mechanical interactions between rigid particles in a deforming ductile matrix analogue experiments in simple shear flow abstract the mechanical interaction between two or more particles is investigated in newtonian simple shear flow the experimental models allow observation of both the particle rotation and the deformation pattern around the particles the finite and instantaneous strain patterns around rigid particles are strongly heterogeneous and asymmetric with high finite strain zones aligned to the direction of maximum finite stretch these correspond to local flow with low vorticity number heterogeneous strain patterns around rigid particles spread over a distance of 1 2 times the particle length and this distance increases with increasing bulk strain where rigid particles are more concentrated these patterns coalesce and the overall pattern is then strongly controlled by the particles and cannot be simply related to the external boundary conditions in rocks the characteristic asymmetric strain pattern around rigid isolated particles is a reliable shear criterion which becomes unreliable with high concentrations of rigid particles particle rotation is significantly disturbed when the distance between adjacent particles of equal size is shorter than their length that is only in very concentrated suspensions of rigid particles in a composite shape fabric the development of the sub fabric corresponding to the smaller minerals will be more disturbed

the motion of rigid ellipsoidal particles in slow flows abstract preferred orientations of fabric elements in tectonites are usually interpreted with reference to two continuum models namely those of march 1932 and jeffrey 1922 it is argued that the first of these is usually inappropriate if the fabric elements are rigid inhomogeneities embedded in a deformable matrix jeffrey s model is more applicable but until recently its use has been limited to problems involving axisymmetric particles and simple flow geometries in this paper jeffrey s equations have been solved numerically in order to investigate the behaviour of more general systems the motions of two particle shapes one a prolate spheroid the other a triaxial ellipsoid are considered in parallel for four specified flow geometries which involve pure or simple shear and combinations of both any departures from particle axisymmetry or from simple flow geometries have a significant effect on particle behaviour compared with that predicted by spheroid simple flow solutions

the initial response of a stratified lake to a surface shear stress laboratory experiments are used to study the initial response of a stratified fluid to the action of a wind stress the experiments are described in the context of a parameterization scheme that quantifies the strength of the applied stress relative to the bulk stability of the fluid and also the duration of the wind stress relative to the periods of the waves generated by the stress this study concentrates on the first fundamental internal wave period in experiments where the fluid is considered to have upwelled i e the stratified region of the fluid reaches the surface at the upwind endwall the majority of the experiments use three layer initial density profiles as an approximation to a continuously stratified water column a linear model using normal modes proved successful prior to the commencement of upwelling and this enabled an estimate to be made of the time at which upwelling occurred at this point the wave development ceased and the flows developed via entrainment mechanisms consideration of the energy budget showed that little of the input energy was stored in the system the initial mixing efficiency defined as the ratio of the mean potential energy gained to the energy imparted by the belt never exceeded 30 peak efficiency occurred when the surface stress was just sufficient to bring the interfacial region to the surface

2 d rotation behavior of a rigid ellipse in confined viscous simple shear numerical experiments using fem abstract the rotation behavior of rigid elliptical inclusions adherent to the viscous matrix in simple shear flow is investigated using a 2 d finite element numerical model several simulations were performed using different ratios s between shear zone width and inclusion s least principal axis a computational strategy was devised to calculate pressure and viscous forces exerted on the inclusion and deduce its angular velocity for large s values results agree remarkably well with theoretical predictions while for small s values results deviate significantly from theory but are in agreement with previous analogue experiments the numerical model provided detailed and coherent information about the physical parameters involved in the process e g pressure strain rate and vorticity distributions within the model

numerical simulation of shoaling broad crested internal solitary waves abstractthe interaction between fully nonlinear miyata choi camassa mcc internal solitary waves and topographic slopes are modeled by direct numerical simulation the immersed boundary method is

types and kinematic stability of triple junctions a triple junction is kinematically stable if the orientation of each plate boundary remains constant relative to other boundaries in the triple junction during a finite time interval instantaneous relative velocity vectors have been used elsewhere to indicate the relative motion of plates during a finite time interval a technique that is not generally valid where finite relative plate motion is not circular in the typical case in which all three plates have non zero velocities around different plate specific poles of rotation the direction and magnitude of relative plate velocity varies systematically with time five plate boundary types are considered in evaluating triple junction stability ridges r right lateral and left lateral transform faults fr and fl and trenches in which the overriding plate is clockwise tc or anticlockwise ta from the trench judged by a rotation around the triple junction one hundred twenty five triplet combinations of boundary types are possible some combinations display symmetry with other combinations grouping all similar configurations 25 types of triple junctions can be distinguished of which 19 types may be stable when finite relative motion is circular vectorial descriptors of the geometry of ridges transform faults and trenches permit the listing of general conditions for the kinematic stability of triple junctions under conditions of both circular and non circular relative motion the tj1 model for the evolution of rrr triple junctions provides estimates of the variation in the geometry of triple junctions in which spreading is orthogonal and near symmetric rrr triple junctions at which spreading is orthogonal and symmetric are always stable when the finite relative motion of all corresponding plates is circular however tj1 indicates that rrr triple junctions are not generally stable when relative motion is non circular in general triple junctions are not kinematically stable but evolve with changes in the finite relative motion of plates

