application of turbulence energy models to the computation of tidal currents and mixing intensities in shelf edge regions abstract the major steps in the formulation of a three dimensional shelf edge model using a sigma coordinate system in the vertical are briefly described vertical diffusion of momentum is parameterized using a range of turbulence closure models and results are compared with earlier calculations using a simple flow related viscosity the influence of the magnitude of horizontal eddy viscosity upon spatial variability at the shelf edge is examined the model is applied to the calculation of m2 and o1 tidal elevations and currents in the shelf edge region off scotland the hebrides shelf and comparisons are made with data collected in the region computed m2 tidal elevations and currents are shown to be in adequate agreement with observations with no significant differences between tidal profiles computed with the turbulence energy models or the earlier calculations using a simple viscosity model the magnitude of the horizontal eddy viscosity does not appear to affect this component of the tide tidal

a three dimensional model of the m2 s2 n2 k1 and o1 tides in the celtic and irish seas abstract a three dimensional model using various parameterizations of eddy viscosity covering the celtic and irish sea region is used to examine the spatial distributions of the m2 s2 n2 k1 and o1 tidal elevations and phases computed cotidal charts and comparisons with observations from shore based and offshore gauges show good agreement comparisons are also made with a standard two dimensional model in shallow water regions the three dimensional model shows significantly less damping than the two dimensional model with an associated improvement in accuracy a detailed examination of differences between computed and observed tidal currents at over thirty locations having three or more current meters in the vertical show that the model can accurately reproduce the tidal current and its vertical profile in the eastern irish sea the region furthest from the model s open boundary good agreement with observations is obtained although in the deeper channel to the south of this the model over predicts current magnitude

multiscaling nature of sonic velocities and lithology in the upper crystalline crust evidence from the ktb main borehole the observed scaling of sonic logs is generally described using a monofractal model fractional brownian motion with hurst exponent typically between 0 1 and 0 2 or fractional levy motion even though such a description recognizes the existence of the self similarity of the logs it offers only a limited account of the actual symmetry as it misses the displayed heterogeneous fractality intermittency of the velocity increments is here observed and calls for the use of a multifractal description we quantify such a multifractality in the case of the p wave sonic log recorded at the ktb main borehole we also show that the associated lithology inferred from the gamma log has a multifractal distribution as well though characterized by a stronger intermittency it can be expected that the multifractality of the sonic log is partially induced by the lithology though the observed discrepancy in the degree of intermittency between the two logs indicates that the scaling symmetry of the seismic velocity is probably due to many different contributions such statistics for both sonic and gamma logs have important implications on our understanding of wave propagation and rock strength and permeability in the crystalline crust as they show the crust to be more heterogeneous than is usually modeled

fracture apertures from electrical borehole scans three dimensional finite element modeling was performed to investigate the response to fractures of the formation microscanner mark of schlumberger which records high resolution electrical scans of the borehole wall it is found that the equation w carmbrx0l describes over two orders of magnitude of resistivity contrasts between borehole mud and the formation the relationship between fracture width w in mm formation sensitivity rx0 mud resistivity rm and the additional current flow a caused by the presence of the fracture a is the additional current which can be injected into the formation divided by the voltage integrated along a line perpendicular across the fracture trace coefficient c and exponent b are obtained numerically from forward modeling tool standoffs of up to 2 5 mm and fracture dips in the range from 0 to 40 were found to have an insignificant effect on the above relation a three step approach to detect trace and quantify fractures is used potential fractures in formation

