ro calibration are significantly lower 150 c than the temperature at which quartz druse precipitated in the same area 190 c an equation directly relating tmb and ro proposed by barker and pawlewicz in 1986 yields maximum burial temperatures 200 210 c only slightly higher than the fluid temperatures the results from this study suggest that hot fluids migrated updip along permeable conglomerates and bedding plane fractures to produce unexpectedly high geothermal gradients 38 c km in the western part of the study area the apparent restriction of hot fluids to the western part of the study area sugge ts that convective heat transfer by fluids may have operated on a scale of only tens of kilometers in lower cretaceous rocks of the alberta deep basin

direct numerical simulation of bedload transport using a local dynamic boundary condition temporally and spatially averaged models of bedload transport are inadequate to describe the highly variable nature of particle motion at low transport stages the primary sources of this variability are the resisting forces to downstream motion resulting from the geometrical relation pocket friction angle of a bed grain to the grains that it rests upon variability of the near bed turbulent velocity field and the local modification of this velocity field by upstream protruding grains a model of bedload transport is presented that captures these sources of variability by directly integrating the equations of motion of each particle of a simulated mixed grain size sediment bed experimental data from the velocity field downstream and below the tops of upstream protruding grains are presented from these data an empirical relation for the velocity modification resulting from upstream grains is provided to the bedload model the temporal variability of near bed turbulence is provided by a measured near bed time series of velocity over a gravel bed the distribution of pocket friction angles results as a consequence of directly calculating the initiation and cessation of motion of each particle as a result of the combination of fluid forcing and interaction with other particles calculations of bedload flux in a uniform boundary and simulated pocket friction angles agree favourably with previous studies

step pool evolution in the rio cordon northeastern italy the principle that formative events punctuated by periods of evolution recovery or temporary periods of steady state conditions control the development of the step pool morphology has been applied to the evolution of the rio cordon stream bed the rio cordon is a small catchment 5 km2 within the dolomites wherein hydraulic parameters of floods and the coarse bedload are recorded detailed field surveys of the step pool structures carried out before and after the september 1994 and october 1998 floods have served to illustrate the control on step pool changes by these floods floods were grouped into two categories the first includes ordinary events which are characterized by peak discharges with a return time of one to five years 1 8 5 15 m3 s 1 and by an hourly bedload rate not exceeding 20 m3 h 1 the second refers to exceptional events with a return time of 30 50 years a flood of this latter type occurred on 14 september 1994 with a peak discharge of 10 4 m3 s 1 and average hourly bedload rate of 324 m3 h 1 step pool features were characterized primarily by a steepness parameter c h ls s the evolution of the steepness parameter was measured in the field from 1992 to 1998 the results indicate that maximum resistance conditions are gradually reached at the end of a series of ordinary flood events during this period bed armouring dominate the sediment transport response however following an extraordinary flood and unlimited sediment supply conditions the steepness factor can suddenly decrease as a result of sediment trapped in the pools and a lengthening of step spacing the analogy of step spacing with antidune wavelength and the main destruction and transformation mechanism of the steps are also discussed copyright 2001 john wiley sons ltd

is the critical shields stress for incipient sediment motion dependent on channel bed slope data from laboratory flumes and natural streams show that the critical shields stress for initial sediment motion increases with channel slope which indicates that particles of the same size are more stable on steeper slopes this observation is contrary to standard models that predict reduced stability with increasing slope due to the added downstream gravitational force processes that might explain this discrepancy are explored using a simple force balance model including increased drag from channel walls and bed morphology variable friction angles grain emergence flow aeration and changes to the local flow velocity and turbulent fluctuations surprisingly increased drag due to changes in bed morphology does not appear to be the cause of the slope dependency because both the magnitude and trend of the critical shields stress are similar for flume experiments and natural streams and significant variations in bed morphology in flumes is unlikely instead grain emergence and changes in local flow velocity and turbulent fluctuations seem to be responsible for the slope dependency due to the coincident increase in the ratio of bed roughness scale to flow depth i e relative roughness a model for the local velocity within the grain roughness layer is proposed based on a 1 d eddy viscosity with wake mixing in addition the magnitude of near bed turbulent fluctuations is shown to depend on the depth averaged flow velocity and the relative roughness extension of the model to mixed grain sizes indicates that the coarser fraction becomes increasingly difficult to transport on steeper slopes