an experimental study of the upwelling response of stratified reservoirs to surface shear stress an experimental study of the dynamic response of non rotating stratified reservoirs to the application of surface shear stresses is presented the experiments were made using two layered and linear stratifications a moving belt was used to supply a shear stress to the fluid detailed measurements of the density field show that upwelling occurs at all values of the wedderburn number w rather than only occurring when w 1 differences between the two layer theory and the present observations are attributed to the fact that the experimental stratifications were continuous rather than layered shearflow dispersion is observed to be an important mechanism for distributing the effects of localized upwelling over the entire length of the mixed layer a model of mixed layer deepening based on upwelling and shearflow dispersion is presented and is compared to the observations of this and other experimental studies

porphyroclast systems as kinematic indicators porphyroclasts of relatively strong minerals in mylonites commonly have an internal monoclinic shape symmetry defined by tails of dynamically recrystallized material the geometry of a porphyroclast and its tails called a porhyroclast system can serve as a valuable indicator of the sense of vorticity porphyroclast systems have been divided into and types on the basis of the geometry of the tails types have wedge shaped recrystallized tails whose median lines lie on opposite sides of a reference plane parallel to the tails and containing the symmetry axis for the system types are further subdivided into a a types in which the porphyroclast is isolated in a relatively homogeneous matrix and b types in which the porphyroclast system is associated with a shear band foliation in the matrix types typically have narrow recrystallized tails whose median lines cross the reference plane adjacent to the porphyroclast consequently embayments of matrix material occur adjacent to the porphyroclasts and the tails display characteristic bends a porphyroclast system in a mylonite develops when the relatively weak dynamically recrystallized grain aggregate in the porphyroclast mantle changes its shape due to non coaxial flow in the adjacent matrix this behaviour has been modelled in shear box experiments passive marker lines around rigid cylinders embedded in silicone putty were subjected to simple shear the experiments were modified to simulate a change in recrystallization rate r with respect to rate of deformation by decreasing the diameter of the rigid cylinder during deformation at variable rates the ratio r appears to be one of the most important factors in determining which porphyroclast system will develop at high r values flow of recrystallized material away from the porphyroclast is continuously appended by the production of new grains and wedge shaped a type tails develop at low r values relatively few new grains are added to the tails which become thinned and deflected by drag due to the spinning motion of the porphyroclast in addition most porphyroclast systems at low shear strains are of a type or lack monoclinic symmetry whereas types are only developed at high shear strain values complex porphyroclast systems characterized by two generations of tails are observed in many of the natural and model shear zones studied and may form due to fluctuating r conditions that allow isolated a and type porphyroclast systems to be used as sense of vorticity indicators are the systems should have a monoclinic shape symmetry matrix grain size should be small with respect to porphyroclast size matrix fabric should be homogeneous deformation history should be simple and observations should be made on sections normal to the inferred bulk vorticity vector for the mylonite

on the reflectance of uniform slopes for normally incident interfacial solitary waves abstract the collision of interfacial solitary waves with sloping boundaries may provide an important energy source for mixing in coastal waters collision energetics have been studied in the laboratory for the idealized case of normal incidence upon uniform slopes before these results can be recast into an ocean parameterization contradictory laboratory findings must be addressed as must the possibility of a bias owing to laboratory sidewall effects as a first step the authors have revisited the laboratory results in the context of numerical simulations performed with a nonhydrostatic laterally averaged model it is shown that the simulations and the laboratory measurements match closely but only for simulations that incorporate sidewall friction more laboratory measurements are called for but in the meantime the numerical simulations done without sidewall friction suggest a tentative parameterization of the reflectance of interfacial solitary waves upon impact with uniform slopes