statistical physics seismogenesis and seismic hazard the scaling properties of earthquake populations show remarkable similarities to those observed at or near the critical point of other composite systems in statistical physics this has led to the development of a variety of different physical models of seismogenesis as a critical phenomenon involving locally nonlinear dynamics with simplified rheologies exhibiting instability or avalanche type behavior in a material composed of a large number of discrete elements in particular it has been suggested that earthquakes are an example of a self organized critical phenomenon analogous to a sandpile that spontaneously evolves to a critical angle of repose in response to the steady supply of new grains at the summit in this stationary state of marginal stability the distribution of avalanche energies is a power law equivalent to the gutenberg richter frequency magnitude law and the behavior is relatively insensitive to the details of the dynamics here we review the results of some of the composite physical models that have been developed to simulate seismogenesis on different scales during 1 dynamic slip on a preexisting fault 2 fault growth and 3 fault nucleation the individual physical models share some generic features such as a dynamic energy flux applied by tectonic loading at a constant strain rate strong local interactions and fluctuations generated either dynamically or by fixed material heterogeneity but they differ significantly in the details of the assumed dynamics and in the methods of numerical solution however all exhibit critical or near critical behavior with behavior quantitatively consistent with many of the observed fractal or multifractal scaling laws of brittle faulting and earthquakes including the gutenberg richter law some of the results are sensitive to the details of the dynamics and hence are not strict examples of self organized criticality nevertheless the results of these different physical models share some generic statistical properties similar to the universal behavior seen in a wide variety of critical phenomena with significant implications for practical problems in probabilistic seismic hazard evaluation in particular the notion of self organized criticality or near criticality gives a scientific rationale for the a priori assumption of stationarity used as a first step in the prediction of the future level of hazard the gutenberg richter law a power law in energy or seismic moment is found to apply only within a finite scale range both in model and natural seismicity accordingly the frequency magnitude distribution can be generalized to a gamma distribution in energy or seismic moment a power law with an exponential tail this allows extrapolations of the frequency magnitude distribution and the maximum credible magnitude to be constrained by observed seismic or tectonic moment release rates the answers to other questions raised are less clear for example the effect of the a priori assumption of a poisson process in a system with strong local interactions and the impact of zoning a potentially multifractal distribution of epicentres with smooth polygons the results of some models show premonitory patterns of seismicity which could in principle be used as mainshock precursors however there remains no consensus on both theoretical and practical grounds on the possibility or otherwise of reliable intermediate term earthquake prediction

a finite element model for tides and resonance along the north coast of british columbia a finite element barotropic tidal model is developed for the north coast of british columbia the model is run with eight tidal constituents and the results are compared with the flather 1987 finite difference model and with extensive tide gauge and current meter observations although the tidal potential earth tide and loading tide are included in the forcing their inclusion is shown to change the largest m2 amplitudes by only 2 5 and the largest k1 amplitudes by less than 1 root mean square differences between observed and calculated sea level amplitudes and phases are within 1 9 cm and 2 9 o for all but one constituent but the model currents do not in general compare as favourably the barotropic currents observed in hecate strait are reproduced well but elsewhere evidence is shown that model inaccuracies are due to baroclinic effects tidal residual currents calculated by the model suggest the existence of eddies off the tip of cape st james cape chacon and around goose island and learmonth banks the shallow water constituents in hecate strait are shown to have significant contributions from the constructive interference of signals propagating into dixon entrance and queen charlotte sound using the model the longest resonant period of the system is estimated to be 7 6 hours with an energy dissipation parameter q of 9 5

a high resolution three dimensional hydrodynamic tidal model of the eastern irish sea abstract a high resolution 0 5 north south by 1 0 west east approximately a 1 km grid hydrodynamic tidal model of the eastern irish sea is used to examine the sensitivity of m2 tidal currents to changes in open boundary data and bottom drag coefficients the model uses a finite difference grid formulation in the horizontal with an expansion technique in the vertical giving a continuous current profile from sea surface to sea bed a slip boundary condition is applied at the sea bed eddy viscosity in the model is a function of the flow field comparison of observed and computed tidal elevation and currents show good agreement although in general currents are slightly higher than observed the effect on tidal current profile of changes in bottom friction coefficient is found to be influenced by the proximity of the open boundary to the region of interest this suggests and calculations confirm that it is not just the local coefficient of bottom friction i e that within the eastern irish sea t

improved statistical multi scale analysis of fractured reservoir analogues abstract this paper includes the results of the application of novel methodologies for the statistical analysis of tensile fracture attributes spacing density and aperture the statistical methods have been applied to a fractured lower cretaceous carbonate succession cropping out in the sorrento peninsula naples area italy representing a geological analogue of buried reservoirs of southern apennines major oil fields as fracture networks observable from outcrop to the crystal scale can significantly affect the hydraulic behavior of a fractured reservoir the definition of appropriate models of fracture spacing and aperture probability distribution at various scales represents an important goal of structural analysis in order to achieve such an objective sampling has been carried out at different scales by means of traditional scan lines at outcrop as well as micro scan lines carried out both by a digital micro camera 50 and by the optical microscope 200 fracture spacing and density analysis are mainly aimed at establishing the characteristics of joint spatial distribution over a range of scales aperture analysis is aimed at verifying that the aperture cumulative frequency is described by a power law and in the latter instance to provide an effective method for a more precise determination of the exponent of the power law finally new expressions are provided in closed form in order to calculate the confidence interval of the power law exponent the proposed criteria provide handy and effective methods for a significantly improved statistical analysis of fracture attributes