spatially averaged flow over a wavy boundary revisited vertical profiles of streamwise velocity measured over bed forms are commonly used to deduce boundary shear stress for the purpose of estimating sediment transport these profiles may be derived locally or from some sort of spatial average arguments for using the latter procedure are based on the assumption that spatial averaging of the momentum equation effectively removes local accelerations from the problem using analogies based on steady uniform flows it has been argued that the spatially averaged velocity profiles are approximately logarithmic and can be used to infer values of boundary shear stress this technique of using logarithmic profiles is investigated using detailed laboratory measurements of flow structure and boundary shear stress over fixed two dimensional bed forms spatial averages over the length of the bed form of mean velocity measurements at constant distances from the mean bed elevation yield vertical profiles that are highly logarithmic even though the effect of the bottom topography is observed throughout the water column however logarithmic fits of these averaged profiles do not yield accurate estimates of the measured total boundary shear stress

unobstructed and obstructed turbulent flow in gravel bed rivers an acoustic doppler velocimeter was used to characterize turbulence in two gravel bed rivers data were collected in unobstructed flow and compared to recent investigations additional data collected in the wake of emergent boulders indicate that mean flow velocity turbulent kinetic energy gradients in the streamwise velocity and reynolds stress downstream from large rocks deviate from unobstructed flow results but similar turbulence patterns are found behind each boulder results of this study are discussed with regard to natural channel design and fish habitat

calculating bed load transport in steep boulder bed channels 1 steep rough channels occupy a large fraction of the total channel length in mountainous regions most sediment mobilized on hillslopes must pass through these streams before reaching lower gradient channels steep channels have wide grain size distributions that are composed of finer more mobile sediment and large rarely mobile grains the large grains can bear a significant portion of the total shear stress and thereby reduce the stress available to move the finer sediment conventional bed load transport equations often overpredict the sediment flux in steep channels by several orders of magnitude we hypothesize that sediment transport equations overpredict the sediment flux because they do not 1 account for the stress borne by rarely mobile grains 2 differentiate between highly and rarely mobile sediment and 3 account for the limited availability of mobile sediment here we modify a conventional bed load transport equation to include these three effects we use measurements of the flow bed properties and sediment flux in a small steep flume to test this equation we supply gravel at a constant rate through fields of regularly spaced immobile spheres and measure the bed coverage by gravel and sphere protrusion the percent of the sphere that protrudes above the gravel deposit for a given sphere spacing the proportion of the bed covered by gravel increases and the sphere protrusion decreases with greater sediment supply thus bed coverage and immobile grain protrusion may serve as proxies for sediment availability in steep rough streams unlike most transport equations that we tested our modified bed load equation predicts sediment fluxes to within an order of magnitude of the measured values our results demonstrate that accurately predicting bed load transport in steep rough streams may require accounting for the effects of local sediment availability coverage by mobile sediment and drag due to rarely mobile particles

influence of sediment supply on mountain streams bedload transport abstract sediment transport and storage in mountain stream channels are closely dependent on hillslope activities and bank erosion this paper analyses bedload measured in 13 mountain streams 989 values with slope higher than 5 in an attempt to investigate how much the sediment supply condition impacts bedload transport rates first the sediment supply condition of each stream was evaluated qualitatively using information available in the original studies in the second step the data set was analysed by comparing bedload transport rates considering a shields stress ratio and by comparing transport rate efficiency with consideration of a dimensionless stream power the two analyses indicate higher sediment transport rates for the streams identified as connected to an active source the consequences for bedload transport prediction are discussed with a nonthreshold bedload equation even though predicting the exact sediment supply condition and the associated transport rate is not yet possible this study suggests that defining an envelope delimiting minimum and maximum transport for a given river reach should be possible

the missing dimension effects of lateral variation on 1 d calculations of fluvial bedload transport most calculations of bedload transport in rivers including those in numerical models of aggradation and degradation are 1 d all hydraulic and transport rate calculations are averaged over the channel width because bedload transport laws are nonlinear width averaged calculations will underestimate the true bedload flux if there is any local spatial variation in either the bed or the flow this paper analyses the effects on bedload transport capacity of spatial variation in applied and critical c shear stress separately and in combination a simple but versatile statistical model is used to represent variability in with allowance for differences between sand and gravel bed rivers and for below bankfull flow bedload flux is shown to increase greatly with the variance of especially in gravel bed rivers variability in c through bed patchiness may increase reduce or make little difference to bedload flux depending on the correlation between and c simple width averaging leads to severe underestimation of bedload transport in most conditions some alternatives are considered the findings have implications for sediment routing models srms but further research is needed to explore the issue fully