rolling structures at large shear strain abstract at large shear strain shear criteria are often obliterated or become ambiguous from examination of both natural examples and experimental models we describe a new criterion called rolling structure widely represented in sheared rocks a typical rolling structure is composed of a rigid or competent object e g porphyroclast boudin fossil etc with two tails asymmetrically disposed around it in most cases tails are of the same material as that of the rotating object and result from strain softening and grain size reduction at the object periphery forming a mantle z and s asymmetries of rolling structures represent dextral and sinistral senses of shearing respectively tails must not be confused with pressure shadows which usually present an opposite asymmetry for a given shear sense besides the determination of the sense of shear the occurrence of these structures allows a minimum estimate of the strain intensity in strongly sheared rocks since rolling structure length is proportional to shear strain

effect of shape and orientation on rigid particle rotation and matrix deformation in simple shear flow the rotation behaviour of rigid particles from a wide range of symmetry classes was analysed in a series of three dimensional analogue experiments in which the particles were embedded in a transparent linear viscous matrix deformed to large shear strains comparison of the measured trajectories with theoretical periodic paths for rigid ellipsoids shows that quadratic slightly orthorhombic and monoclinic particles have trajectory paths and rotation rates closest to theory orthorhombic and monoclinic particles with a minimum aspect ratio 1 5 develop non periodic trajectories the results establish that the simplified theoretical model for ellipsoidal forms is a good approximation for a wide range of natural particle shapes the relationship between the rotation of a rigid particle and deformation of the adjacent matrix was also determined in a series of experiments by placing the particle at different depths relative to an imprinted grid the results are well illustrated by the surface passing through the centre of the particle and initially parallel to the shear plane two deformed regions in the matrix are recognised in the first region the matrix rotates with the particle together forming an approximately ellipsoidal object the second region is dominated by folds of limited extent along the rotation axis and greatest extent in a direction that rotates asymptotically toward the shear direction the folds rotate more slowly than the principal direction of maximum finite stretch

internal hydraulic jumps in a long narrow lake high resolution three dimensional numerical modeling and field observations were used to describe the nonlinear response of cayuga lake to surface wind forcing the degeneration of the basin scale internal wave field was characterized according to the composite froude number g2 wedderburn number wn and lake number ln which are measures of hydraulic control and bulk and integral wind disturbance force to the baroclinic restoring force respectively the typical cayuga lake response was a nonlinear surge when 1 1 in a lake the occurrence of the hydraulic jump was correctly predicted using scaling parameters it was also shown that topographically induced internal hydraulic jumps form when the nonlinear surges interact with a sill contraction topographic feature in contrast to published literature the observed high frequency nonlinear internal waves were preferentially associated with internal jumps as opposed to steepened internal surges computed vertical diffusivities showed mixing was enhanced by two orders of magnitude within both the surges and hydraulic jumps as they propagated through the basin and interacted with topography our results can be generalized to other lakes and fjords with similar long narrow geometry and topographically separate side basins

strain insensitive preferred orientation of porphyroclasts in mont mary mylonites abstract the shape preferred orientation spo of porphyroclasts was determined in high temperature mylonites the porphyroclasts approach rhomboidal sillimanite or elliptical garnet plagioclase sillimanite shapes and exhibit aspect ratios r as high as 11 particles with r 3 are dominantly rhomboidal the long axis of the best fit ellipse defines a very strong spo inclined at 5 10 to the mylonitic foliation in an antithetic sense with respect to the shear direction this angle is independent of r the inclination of the long sides of rhomboidal sillimanite increases from 10 to 20 with decreasing r in contrast the short sides have a constant orientation of 15 to 17 irrespective of r and are parallel to extensional crenulation cleavage low aspect ratio mainly elliptical objects show low intensity spo close to the shear plane the two spos appear strain insensitive in the case of r r 3 a stable position is acquired this is not explained by any of the current theoretical and experimental models of spo

fabric evolution of rigid inclusions during mixed coaxial and simple shear flows abstract in a slowly moving viscous fluid a population of non interacting rigid inclusions evolves in an oscillatory fashion or creates a stable fabric depending on the flow geometry and the shape of the inclusions using jeffery s equations for the motion of a rigid ellipsoidal inclusion a mixed coaxial and simple shear flow was investigated both analytically and by numerical modeling exact results were obtained for spheroidal inclusions depending on the axial ratio of the inclusion and the amount of the coaxial component of flow individual inclusions can move cyclically or rotate to a stable orientation in one of two mutually orthogonal directions equations were found which allow us to distinguish between these types of motion and to determine the stable inclusion orientation the relative motions of individual inclusions determine the preferred orientation in a population of inclusions in a heterogeneous population with diverse axial ratios the fabric evolves as the superposition of subfabrics corresponding to subsets with different axial ratios the orientations of stable subfabrics depend on axial ratios and could thus be used as kinematic indicators in cases of a sufficiently large coaxial component of flow the fabric created by a heterogeneous population may comprise two stable mutually orthogonal subfabrics no exact results are available for general i e non spheroidal ellipsoidal inclusions and numerical modeling must be used if the coaxial component of flow is sufficiently strong the non spheroidal inclusions move much like the spheroidal ones orthogonal subfabrics may appear as transient features in the evolution of a homogeneous population of non spheroidal ellipsoidal inclusions