tidal computations for morecambe bay summary a numerical finite difference technique for computing tides in areas of shoaling water has been established and used to calculate the m2 tide in morecambe bay an essential feature of the method is the representation of drying banks which appear as the water level falls on the ebb and which are re submerged on the flood as the level rises again since the non linear advective acceleration should be important in shallow water schemes for incorporating these terms are examined and the influence of advection on the tide assessed in a series of tests the open sea tides applied to the outer boundary of the numerical bay model were taken first from existing tidal charts then from calculations with a larger scale encompassing model and finally from observations of current in each case the computed tidal elevations within the bay turned out to be in satisfactory agreement with those obtained from observations however it is significant that in the first case inaccuracy of the input tidal distribution deduced from charts gives rise to erroneous currents near the boundary

estimating average fracture spacing in subsurface rock knowledge of the spacing of fractures in reservoir rocks i e the distance between parallel fractures in a subsurface joint set can lead to a better understanding of the production characteristics of a reservoir and serve to quantify the relative degree of deformation in subsurface rocks in this paper i present a new method for estimating the spacing of subsurface fractures this new method is easy to use from the standpoint of both data collection and data analysis the average fracture spacing method can be applied with boreholes of any orientation relative to a fracture set the method is especially powerful when it is used for the relatively common case of a borehole nearly parallel to a fracture set e g vertical borehole intersecting vertical fractures average fracture spacing is estimated from an analytical solution based on observed borehole fracture intersections and observed fracture porosity the only data required are the dimensions of the core or imaged borehole and the total height of all sampled fractures because the likelihood of intersecting fractures increases when a well is deviated perpendicular to the fractures of a set fracture reservoirs commonly are candidates for deviated boreholes an informed decision on borehole deviation requires predicting the fracture intersection frequency as a function of both deviation magnitude and direction a new method based on probabilities of borehole fracture intersections uses spacing and height data from subsurface joint like fractures and the borehole diameter to predict fracture intersection frequencies for all possible well deviations fracture intersection frequency solutions are presented with respect to a conventional geographic reference frame thus simplifying even the most complex three dimentional situations

multifractal characteristics of natural fracture apertures using information acquired from microscanner logs in horizontal boreholes fracture apertures are shown to be characterized by multifractal scaling a representative f spectrum can be modeled using a multiplicative cascade based on a two scale cantor set the resulting cascade can be used to simulate fracture aperture distributions at any scale when compared to well data the simulations show good agreement with aperture sizes and reproduce the clustering commonly recognized in fracture networks

a three dimensional model of diurnal and semidiurnal tides on the european shelf a three dimensional hydrodynamic model of the continental shelf is used to examine the sensitivity of computed diurnal k1 and o1 and semidiurnal m2 s2 and n2 tidal elevations and currents to changes in eddy viscosity profile friction coefficient and water depth the influence of the tide generating potential is also considered the model uses a standard finite difference grid in the horizontal with a functional approach in the vertical thereby giving a continuous tidal current profile from sea surface to seabed the magnitude of the vertical eddy viscosity depends upon the flow field comparisons are made between model computed profiles and harmonic analyses of 278 current time series at a range of locations in varying water depths with particular emphasis on locations where there are current measurements at a number of points in the vertical a detailed examination of these comparisons shows that frictional effects in the near bed region are particularly important in determining near bed shear and that an accurate specification of water depth is critical for tidal current magnitude the spatial distribution of computed current ellipses shows that the semidiurnal currents are strongest in shallow water with the diurnal currents exhibiting an intensification in the shelf edge region the inclusion of the equilibrium tide is particularly important for the correct determination of the magnitude of the k1 tidal current as well as k1 elevations in the north sea the detailed comparisons show that the magnitude of the tidal currents is correctly determined to within 5 cm s 1 at 220 locations with the model accurately to within 2 cm s 1 reproducing the vertical variation the most sensitive test of a three dimensional model of the tidal current at most locations