the formation of a clinopyroxene corona mass balance considerations abstract the formation of a cpx corona is discussed from the viewpoint of continuous reaction techniques two cases are distinguished a closed and open system the first case is based on the equation e ol w a pl u b pl v opx x c cpx y d spl y plagioclase is assumed to be a solid solution between anorthite and albite na u ca 1 w al 2 u si 2 u o 8 the other minerals are solutions of their fe and mg end members e g mg w fe 1 w 2 sio 4 for olivine spinel forms a ternary system of hercynite spinel magnetite stoichiometric coefficients are expressed in terms of the exchange parameters t u v w x y and z according to stoichiometries the net molar quantity of phaligioclase consumed equals the number of moles of clinopyroxene and spinel produced for each mole of olivine consumed there is one mole of opx produced a closed system is suggested by the ability to predict one of the mineral compositions in terms of the others using one of the six mass balances na ca mg fe al si left from the calculation of five stoichiometric coefficients this model allows the calculation of mass transfer between different shells and explains coronas from the adirondacks scandinavia and the niquel ndia layered complex brazil in the second case the system is open and is described by the equation opx x a pl u k ca 2 h si 4 f fe 2 c cpx y l na l al 3 g mg 2 the compositional variation of orthopyroxene and clinopyroxene allows the determination of c cpx fe 2 and g mg 2 which are interdependent with a known value of c and assuming a constant volume of reaction the value of a may be determined the final equation for a plagioclase composition of x an 0 75 is 1 opx 0 35 pl 0 74 ca 2 0 21 si 4 0 10 mg 2 1 cpx 0 61 al 3 0 10 fe 2 0 09 na this is the reaction responsible for the formation of cpx coronas in the bushveld complex

a systematic analysis of eight decades of incipient motion studies with special reference to gravel bedded rivers data compiled from eight decades of incipient motion studies were used to calculate dimensionless critical shear stress values of the median grain size t c 50 calculated t c 50 values were stratified by initial motion definition median grain size type surface subsurface or laboratory mixture relative roughness and flow regime a traditional shields plot constructed from data that represent initial motion of the bed surface material reveals systematic methodological biases of incipient motion definition t c 50 values determined from reference bed load transport rates and from visual observation of grain motion define subparallel shields curves with the latter generally underlying the former values derived from competence functions define a separate but poorly developed field while theoretical values predict a wide range of generally higher stresses that likely represent instantaneous rather than time averaged critical shear stresses the available data indicate that for high critical boundary reynolds numbers and low relative roughnesses typical of gravel bedded rivers reference based and visually based studies have t c50 ranges of 0 052 0 086 and 0 030 0 073 respectively the apparent lack of a universal t 50 for gravel bedded rivers warrants great care in choosing defendable t c50 values for particular applications

very high temperature moderate pressure metamorphism in the new russia gneiss complex northeastern adirondack highlands metamorphic aureole to the marcy anorthosite the new russia gneiss complex in the northeastern adirondack highlands of new york includes meta anorthosite gneiss and anatectic gneiss derived from metagabbro mangerite and charnockite metamor

effects of macro scale bed roughness geometry on flow resistance 1 flow field over macro roughness elements as for example in flow conditions such as of steep mountain streams is investigated by means of a theoretical model and a laboratory study with the main aim of understanding the influence of concentration and planimetric disposition of grain roughness on flow resistance a theoretical model for the average velocity distribution profile over a bed with macro roughness elements is developed herein the model is based on a two layer approach which takes into account the displacement of the main flow due to the drag around the roughness the laboratory study is composed of an extensive set of flume experiments in the case of steep slopes and large relative roughness conditions for a given flow discharge and bed slope various experiments have been carried out with different pattern and spacing of the roughness elements constituted by river pebbles application of the theoretical model to the experimental results enables the determination of how flow resistance is affected by the macro roughness in particular it appears that when the concentration of the roughness is within an optimal range flow resistance is maximum

flow resistance of rock chutes with protruding boulders steep and short rough channels such as rock chutes are used in river restoration as grade stabilization structures the stability of these channels can be increased using boulders placed over the base material the boulders can be placed with different configurations such as randomly or in rows in each case their presence affects the geometry of the channel and modifies the hydraulic resistance this paper shows the results of tests conducted on rough channels with or without the insertion of protruding boulders the parameters that influence the flow resistance such as slope relative submergence and blocks disposition were systematically investigated to describe the hydraulic behavior of the structure the aim is to define a relationship useful for practical design which relates the flow resistance in terms of both darcy weisbach friction factor and manning coefficient the results were combined with available data for loose rock riprap to determine new experimental relationships