rotation of rigid elliptical cylinders in viscous simple shear flow analogue experiments we used experiments to investigate the behaviour of rigid elliptical cylinders embedded in a viscous fluid of finite thickness and for very small ratios s between shear zone width z and the shortest principal axis e2 of the ellipse that constitutes the base of the elliptical cylinder 3 5 s z e2 1 2 former theoretical and experimental work on the rotation of rigid inclusions immersed in a viscous matrix considered infinite shear zone thickness and or a very large ratio between shear zone thickness and inclusion size s 1 and concluded that inclusions rotate continuously and synthetically with the applied bulk simple shear flow except for inclusions with infinite axial ratio our results depart greatly from the analytical predictions experiments were carried out at constant shear zone thickness but variable s and degree of coupling at the inclusion matrix interface the results show that 1 confined inclusion rotation always deviates from theoretical predictions for infinite shear zone thickness even for synthetic rotation 2 the deviation in the angular velocity and or in the sense of rotation increases as s approaches 1 and antithetic rotation is possible from a position with ellipse longest axis parallel to the shear plane and 3 a slipping inclusion matrix interface greatly enhances deviation from theoretical predictions with antithetic rotations to as much as 20

the climatology of internal waves in a deep temperate lake kootenay lake is a long 100 km deep 140 m dimictic lake in southeastern british columbia internal waves were observed over an 18 month period using three thermistor chains moored along the major axis of the lake to characterize their seasonal aspects four types of oscillations are recognized 1 classical seiches with amplitudes of 10 30 m and periods of 1 2 weeks 2 intrabasin waves with periods of 2 4 days 3 large amplitude waves resembling nonlinear surges and 4 high frequency waves associated with both the internal surge and large amplitude internal seiche motions the periods of the major components of the internal wave field are determined mainly by morphometry but vary seasonally with stratification thus the wind which not only forces internal waves but can also modify stratification is important in large lakes like kootenay the thermal structure may vary not only spatially but also temporally at periods comparable to those of the internal waves themselves hence the shape and frequency of these waves may be altered as they pass through the lake

high frequency internal waves in lake geneva trains of high frequency internal waves have been observed in the thermocline of lake geneva within a few hours after the passing of disturbances which cause a rapid increase or jump in the depth of the thermocline three possible mechanisms for the source of the internal waves are proposed and compared with available data i that the waves are a soliton packet following the jump ii that the waves are generated as the jump passes over or around a local region of rough topography and iii that the jump produces a moving disturbance near the shoreline with internal waves forming a wake behind it the investigation of the last possibility involves the solution of the problem of the form of an internal wave wake in the presence of mean currents which vary in depth both in their strength and direction the wave pattern of the wake in the observed current distribution and stratification of the lake is described and compared with that in the absence of shear an expression for the energy of internal waves propagating in a shear flow is also derived and it is found that the rate of energy loss from the jump to the waves is small the minimum richardson number resulting from the co existence of the mean shear and the internal waves is marginally greater than 1 4 suggesting that the waves may be limited by shear flow instability however none of the mechanisms for their generation and propagation is fully compatible with the available data

rigid inclusions rotate in geologic materials as shown by torsion experiments jeffery showed 86 years ago that a sphere rotates synthetically with applied simple shear at a rate equal to half the shear strain rate however it can be argued that rocks do not behave like viscous fluids hence jeffery s model does not apply in order to test this argument we took a two phase synthetic aggregate rock made of 70 halite and 30 muscovite as anisotropic ductile matrix with embedded rigid bodies with contrasting shapes circular cylinder sphere and cube the sphere approximates the shape of a garnet and the cube the shape of pyrite crystals both so common in nature when subject to torsion at 250 mpa and 100 c the matrix deformed homogeneously and all rigid bodies rotated as theoretically predicted for a viscous fluid matrix therefore we conclude that rocks deforming in a ductile fashion behave macroscopically like a continuum hence fluid mechanics can be used to study rigid inclusion rotation behaviour