a permeability model for naturally fractured carbonate reservoirs abstract based on a detailed structural study performed on a reservoir surface analogue a fracture permeability model for carbonate reservoirs is proposed this involves four hierarchical systems each one assumed to convey fluids exclusively to that of immediately higher order new basic equations are then provided simulating hydrodynamic reservoir response the large scale first order structures consist of faults to which high permeability structures damage zones are associated at the meter scale stratabound joint systems together with bedding joints bounding the mechanical layers form a connected network transporting fluids to the fault system at a lower scale down to crystal size non stratabound joints constitute a pervasive and capillary fracture network which conveys fluids within the rock mass the non fractured host rock constitutes the lower permeability system at the crystal scale as no published works include an effective integration of detailed structural and numerical models the present study aims at covering a significant gap in the literature also providing appropriate theoretical basis for subsequent studies on fracture network modeling and reservoir simulation besides its application in the field of reservoir development and management the illustrated model may also be useful in environmental studies involving ground fluids such as e g in the field of special toxic nuclear waste management

a high resolution three dimensional model of the m2 m4m6 s2 n2 k1and o1tides in the eastern irish sea abstract the spatial distribution of the m 2 s 2 n 2 m 4 m 6 k 1 and o 1 tidal elevations and currents in the eastern irish sea is examined using a high resolution three dimensional model of the region the model uses a functional representation of the current in the vertical and can resolve the near bed high shear bottom boundary layer comparison of computed and observed tidal elevations and currents shows that the grid is sufficiently fine of order 1 km and the near bed region sufficiently well resolved to enable tidal elevations and currents particularly near bed currents to be accurately reproduced in order to accurately reproduce the near bed currents its is essential to reduce eddy viscosity close to the bed and enhance the bottom friction coefficient above that used in two dimensional models calculations of the m 2 m 4 and m 6 tidal currents with and without the other tidal constituents show that it is essential to include the other constituents if tidal elevations and currents are to be determined with a high level of accuracy with the m 6 tide being significantly influenced by the presence of the other constituents the presence of other tidal constituents not only increases bottom friction in an analogous manner to a two dimensional model but because the model involves a flow dependent viscosity they increase its magnitude which affects current structure the calculation of parameters such as the maximum bed stress which is important in sediment transport can be severely underestimated if the other tidal constituents are not included

right lateral displacements and the holocene slip rate associated with prehistoric earthquakes along the southern panamint valley fault zone implications for southern basin and range tectonics and coastal california deformation the n20 w trending panamint valley fault zone is linked to the n60 w trending hunter mountain strike slip fault and the saline valley fault system which represents one of the three major fault systems accommodating active crustal extension in the southern great basin a 25 km long zone of fault scarps along the southern panamint valley fault zone is recognized as the surface rupture zone associated with the most recent prehistoric earthquake the displacement associated with the most recent event determined through six detailed topographic maps of offset features is 3 2 0 5 m and a number of larger offsets in range of 6 7 m and 12 m are also observed if the larger displacements represent respectively two and three events each of 3 m then the fault zone appears to be associated with a characteristic earthquake which we estimate from the length of the rupture zone and the displacement to be between ms 6 5 and 7 2 the holocene slip rate is 2 36 0 79 mm yr is determined from the displacement of two alluvial features whose maximum age is estimated from pluvial shorelines assuming a characteristic earthquake model the recurrence interval is between 860 and 2360 years the holocene slip rate appears to be similar to the 4 million year slip rate of 2 2 7 mm yr determined from the hunter mountain fault which we suggest reflects the relatively constant tectonics in this region over the last 4 million years we further speculate that this supports the san andreas discrepancy in that the holocene slip rate of the san andreas fault probably represents its very long term several ma slip rate the total slip vector of the southern panamint valley fault system is oriented toward n35 w making this a predominantly strike slip fault in conjunction with the n60 w orientation of the hunter mountain strike slip fault we suggest that the displacement vector for the southern great basin is toward the nw consistent with results from vlbi data rather than wnw as determined by combining vlbi and geological data this in turn suggests that the coastal california deformation component involves respectively less shortening and more strike slip displacement perpendicular and parallel to the san andreas fault than is currently proposed