mineral zoning p t x m phase relations and metamorphic evolution of some adirondack granulites new york detailed petrologic analysis of ten meta anorthosites and related introduction rocks from the adirondack highlands new york has been used to the adirondack highlands of new york are one of constrain the p t history of the region metamorphic orthopyroxene the best studied granulite facies terranes of the world and clinopyroxene occur in aggregates of 1 mm diameter grains e g bohlen et al 1985 valley et al 1990 and that are zoned concentrically with decreasing al and fe fe mg references therein based on this considerable volume and increasing ca towards the rim moreover zoning is not related of work the peak metamorphic conditions in the to the presence of garnet zoning is interpreted to have been produced adirondack highlands have been fairly well constrained during growth by the reaction igneous pyroxene plagioclase at pressures of 7 8 kbar crustal depths of 25 30 metamorphic opx metamorphic cpx along a cooling path with a km and temperatures that range from 775 c in slope of 6 bars c starting at 850 c and 6 5 8 kbar garnet the central highlands to t 675 c in the southern occurs as isolated clusters of 5 25 grains of 1 mm diameter adirondacks e g bohlen et al 1985 p t paths have crystals and as necklaces of 1 mm diameter crystals surrounding been shown to follow nearly isobaric cooling trajectories metamorphic pyroxenes or oxides plagioclase quartz typically e g bohlen 1987 because of this wealth of inseparates garnet from pyroxene but locally garnet embays metaformation some fundamental questions about the origin morphic pyroxene suggesting that garnet grew at the expense of of the adirondack granulite facies terrane have emerged pyroxene garnet clusters have slightly lower fe fe mg than e g bohlen et al 1985 how did the crust achieve garnet in necklaces fe fe mg 0 73 and 0 75 0 78 rethe relatively high temperature conditions necessary to spectively and slightly higher grossular xgrs 0 20 vs 0 19 produce granulite facies rocks at depths of 25 30 km neither is zoned in mn and zoning towards increasing fe and what is the relative importance of magmatic fe mg is restricted to contacts with biotite and locally clinoheating vs continental burial in this process pyroxene biotite adjacent to garnet is zoned towards decreasing this study will present new data on mineral comfe fe mg production of garnet in necklaces is interpreted position and element zoning in garnet pyroxene to be the result of the continuous fe mg reaction opx pl biotite amphibole and plagioclase from adirondack grt cpx qtz p t x m modeling of this reaction reveals a meta anorthosite and related rocks with the goal of p t path with a slope of 6 bars c no evidence for early prefurther constraining the metamorphic evolution of this metamorphic peak garnet is observed which rules out any possibility terrane mineral compositions will be used to construct of early higher pressure metamorphism the p t path is therefore phase diagrams in an attempt to evaluate approach to inferred to be counterclockwise with loading to 6 5 8 kbar at a chemical equilibrium theoretical analysis will be used maximum temperature of 850 c occurring during or immediately to construct p t x m phase diagrams depicting how following an influx of heat presumably from early orogenic plutons mineral composition and modes change with p and t this theoretical analysis will then be applied to the mineral zoning to constrain the p t path and the results will be discussed in the context of a tectonic

oxygen isotope thermometry using quartz inclusions in garnet oxygen isotope ratios of quartz inclusions within garnet from granulite and amphibolite facies gneisses in the adirondack mountains ny were analyzed and used to determine metamorphic temperatures primary quartz inclusions for eight of 12 samples have 18o values significantly lower than matrix quartz the primary quartz inclusions retain 18o values representative of thermal conditions during garnet crystallization whereas the 18o values of matrix quartz were raised by diffusive exchange with other matrix minerals e g mica and feldspar during cooling the 18o differences between quartz inclusions and matrix quartz show that garnet a mineral with slow diffusion of oxygen can armour quartz inclusions from isotopic exchange with surrounding matrix even during slow cooling these differences between 18o in matrix quartz and quartz inclusions can further be used to test cooling rates by fast grain boundary diffusion modelling criteria for identifying quartz inclusions that preserve primary compositions and are suitable for thermometry were developed based on comparative tests relations between 18o and inclusion size distance of inclusion to host garnet rim core rim zonation of individual inclusions and presence or absence of petrological features healed cracks in quartz inclusions inclusions in contact with garnet cracks lined by secondary minerals and secondary minerals along the inclusion grain boundary were investigated in this study 61 of quartz inclusions preserve primary 18o and 39 were associated with features that were linked to reset 18o values if 18o in garnet is homogeneous and inclusions are removed laser fluorination 18o values of bulk garnet are more precise more accurate and best for thermometry intragrain 18o grt profiles measured in situ by ion microprobe show no 18o zonation almandine rich garnet alm 60 75 from each sample was measured by laser fluorination mass spectrometry lf ms for 18o and compared with ion microprobe measurements of 18o in quartz inclusions for thermometry the 18o qz grt values for adirondack samples range from 2 66 to 3 24 corresponding to temperatures of 640 to 740 c a qz alm 2 71 out of 12 samples that were used for thermometry nine are consistent with previous estimates of peak temperature 625 to 800 c based on petrological and carbon isotope thermometry for regional granulite and upper amphibolite facies metamorphism the three samples that disagree with independent thermometry for peak metamorphism are from the anorthosite mangerite charnockite granite suite in the central adirondacks and yield temperatures of 640 to 665 c approximately 100 c lower than previous estimates these low temperatures could be interpreted as thermal conditions during late post peak crystallization of garnet on the retrograde path this article is protected by copyright all rights reserved