stable positions of rigid objects in non coaxial flow a study in vorticity analysis abstract distortions of a homogeneous fabric which occur around rigid objects in rocks deformed by non coaxial ductile flow are useful to determine the sense of shear but also contain information on other aspects of the flow rigid objects in a non coaxial flow fall into two categories those which are permanently rotating and those which can reach stable positions at high finite strain the orientation of such immobilized objects with respect to eigenvectors of instantaneous flow is a function of the vorticity number of the flow the ratio of instantaneous stretches and the axial ratio of the object in naturally deformed rocks immobilized rigid objects may be recognized from the geometry of the surrounding fabric tails of recrystallized material around porphyroclasts in a mylonite rotate towards parallellism with the extensional eigenvector of the flow and the shape of tails reflects the rotational behaviour of the porphyroclast the axial ratio of immobilized porphyroclasts and their orientation with respect to the tails can theoretically be used to determine the vorticity number of the flow and deviations from isochoric plane strain in practice such an analysis is as yet difficult but a tentative example is given of the way in which the vorticity number can be calculated from a population of feldspar porphyroclasts in a quartzite mylonite from the french pyrenees

deformation around rigid particles the influence of slip at the particle matrix interface abstract theoretical and previous experimental studies of rigid particle structures have only considered the behaviour of rigid particles for which the interface between particle and matrix is coherent in natural rocks the boundary behaviour may cover the whole range from free slip to complete coherence examples where slip may be promoted include crack seal deformation during the development of pressure shadows core mantle structures where the mantle is composed of much weaker fine recrystallized material and crystallizing magmas or partially molten rocks where grain boundaries are lubricated by the melt phase analogue scale model experiments have been performed under pure shear and simple shear conditions to compare the particle rotation and the flow in the matrix for both slipping and non slipping particle matrix interfaces when slip does occur particles rotate faster in pure shear and slower in simple shear than for non slip leading to the more rapid development of a shape preferred orientation the preferred orientation tends to be bimodal in simple shear flow the flow and finite strain patterns in the matrix are also strongly influenced by slip at the interface and porphyroclast systems can develop geometries with ambiguous or contradictory shear senses dependent on the original particle orientation in multi particle experiments slip on the interfaces enhances strong strain localization in non linear viscous material to produce patterns very similar to natural s c fabrics

2 d shape preferred orientations of rigid particles in transtensional viscous flow ghosh and ramberg tectonophysics 34 1976 1 70 studied the two dimensional 2 d rotational behaviour of individual rigid particles embedded in a viscous medium subject to simple shear and transpression sr 0 at low medium shear strains we now extend this theoretical study to transtension sr 0 by deriving a new analytical solution to non interacting populations of rigid particles and to high shear strains we used different initial orientations of particles in the same graph to simulate populations of particles in an originally isotropic rock our results show that 1 shape preferred orientations spos developed in viscous simple shear flow are transient and cyclical except for particles with aspect ratio or material lines which tend to the shear direction 2 stable spos can develop in transpression they dip towards the shear sense but when defining an s c structure with the shear foliation this composite fabric is always antithetic and thus indicates the wrong sense of shear 3 stable spos can also develop in transtension they dip opposite to the shear sense but when defining an s c structure with the shear foliation this composite fabric is always synthetic and thus indicates the correct sense of shear 4 spos produced in transpression or transtension can be used as vorticity gauges only when they represent stable orientations which must be demonstrated a priori

the degeneration of large scale interfacial gravity waves in lakes mechanisms for the degeneration of large scale interfacial gravity waves are identified for lakes in which the effects of the earth s rotation can be neglected by assuming a simple two layer model and comparing the timescales over which each of these degeneration mechanisms act regimes are defined in which particular processes are expected to dominate the boundaries of these regimes are expressed in terms of two lengthscale ratios the ratio of the amplitude of the initial wave to the depth of the thermocline and the ratio of the depth of the thermocline to the overall depth of the lake comparison of the predictions of this timescale analysis with the results from both laboratory experiments and field observations confirms its applicability the results suggest that for small to medium sized lakes subject to a relatively uniform windstress an important mechanism for the degeneration of large scale internal waves is the generation of solitons by nonlinear steepening since solitons are likely to break at the sloping boundaries leading to localized turbulent mixing and enhanced dissipation the transfer of energy from an initial basin scale seiche to shorter solitons has important implications for the lake ecology