a numerical study of passive transport through fault zones we have numerically simulated contaminant transport through heterogeneous fault zones that consist of three components a core a damaged zone and a protolith each with a different permeability the interface between each of the components was assigned a fractal topography this was done to quantify the scaling of a contaminant plume through a fault as large scale faults can dominate regional flow the numerical method used was a modified lattice gas scheme for flow in porous media coupled to a finite difference solution to the advection dispersion equation the introduction of heterogeneity leads to complex behaviour of a chemical plume in several faults with the same statistical properties a range of arrival times is observed along with bimodal break through curves this behaviour was a common feature in each heterogeneous fault model the mean and the variance of the plume were calculated for every simulation and indicated that the transport is anomalous the mean scaled through time from t1 00 to t0 54 for the different models thus the mean velocity decreased with time in each of the fault models the minimum and maximum scaling through time of the variance of the plume was from t1 0 to t1 87 indicating anomalous transport the simulated break through curves were analysed using the continuous time random walk method that quantifies the scaling of migrating contaminants using a single parameter for 2 the transport is gaussian and for 2 the transport is anomalous and the variance scales as t 3 for 1 2 the average value of for the different models ranged from 1 65 to 2 00 we have also shown that the scaling of the transport can vary significantly over short distances relative to the size of our models

from field data to fracture network modeling an example incorporating spatial structure this paper describes a technique for processing field data for a fracture network model which accounts for the observed spatial variability this has been done by generating a network subregion by subregion where the properties of each subregion are predicted through geostatistics once the geometry of a particular realization is specified flow through the network is studied we develop the method for a two dimensional analysis based on data from fanay augeres a uranium mine in france we plan to extend the analysis to three dimensions and compare the results with in situ test results in particular we have focused on the data collected in a long section of a drift where fractures have been mapped and steady state permeability tests have been performed in 10 boreholes in order to generate fractures in a statistically heterogeneous region we first divided the region into statistically homogeneous subregions in each subregion and for each fracture set we must specify the areal fracture density and the orientation length and aperture distributions we divided the fractures into five sets based on tectonic history and observed that for each set fractures spaced close together tended to have similar orientations this was built into the simulation an estimate of the aperture distribution for each set was made by assuming that the hydraulic apertures of the fractures intersecting a well test zone were proportional to the fracture opening observed in the core data input to the geostatistical analysis for each set consisted of 16 values of mean length and density of fractures in each 5 m by 2 m section of the drift wall the results of the simulation are tables of values for mean length and fracture density for each of the five sets the value of density simulated for each subregion was used directly to determine the number of fractures to be generated of that set in the subregion the value of mean length was used as the mean of the length distribution in the subregion the local coefficient of variation for length was the same in every subregion using the data described above we generated a 100 m by 100 m fracture network in a series of 100 statistically homogeneous subregions the fractured region generated has a total of 65 740 fractures a 70 m by 70 m region was isolated for directional permeability testing results show that the system is barely connected about 0 1 of the fractures essentially control permeability in the language of percolation theory this mesh is close to the critical density for which infinite clusters of fractures are found problems remaining include that 1 the analysis should be extended to three dimensions 2 the geostatistical simulation and network simulation should be combined rather than used as two separate operations and 3 the nature of flow through single fractures at fanay augeres should be investigated

tidal spectroscopy of the english channel with a numerical model abstract the possibility of reproducing the complexity of tides in shallow water areas with a classical finite difference numerical model is examined this hydrodynamic model is two dimensional but incorporates topography nonlinear advection and quadratic bottom friction particular care is taken to prescribe sea surface elevations at the open boundaries a one month simulation of real tides is run with a simplified spectrum restricted to only 24 constituents corresponding to the nine main astronomical tides and their nonlinear significant interactions the results are analyzed by spectral decomposition elevations and vertically integrated currents and compared with observational data from the tide gages and current meters and with other solutions produced in the literature it is found that the dominant m2 constituent greatly influences the damping of the other constituents so that it is necessary to run them together for any correct simulation however the quadratic friction law introduced in