13c 12c exchange between calcite and graphite a possible thermometer in grenville marbles the fractionation of 13c between calcite and graphite cc gr is consistently small 2 6 4 8 permil in 34 assemblages from upper amphibolite and granulite facies marbles of the grenville province in 25 samples from the adirondack mountains new york it decreases regularly with increasing metamorphic temperature the fractionations are independent of absolute 13c values of calcite 2 9 to 5 0 for t 600 800 c the adirondack data are described by cc gr 0 00748t c 8 68 this good correlation between and t suggests that carbon isotope equilibrium was attained in these high grade marbles and that the theoretical calculations of this fractionation by bottinga are approximately 2 permil too large in this temperature range because of the relatively high temperature sensitivity suggested by these results and by bottinga s calculations and the pressure independence of isotope fractionation cc gr may provide a very good thermometer for high grade marbles comparison of this field calibration for cc gr vs temperature with results from other terranes supports the utility of cc gr for geothermometry and suggests that graphite is much more sluggish to exchange than calcite that exchange between calcite and graphite occurs at temperatures as low as 300 c and that equilibrium may normally be attained only when peak metamorphic temperatures are greater than 500 600 c because 13c exchange is an unavoidable metamorphic process at temperatures above 300 c high values of 13c gr in moderate to high grade carbonate bearing rocks do not provide a sufficient criterion to infer an abiogenic origin for the graphite

effects of bed forms and large protruding grains on near bed flow hydraulics in low relative submergence conditions in mountain rivers bedforms large relatively immobile grains and bed texture and topographic variability can significantly alter local and reach averaged flow characteristics the low relative submergence of large immobile grains causes highly three dimensional flow fields that may not be represented by traditional shear stress flow velocity and turbulence intensity equations to explore the influence of large protruding grains and bedforms on flow properties we conducted a set of experiments in which we varied the relative submergence while holding the sediment transport capacity and upstream sediment supply constant flow and bed measurements were conducted at the beginning and end of each experiment to account for the absence or presence of bedforms respectively detailed information on the flow was obtained by combining our measurements with a 3d numerical model commonly used velocity profile equations only performed well at the reach scale when shallow flow effects and the roughness length of the relatively mobile sediment were considered however at the local scale large deviations from these profiles were observed and simple methods to estimate the spatial distribution of near bed shear stresses are likely to be inaccurate zones of high turbulent kinetic energy occurred near the water surface and were largely controlled by the immobile grains and plunging flow the reach averaged shear stress did not correlate to depth or slope as commonly assumed but instead was controlled by the relative boulder submergence and degree of plunging flow for accurate flow predictions in mountain rivers the effects of bedforms and large boulders must be considered

mafic granulites from the eastern ghats india further evidence for extremely high temperature crustal metamorphism mafic granulites occurring as conformable lenses within khondalite leptynite and calc silicate rocks from the anantagiri araku areas of the eastern ghats belt contain orthopyroxene clinopyroxene garnet quartz ilmenite and plagioclase as major constituents orthopyroxene contains 100 lamellae of clinopyroxene and clinopyroxene contains 100 orthopyroxene lamellae and 001 spindles of pigeonite reaction textures indicate formation of garnet through coupling of two reactions viz orthopyroxene anorthite garnet clinopyroxene quartz and anorthite ilmenite hematite ss quartz garnet ilmenite o 2 thermobarometry indicates exsolution of pigeonite at 950 c of 100 clinopyroxene in orthopyroxene and vice versa at 750 820 c and formation of garnet at around 700 725 c 7 kb all in response to cooling of the rock this shows a nearly isobaric cooling path subsequent to peak metamorphic conditions subsequently the rock suffered nearly isothermal decompression to 5 kb

stochastic incipient motion criterion for spheres under various bed packing conditions incipient motion criteria based solely on time averaged bed shear stress may underpredict sediment transport the focus of this study is on the stochastic aspect of the problem of incipient motion specifically the role of near bed turbulent structures and bed packing density on the commencement of sediment motion is investigated the cornerstone of the proposed model is based on the concept that the particle motion is governed by the intermittent nature of near bed turbulence based on this mechanism in this article we provide a quantitative model for predicting the commencement of sediment entrainment for the first time under three representative bed packing densities corresponding to the isolated wake interference and skimming flow regimes the performance of the proposed model is compared to published experimental data and the conventional approach that is based on the consideration that flow parameters are statistically well represented by a normal distribution