microstructure and mechanical properties of halite coarse muscovite synthetic aggregates deformed in torsion abstract we investigated the behavior of a synthetic two phase aggregate composed of 80 halite 20 coarse muscovite under torsion deformation at 100 200 and 300 c a confining pressure of 250 mpa and a constant strain rate of 3e 4 s 1 at all temperatures the two phase aggregate deformed homogeneously at the sample scale the strength of the aggregate and muscovite deformation depended on temperature strain rate and initial orientation of muscovite greatest dimension relative to the shear plane with muscovite initially parallel to the shear plane halite flowed plastically and long muscovite grains were not strong enough to behave as a rigid inclusion rotating in a ductile matrix instead high aspect ratio grains deformed by folding which was visibly accomplished by slip along mica 001 cleavage and by great flattening of halite in the core of the folds when initially normal to the shear plane high aspect ratio muscovite grains passively rotated towards the shear plane in both cases small and low aspect ratio muscovite grains behaved mostly as mica fish with mica grains tilted opposite to shear sense similarly to natural mylonites porphyroclast systems and rolling structures were also common in the microstructure a strong foliation made of halite ribbons and aligned muscovite flakes rapidly developed but did not make the composite aggregate weaker when compared with single phase halite comparison with synthetic aggregates of single phase halite shows that the two phase aggregate was much stronger than single phase halite in all cases comparison with a synthetic aggregate with calcite porphyroclasts shows that the strength of the aggregate with muscovite at 100 c was lower below a strain of ca 2 6 and higher beyond this value and that the aggregate with calcite was stronger at 200 c strain rate stepping tests 1e 5 s 1 2e 3 s 1 indicate that the two phase aggregate behaved as power law viscous with stress exponents of ca 12 and 10 at 100 and 200 c respectively the mechanical data obtained in this study represent the actual rheological behavior of the aggregates because we used soft polymer jackets

internal wave weather in a stratified lake thermistor chain data collected in lake biwa japan during a period of strong stratification were used to determine the nature of the water column response to wind forcing the evolution of the basin scale waves in the lake were reproduced in three dimensional numerical simulations and the time variability of the internal wave spectrum is discussed based on spectral analysis of the thermistor chain records severe winds associated with the passage of three typhoons during the sampling period excited basin scale kelvin and poincare waves which by interaction with the topography of the lake and non linear effects generate trains of high frequency internal waves time frequency analysis of the temperature signals suggests that the 2 slope of the internal wave spectrum is probably the result of the composition of groups of waves with high intermittence travelling through the wave guide the observed rapid decay of internal wave energy after severe wind events seemed to be due mostly to high dissipation at the sloping boundaries of the lake

are isolated stable rigid clasts in shear zones equivalent to voids abstract particles in shear enclose important information about a rock s past and can potentially be used to decipher the kinematic history and mechanical behavior of a certain outcrop or region isolated rigid clasts in shear zones often exhibit systematic inclinations with respect to the shear plane at small angles tending towards the instantaneous stretching direction of the shear zone this shape preferred orientation cannot be easily explained by any of the analytical theories used in geology it was recently recognized that a weak mantle surrounding the clast or a slipping clast matrix interface might be responsible for the development of the observed inclinations physical considerations lead us to conjecture that such mantled rigid clasts can be effectively treated as voids that are not allowed to change their shape the resulting equivalent void conjecture agrees well with numerical and field data and has the following important geological implications i clasts in shear zones can have stable positions in simple shear without the requirement of an additional pure shear component ii the stable orientation can be approached either syn or antithetically hence the clast can rotate against the applied shear sense iii the strain needed to develop a strong shape preferred orientation is small 1 and therefore evaluations based on other theories may overestimate strain by orders of magnitude iv the reconstruction of far field shear flow conditions and kinematic vorticity analysis must be modified to incorporate these new findings

tectonic implication of quantitative micro fabric analyses of quartz c axis development within the tutak gneiss dome zagros hinterland fold and thrust belt quartz c axis fabrics finite strain and kinematic vorticity number analyses were used to investigate deformation characteristics of the tutak gneiss dome located in the eastern edge of the basement involved zagros hinterland fold and thrust belt the opening angle of the quartz c axis fabric patterns was used to estimate deformation temperatures which suggest greenschist to amphibolite facies conditions 430 50 c to 660 50 c the kinematic vorticity number varies from 0 6 to 0 95 mean kinematic vorticity number of 0 81 which indicates that the metamorphic rocks of the tutak gneiss dome experienced a sub simple shear regime by contribution of both pure shear 39 and simple shear 61 deformation components nw se striking foliations have commonly sw and ne dips accompanied by mostly nw se plunging and subordinate ne sw plunging stretching lineations these indicate more extension along the nw se trend to produce a prolate elliptical wedge shape in map view structural and vorticity analysis suggests that the tutak gneiss dome has experienced earlier dome formation followed by thrust stacking rather than the two deformations occurring synchronously and a protracted progressive deformation through a decreasing temperature regime