a three dimensional model of the m4 tide in the irish sea the importance of open boundary conditions and influence of wind a fully nonlinear three dimensional hydrodynamic model of the irish sea is used to examine the processes determining the spatial variability of the m4 tide in the irish sea the model is based upon a mixed spectral finite difference approach with an expansion of functions in the vertical yielding a continuous current profile and a finite difference grid in the horizontal the model has a sufficiently fine grid to enable the nonlinear advective terms to be resolved in their finite difference form and the spatial variability of the m4 tide to be represented computed m4 elevations and currents determined using a radiation open boundary condition with both m2 mid m4 elevation and current input and a flow dependent viscosity are found to be in satisfactory agreement with observations considering the limited grid resolution of the model and the level of noise in the m4 tide as a percentage of the signal is much higher than for m2 this agreement is good enough to establish the credibility of using the model to examine the processes influencing the m4 tide which are discussed in detail the importance of an m4 current input to the radiation condition and the difficulty of using an elevation specified open boundary condition to reproduce the m4 tide in this region are considered in some detail the nonlinear advective terms are shown to have a limited local influence namely around headlands in generating the m4 tide the influence of wind effects upon m4 tidal currents particularly through the nonlinear term associated with a time dependent eddy viscosity is examined and shown to produce a significant increase in the m4 near surface tidal current and a modification of the current profile in essence the change of the m4 tidal current by meteorological effects will give rise to noise in any observed m4 current due to the random nature of the wind fields

influence of fracture intersections under unsaturated low flow conditions recent experimental evidence suggests that the capillary heterogeneity associated with fracture intersections can act to impose temporal and spatial structure on network scale flows a simple intersection between orthogonal fractures one horizontal and the other vertical has been shown to integrate unsaturated flows at low flows the intersection forms a capillary barrier that accumulates water in a growing pool eventually the retaining meniscus snaps discharging a pulse of water here we develop a mechanistic explanation for this observed behavior and experimentally consider three perturbations to the geometry of the simple orthogonal intersection two of the perturbations also act as capillary barriers while the third formed a capillary bridge across the intersection at low flow all of our experimental intersections imposed a temporal signal with the nature of that signal dependent on intersection geometry and participation by the horizontal fractures in dynamic storage at high flow a continuous fluid tendril spanned the system from inlet to outlet with water pooled above the intersection caused by a narrow fluid connection that restricted flow across the intersection results from all experiments suggest that pulsation is critically sensitive to small variations in the geometry of fracture intersections and storage in the horizontal fractures when combinedmore with dependency on supply rate this sensitivity can generate pulsation of flow across a wide range of time periods and discharge volumes less

a three dimensional model of the northwest european continental shelf with application to the m4 tide abstract the solution of the fully nonlinear three dimensional hydrodynamic equations in polar coordinates for tides is developed using a finite difference grid in the horizontal and the galerkin method in the vertical using this method a three dimensional model of the northwest european continental shelf is used to investigate the spatial distribution of the m4 tidal elevations and currants over the shelf computed m4 currents are compared with observations and found to he in good agreement in the celtic sea although there are significant errors in the north sea the reasons for these discrepancies and the spatial and depth variations in the m4 currants are discussed in detail

application of a three dimensional turbulence energy model to the determination of tidal currents on the northwest european shelf a three dimensional turbulence energy tidal model employing a sigma coordinate system through the vertical with a logarithmic type transformation to enhance near bed resolution is used to examine m2 tidal currents on the european continental shelf a no slip bottom boundary condition is applied in the model and vertical eddy viscosity is computed from a turbulence energy closure scheme comparisons of observed and computed current profiles determined using the present model and an earlier model employing a spectral representation davies 1986 in the vertical and a slip bottom boundary condition are made in this spectral model a simple relationship between eddy viscosity and depth mean current was employed these comparisons of current profile suggest that above the near bed layer the spectral model can reproduce tidal currents with a comparable accuracy to that of the present turbulence energy model however in the near bed region the turbulence energy model is significantly more accurate computed spatial distributions of current magnitude turbulence energy intensity and eddy viscosity show similar distributions over the model region suggesting that a relationship between eddy viscosity and current intensity the form used in the spectral model is a valid alternative to using a turbulence energy model turbulence energy intensity in particular exhibits significant spatial variations both horizontally and vertically with surface contours of turbulence corresponding to known positions of tidal fronts

a three dimensional model of the principal tides on the european shelf abstract a three dimensional hydrodynamic model of the continental shelf is used to examine the spatial distribution both elevations and currents of 28 of the major tides in the region tidal constituents in the diurnal and semi diurnal band together with higher harmonics and long period tides are used to illustrate the magnitude and spatial variability of the tides over the shelf comparisons are made between model computed profiles and harmonic analyses of 278 current time series at a range of locations in varying water depths with particular emphasis on locations where there are current measurements at a number of points in the vertical observed and computed tidal elevation amplitudes and phases are also compared at up to 257 shore based and off shore tide gauges these detailed comparisons are used to determine any bias in the model and the accuracy of predicted elevations and currents derived with the model results of these comparisons show that although the diurnal and semi diurnal tidal elevations and currents can be accurately reproduced using a 12 km grid the error in the higher harmonics is significantly larger the fact that the model contains all the non linear terms advection quadratic friction wave drift time varying viscosity necessary to generate these harmonics together with a full set of tidal harmonics in order to have the correct level of friction suggests that potentially it should reproduce these constituents however a rigorous comparison was found to be very difficult because of the rapid variation of the higher harmonics in shallow water which cannot be adequately resolved in the model and possible inaccuracy in the measurements of the small currents associated with the higher harmonics