validation of a three dimensional numerical code in the simulation of pseudo natural meandering flows validation of a three dimensional finite volume code solving the navier stokes equations with the standard k epsilon turbulence model is conducted using a high quality and high spatial resolution data set the data set was collected from a large scale meandering channel with a self formed fixed bed and comprises detailed bed profiling and laser doppler anemometer velocity measurements comparisons of the computed primary and secondary velocities are made with those observed and it is found that the lateral momentum transfer is generally under predicted at the apices this results in the predicted position of the primary velocity maximum having a bias towards the channel center compared to the position where it has been measured using a simplified two zone roughness distribution whereby a separate roughness height was prescribed for the channel center and channel sides relative to a single distributed roughness height generally led to a slightly improved longitudinal velocity distribution the higher velocities were located nearer to the outside of the bend improving both the free surface calculation and scheme for discretization of the convection terms led to no appreciable difference in the computed velocity distributions a more detailed study involving turbulence measurements and bed form height distribution should discriminate whether using distributed roughness height is a precursor to using an anisotropic turbulence representation for the accurate prediction of three dimensional river flows

sediment supply and the development of the coarse surface layer in gravel bedded rivers the bed surface of most gravel rivers is considerably coarser than the sub surface or the gravel load transported over it a phenomenon affecting river dynamics morphology and ecology the coarse surface layer often called an armour or pavement has been attributed to an inherent tendency for small grains to settle between larger ones during active transport of all sizes1 2 and to selective erosion or trapping of finer particles when the coarse grains are relatively immobile3 4 where bedload supply is cut off below dams selective erosion causes coarsening5 6 using a simple quantitative model we propose that surface coarsening develops in gravel bedded rivers when local bedload supply from upstream is less than the ability of the flow to transport that load we present laboratory results which support this hypothesis and show that supply reduction causes changes in bedforms and progressive confinement of active bedload transport to a narrow band of finer bed surface bordered by a coarse less active bed it may therefore be possible to relate the degree of river bed surface coarsening to sediment supply resulting from land use

spectral analysis of turbulent flow and suspended sediment transport over fixed dunes laboratory measurements of turbulent fluctuations in velocity and suspended sediment concentration were obtained synchronously over fixed two dimensional dunes in a sediment starved flow contour maps of turbulent flow parameters demonstrate that the flow separation cell and a perturbed shear layer are the main sources of turbulence production and that the distribution of suspended sediment is controlled by spatially dependent macro turbulent flow structures spectral analysis reveals that peak spectral energies generally occur at 1 2 hz for the stream wise velocity component and 2 4 hz for the cross stream and vertical velocity components spectra show larger and better defined energy peaks near the shear layer peak spectral energies for suspended sediment concentration occur near 1 hz throughout the flow squared coherency values for cospectral analysis of velocity and sediment concentration are insignificant integral timescales for velocity range from 0 20 s for the streamwise component to 0 06 s for the cross stream and vertical components integral length scales for velocity range from 0 065 to 0 135 m for the streamwise component which is comparable to flow depth and from 0 020 to 0 030 m for the crossstream and vertical components which is comparable to dune height for suspended sediment concentration integral timescales and length scales are similar to the streamwise velocity component

estimation of flow resistance in gravel bedded rivers a physical explanation of the multiplier of roughness length the need to estimate velocity and discharge indirectly in gravel bedded rivers is a commonly encountered problem semilogarithmic friction equations are used to estimate mean velocity using a friction factor obtained from depth and grain size information although such equations have a semi theoretical basis in natural gravel bed channels an empirical constant 6 8 or 3 5 has to be introduced to scale up the characteristic grain size d50 or d84 to represent the effective roughness length in this paper two contrasting approaches are used to suggest that the multiplier of characteristic grain size is attributable to the effect of small scale form resistance reflecting the occurrence of microtopographic bedforms in gravel bedded environments first spatial elevation dependence in short detailed bed profiles from a single gravel bedded river is investigated using semivariogram and zero crossing analyses this leads to objective identification of two discrete scales of bed roughness associated with grain and microtopographic roughness elements second the autocorrelation structure of the three dimensional near bed velocity field is examined to identify regularities associated with eddy shedding and energy losses from larger grains and microtopographic bedforms apart from improving the capacity to determine friction factors for velocity and discharge estimation the findings have implications in general for the initial motion of gravelly bed material

an evaluation of garnet clinopyroxene geothermometry in granulites four new formulations of the garnet clinopyroxene geothermometer ellis and green 1979 ganguly 1979 saxena 1979 dahl 1980 have been evaluated in the adirondacks and five other granulite terranes using results from 94 mineral pairs the saxena and ganguly formulations give temperatures that are generally 100 150 c above those constrained by phase equilibria and other independent thermometry while the empirical calibration of dahl gives widely scattered erratic results despite some scatter in the data the ellis and green calibration appears to be more accurate and precise than the others and is the most useful garnet clinopyroxene thermometer currently available for quantitative thermometry in granulites all four formulations are sensitive to large variations 70 80 c in temperature suggesting that problems with accuracy and precision can be improved with further refinement of model based aspects of the thermometers