sheath folds formed by drag induced by rotation of rigid inclusions in viscous simple shear flow nature and experiment abstract natural examples of fold patterns associated with rotated boudins occur in the ossa morena zone s portugal and triggered the present study in ductile marbles with embedded competent mafic boudins the folds seem to have originated by rotation of these bodies and show differential development from gentle deflections to sheath folds this suggests a dependence of the structure type on the distance of the metamorphic layering to the rigid body the experimental work presented here was performed with rotating inclusions in bulk simple shear and introduces a new variable the distance of the marker layer from the rigid inclusion d expressed in terms of e the ratio between the spacing between marker layers d and the greater principal dimension of the inclusion a contrary to previous experimental work in the literature we used planar marker layers without concomitant boudinage our results show new processes of development of sheath folds from planar layers and also that some non cylindrical layer deflections are transient and thus that sheath folds do not originate from them when d is small and the inclusion starts with its longest axis normal to the shear plane sheath folds develop by drag pull processes on originally planar marker layers transient non cylindrical deflections develop on originally planar marker layers when the distance between the marker layers is smaller than the longest principal dimension of the rigid particle the monoclinic symmetry of the drag sheath fold patterns associated with rotating rigid inclusions indicate non coaxial flow and can be used as a shear sense criterion quarter structure

a parametric study of the generation and degeneration of wind forced long internal waves in narrow lakes the generation and energy downscaling of wind forced long internal waves in strongly stratified small to medium sized narrow lakes are studied a two layer nonlinear model with forcing and damping is employed even though the wave field is fundamentally bidirectional in nature a domain folding technique is employed to simulate the leading order internal wave field in terms of a weakly nonlinear weakly dispersive model equation of korteweg devries type parametric effects of wind forcing and environmental conditions including variable topography and variable basin width are examined energy downscaling from basin scale waves to shorter scales are quantified by means of a time evolution of the wave energy spectra it is demonstrated that an internal wave resonance is possible when repetitive wind forcing events arise with a frequency near the linear seiche frequency an attempt is made to apply the model to describe the shoaling of long waves on sloping endwall boundaries modelling of the energy loss and energy reflection during a shoaling event is calibrated against laboratory experiments

thick dyke emplacement and internal flow a structural and magnetic fabric study of the deep seated dolerite dyke of foum zguid southern morocco 1 knowledge on forced magma injection and magma flow in dykes is crucial for the understanding of how magmas migrate through the crust to the earth s surface because many questions still persist we used the long thick and deep seated foum zguid dyke morocco to investigate dyke emplacement and internal flow by means of magnetic methods structural analysis petrography and scanning electron microscopy we also investigated how the host rocks accommodated the intrusion regarding internal flow 1 important variations of the rock magnetic properties and magnetic fabric occur with distance from dyke wall 2 anisotropy of anhysteretic remanent magnetization reveals that anisotropy of magnetic susceptibility ams results mainly from the superposition of subfabrics with distinct coercivities and that the imbrication between magnetic foliation and dyke plane is more reliable to deduce flow than the orientation of the ams maximum principal axis and 3 a dominant upward flow near the margins can be inferred the magnetic fabric closest to the dyke wall likely records magma flow best due to fast cooling whereas in the core the magnetic properties have been affected by high temperature exsolution and metasomatic effects due to slow cooling regarding dyke emplacement this study shows that the thick forceful intrusion induced deformation by homogeneous flattening and or folding of the host sedimentary strata dewatering related to heat as recorded by thick quartz veins bordering the dyke in some localities may have also helped accommodating dyke intrusion the spatial arrangement of quartz veins and their geometrical relationship with the dyke indicate a preintrusive to synintrusive sinistral component of strike slip

development of highly non cylindrical folds around rigid ellipsoidal inclusions in bulk simple shear regimes natural examples and experimental modelling abstract the three dimensional development of strongly non cylindrical folds around competent ellipsoidal inclusions in bulk simple shear regimes is studied in experiments and natural examples examples from the continental allochthonous terrane of the braganca nappe complex ne portugal show rim folds and sheath folds associated with different parts of rigid ellipsoidal boudins experimental work has been carried out with models made from analogue materials silicone putty and plasticine and deformed in a simple shear machine we have considered three different models to simulate natural examples and the results show that fold morphology depends on the shape of the inclusion and position around the inclusion although the bulk deformation regime is layer parallel homogeneous simple shear we can distinguish local deformation regimes responsible for the folding associated with different parts of the rigid body flow and strain patterns must therefore be complex around inclusions or populations of inclusions prolate to oblate strain ellipsoids can be expected in different positions close to the rigid inclusion in our experiments the competent inclusions do not rotate synthetically with the applied bulk simple shear e g clockwise rotation of inclusion in dextral shear instead they back rotate early in the shearing history and keep this position throughout the experiment this is the result of the size relationship between the inclusion and the finite width of the shear zone the fold pattern around rigid inclusions may be used as a shear sense criterion