a numerical model investigation of tides and diurnal period continental shelf waves along vancouver island abstract a numerical model study of the tidal regime west of vancouver island is presented ale model employed is a nonlinear barotropic two dimensional tidal model incorporating realistic bathymetry the m2 and k1 constituents are examined and comprehensive comparisons between computed and observed elevations and currents are given for m2 the model reproduces observed motion very accurately however k1 is of greater interest since it contains a substantial contribution in the form of a continental shelf wave csw the model correctly predicts the existence of the csw but consistent with the neglect of stratification and the influence of mean flows underestimates its wavelength it is shown that the csw component of k1 is generated by the tidal flow in juan de fuca strait the influence of mean currents on the tidal regime is investigated by including them in a further model solution consistent with theory the wavelength of the csw component of k1 is increased giving improved agreement with obser

a comparison of the nonlinear frictional characteristics of two dimensional and three dimensional models of a shallow tidal embayment the nonlinear frictional behavior of two dimensional 2 d and three dimensional 3 d models are compared in this study of tides in the bight of abaco the shallow depths and the existence of an extensive set of tidal elevation data five astronomical and two overtide constituents at 25 stations from filloux and snyder 1979 offer an excellent opportunity to compare the effects of different frictional formulations in addition previous modeling efforts in the bight have consistently overpredicted the m6 and generally overdamped the o1 k1 and s2 tides the results indicate that although the 2 d and 3 d models may be calibrated to produce nearly identical responses for the dominant m2 tide there are systematic differences in the responses of the primary overrides these differences are explained using analytical expansions of the friction terms and are shown to be due to differences in the terms that are nonlinear in velocity and in water level the investigation concludes that the overgeneration of m6 and the overdamping of secondary astronomical tides will occur in 3 d models as well as 2 d models although several causes for these problems were considered improvement in these constituents could be achieved only by modifying the standard quadratic friction or flow dependent eddy viscosity relations to reduce the nonlinear frictional effect relative to the linear frictional effect the required modifications suggest the presence of a constant background velocity residual turbulence field or possibly the need for a more advanced frictional closure

fluid velocity fields in 2d heterogeneous porous media empirical measurement and validation of numerical prediction the scale invariance of geological material and the consequent absence of a length scale on which to base the upscaling of measurements made on geological samples represent a serious challenge to the prediction of fluid behaviour in rock at economically interesting scales numerical simulation is an important tool for understanding constraints in this problem and current discrete fluid models in which complex boundary conditions can be represented have the potential for testing many possible upscaling schemes at present however there are no accurate empirical data on the distributions of fluid velocities in complex scale invariant geometries with which to validate such models to address this fluid velocity fields in complex 2d media with fractal heterogeneity were measured digital models of rock geometries were created and translated into physical form using electric discharge machining and stereolithography these physical models were then enclosed between parallel sheets of glass and perspex forming a hele shaw cell which was permeated with water doped with small neutrally buoyant spheres and pumped at accurately steady and reproducible velocities local velocity vectors were estimated by the analysis of sequential images captured using high resolution video precision digital control systems were used to move the cell relative to the camera and repeated measurements allowed the construction of full 2d velocity fields the accuracy of the technique was assessed by comparison between automated and manual measurements confirming the accuracy over approaching three orders of magnitude in velocity the results have been compared to the output of lattice boltzmann lb simulations of flow in identical geometries showing that the correlation between simulated and measured velocity fields is strongly dependent on the viscosity used in the numerical simulation in particular the lb scheme used in these tests is incapable of simulating correct viscosities for complex geometries some important effects are shown to be strongly viscosity dependent and it is concluded that some simulations may be able to predict the behaviour of high viscosity fluids only nonlinear effects between fracture and matrix flow are likely to be more important in these cases