the formation of garnet in olivine bearing metagabbros from the adirondacks a regional study of olivine bearing metagabbros in the adirondacks has permitted testing of the p pressure t temperature x composition dependence of garnet forming reactions as well as providing additional regional metamorphic pressure data six phases olivine orthopyroxene clinopyroxene garnet plagioclase and spinel which can be related by the reactions orthopyroxene clinopyroxene spinel anorthite garnet and forsterite anorthite garnet occur together both in coronal and in equant textures indicative of equilibrium compositions of the respective minerals are typically fo25 72 en44 75 en30 44fs9 23wo47 49 pp13 42alm39 63gr16 20 an29 49 and sp16 58 when they occur in the same rock equant and coronal garnets are homogeneous and compositionally identical suggesting that chemical equilibrium may have been attained despite coronal textures extrapolating reactions in the simple cmas system to granulite temperatures and making thermodynamic corrections for solid solutions gives equilibration pressures using the thermometry of bohlen et al 1980b ranging from about 6 5 kb in the lowlands and southern adirondacks to 7 0 8 0 kb in the highlands for the assemblage olivine plagioclase garnet these results are consistent with inferred peak metamorphic conditions in the adirondacks valley and bohlen 1979 bohlen and boettcher 1981 thus the isobaric retrograde path suggested by whitney and mclelland 1973 and whitney 1978 for the formation of coronal garnet in olivine metagabbros may not be required application of the same equilibria gives 8 7 kb for south harris scotland and 0 9 kb for the nain complex disagreement of the latter value with orthopyroxeneolivine quartz barometry bohlen and boettcher 1981 suggests that the use of iron rich rocks olivines fa50 results in errors in calculated pressures

turbulent flow over three dimensional dunes 2 fluid and bed stresses 1 dunes formed in response to fluid flow exert a total boundary stress on the fluid that is made up of form drag and skin friction the latter of which is generally considered important for predicting sediment transport and dune evolution previous research has used various methods to estimate the total stress and its subcomponents with recent work suggesting the application of a spatial average to the equations of motion a complete three dimensional 3 d form of this analysis is derived and applied to recent measurements of turbulent open channel flow over 3 d dunes spatial averages of reynolds shear stresses over 3 d dunes cannot be used to predict total boundary shear stress however estimations of total boundary shear stress from the spatially averaged equations of motion agree with not only the sum of form drag and skin friction but also the direct measurements of average free surface slope form induced stresses from secondary circulations augment the relatively low reynolds shear stresses over the 3 d dunes these low turbulence levels have ramifications for sediment transport predictions in that use of the total boundary shear stress in prediction of sediment transport over 3 d dunes must account for these low turbulence levels so as not to overpredict transport rates

when does bedload transport begin in steep boulder bed streams the paper presents the results of field measurements of critical conditions for bedload motion conducted in the rio cordon a steep boulder bed stream in the italian alps under conditions of high reynolds numbers and low relative submergence poorly explored before two methods have been used to determine threshold of motion the displacement of marked clasts and the flow competence approach which uses the largest grain size diameter transported by each flood event the high values of confirm the great relevance of non bedload effective shear stresses in step pool streams given by the additional form drag associated with this morphology relative submergence effects on the dimensionless critical shear stress have been quantified by considering the relative submergence ratio rh d84 and the major effect of relative size on the mobility of each particle in steep widely graded bed mixtures has been evaluated finally the dimensionless critical unit discharge has also been adopted in the regression equations as the critical hydraulic parameter because it may represent an easier parameter to use than the critical shear stress for steep rough mountain rivers copyright 2006 john wiley sons ltd

fluid heterogeneity during granulite facies metamorphism in the adirondacks stable isotope evidence the preservation of premetamorphic whole rock oxygen isotope ratios in adirondack metasediments shows that neither these rocks nor adjacent anorthosites and gneisses have been penetrated by large amounts of externally derived hot co2 h2o fluids during granulite facies metamorphism this conclusion is supported by calculations of the effect of fluid volatilization and exchange and is also independently supported by petrologic and phase equilibria considerations the data suggest that these rocks were not an open system during metamorphism that fluid rock ratios were in many instances between 0 0 and 0 1 that externally derived fluids as well as fluids derived by metamorphic volatilization rose along localized channels and were not pervasive and thus that no single generalization can be applied to metamorphic fluid conditions in the adirondacks