the degeneration of internal waves in lakes with sloping topography in a laboratory study we quantified the temporal energy flux associated with the degeneration of basin scale internal waves in closed basins the system is two layer stratified and subjected to a single forcing event creating available potential energy at time zero a downscale energy transfer was observed from the wind forced basin scale motions to the turbulent motions where energy was lost due to high frequency internal wave breaking along sloping topography under moderate forcing conditions steepening of nonlinear basin scale wave components was found to produce a high frequency solitary wave packet that contained as much as 20 of the available potential energy introduced by the initial condition the characteristic lengthscale of a particular solitary wave was less than the characteristic slope length leading to wave breaking along the sloping boundary the ratio of the steepening timescale required for the evolution of the solitary waves to the travel time until the waves shoaled controlled their development and degeneration within the domain the energy loss along the slope the mixing efficiency and the breaker type were modeled using appropriate forms of an internal iribarren number defined as the ratio of the boundary slope to the wave slope amplitude wavelength this parameter allows generalization to the oceanographic context analysis of field data shows the portion of the internal wave spectrum for lakes between motions at the basin and buoyancy scales to be composed of progressive waves both weakly nonlinear waves sinusoidal profile with frequencies near 10 24 hz and strongly nonlinear waves hyperbolic secant squared profile with frequencies near 10 23 hz the results suggest that a periodically forced system may sustain a quasi steady flux of 20 of the potential energy introduced by the surface wind stress to the benthic boundary layer at the depth of the pycnocline

mineral lineation produced by 3 d rotation of rigid inclusions in confined viscous simple shear abstract the solid state flow of rocks commonly produces a parallel arrangement of elongate minerals with their longest axes coincident with the direction of flow a mineral lineation however this does not conform to jeffery s theory of the rotation of rigid ellipsoidal inclusions reis in viscous simple shear because rigid inclusions rotate continuously with applied shear in 2 dimensional 2 d flow the rei s greatest axis e1 is already in the shear direction therefore the problem is to find mechanisms that can prevent the rotation of the rei about one axis the vorticity axis in 3 d flow the problem is to find a mechanism that can make e1 rotate towards the shear direction and so generate a mineral lineation by rigid rotation about two axes 3 d analogue and numerical modelling was used to test the effects of confinement on rei rotation and for narrow channels shear zone thickness over inclusion s least axis wr 1 can rotate backwards from an initial orientation w e1 parallel to the shear plane in great contrast to jeffery s model 3 back rotation is limited because inclusions reach a stable equilibrium orientation 4 most importantly and in contrast to jeffery s model and to the 2 d simulations in 3 d the confined rei gradually rotated about an axis orthogonal to the shear plane towards an orientation with e1 parallel to the shear direction thus producing a lineation parallel to the shear direction the modelling results lead to the conclusion that confined simple shear can be responsible for the mineral alignment lineation observed in ductile shear zones

effect of mechanical interactions on the development of shape preferred orientations a two dimensional experimental approach abstract modifications in the development of preferred orientations of rigid particles due to mechanical interactions between particles are studied experimentally in two dimensions experiments in both pure shear and simple shear were performed and the results analysed using an easy and fast new automatic method for increased concentration of rigid particles the rotation of individual particles may be slowed down or even stopped due to collisions or disturbance of the flow in the matrix caused by neighbours in coaxial flow the fabric intensity is consequently reduced in simple shear flow the fabric evolution is no longer cyclic the intensity is on average weaker and the fabric axis rotates asymptotically toward the shear plane in the case of preferred orientations of particles having a low aspect ratio 2 5 the fabric rotates through the shear plane then undergoes a reverse rotation and rotates toward the shear plane again in the light of these experimental results we emphasize that quantification of finite strain based on such fabrics may lead to significant underestimates and calculated values should be taken as minimum estimates the kinematic significance of concentrated rigid particle preferred orientations in rocks is modified by interactions between particles techniques for qualitative or quantitative kinematic analysis may become unreliable for simple shear flows the concentrated population fabrics show an angular behaviour close to that of passive markers they tend to align parallel to the shear plane in simple shear flow