prediction of sediment transport in step pool channels 1 in mountainous drainage networks sediment mobilized on hillslopes must first pass through steep streams before reaching lower gradient channels the bed of steep channels is typically composed of large relatively immobile boulders and finer more mobile gravel most sediment transport equations overpredict sediment flux in steep streams by several orders of magnitude because they do not account for the stress borne by immobile grains and the limited availability of the more mobile sediment we previously developed and tested in flume experiments a sediment transport equation that accounts for these two effects here we modify the parker 1990 bed load equation to include the resistance borne by steps and selective transport of the relatively mobile sediment using a range of hiding functions we test a number of resistance equations and hiding functions combined with our modified and the original parker equations against measured flow and sediment transport in three steep channels our modified sediment transport equation generally predicts the transported sediment volumes to within an order of magnitude of the measured values whereas the unmodified equations do not the most accurate sediment flux predictions were obtained from using our modified equation combined with a hiding function that calculates highly selective transport of the relatively mobile sediment furthermore this hiding function has a critical shields stress that is similar to those reported for lower gradient channels the effects of the immobile steps on flow and sediment transport are not adequately captured by simply increasing the critical shields stress to values reported in steep streams

on the entrainment of sediment and initiation of bed defects insights from recent developments within turbulent boundary layer research sediment entrainment and the initiation of bed defects has commonly been ascribed to the impact of high velocity sweeps upon mobile sand beds results of visualization experiments suggest that these sweep impacts are grouped and may define patches of entrainment upon a mobile bed that may be wider than an individual sweep impact additionally the presence of longitudinal ribs of sediment generated by sweep impacts may stabilize the position of sweeps and low speed streaks these observations are interpreted in the light of recent boundary layer research which suggests the formation of multiple hairpin shaped vortices within turbulent flows these are postulated to generate multiple sweeps that manifest themselves as entrainment patches on a mobile bed these features of the turbulent boundary layer and its modification by sweep generated sediment ridges can be used to propose a model for bed defect formation and the subsequent development of current ripples

granulites in and around the bengal anorthosite eastern india genesis of coronal garnet and evolution of the granulite anorthosite complex granulites occur in and around an anorthosite massif commonly referred to as the bengal anorthosite in eastern india the central part of the anorthosite is massive in nature with locally developed fluxion structure in isolated blocks banding in the peripheral part is typical of that of the massif anorthosites of anderson morin the granulites bear imprints of polyphase deformation and the xenoliths of granulites within the anorthositic massif maintain their regional structural alignment the anorthosite syntectonic with the second fold movement in the terrane has developed second generation structures hornblende orthopyroxene clinopyroxene plagioclase and quartz with or without garnet and other minor phases consitute the granulites in the anorthosites orthopyroxene clinopyroxene hornblende and magnetite with or without garnet may constitute more than 15 of the mode garnet when present in the rocks is a late overprint symplectitic growth of garnet with one or more of the phases such as ilmenite quartz clinopyroxene and sodic plagioclase indicates genesis of garnet through decomposition of orthopyroxene and or prograde hornblende in the presence of calcic plagioclase the garnet formed during prograde dehydration reactions rather than cooling of the complex chemical characteristics of the mafic phases in the rocks indicate attainment of exchange equilibrium with respect to the major cations in closely associated hornblende clinopyroxene orthopyroxene and garnet estimated physical conditions of metamorphism from contrasted assemblages suggest a final equilibration of different granulitic assemblages as well as of the anorthositic assemblages under similar conditions there was however belated building up of water pressure in the anorthositic domains stabilizing a late hornblende during cooling of the complex absence of chilled margins in the anorthosite as well as absence of contact aureoles in the enveloping and enclosed granulites indicate emplacement of the anorthosite in a hot environment prior to cooling of the complex

characteristics of turbulent unidirectional flow over rough beds double averaging perspective with particular focus on sand dunes and gravel beds 1 we address some unsolved methodological issues in modeling of natural rough bed flows by critically examining existing approaches that parameterize rough bed flows these often utilize loosely defined variables here we suggest that double averaging in time and in a volume occupying a thin slab in a plane parallel to the mean bed provides a rigorous straightforward alternative that can aid in the parameterization process we further present two examples two dimensional bed form and gravel bed flows we argue that the double averaging approach based on momentum equations should serve as a better methodological basis for modeling phenomenological developments and parameterizations these equations explicitly include drag terms and form induced momentum fluxes due to spatial heterogeneity of the time averaged flow in the near bed region they also provide a solid basis for better definitions of basic flow variables including the shear stress partitioning into turbulent and form induced momentum fluxes skin friction and pressure form drag we show that for a range of rough bed flows the vertical distribution of the double averaged velocity consists of two distinct regions 1 a linear region below roughness tops and 2 a logarithmic region above them