Basic-state Flow Research Articles

Three-Dimensional Structure and Dynamics of African Easterly Waves. Part I: Observations

Abstract The mean structure of African easterly waves (AEWs) over West Africa and the adjacent Atlantic is isolated by projecting dynamical fields from reanalysis and radiosonde data onto space–time-filtered satellite-derived outgoing longwave radiation. These results are compared with previous studies and an idealized modeling study in a companion paper, which provides evidence that the waves bear a close structural resemblance to the fastest-growing linear normal mode of the summertime basic-state flow over Africa. There is a significant evolution in the three-dimensional structure of AEWs as they propagate along 10°N across West Africa. At this latitude, convection occurs in northerly flow to the east of the Greenwich meridian, then shifts into the wave trough, and finally into southerly flow as the waves propagate offshore into the Atlantic ITCZ. In contrast, to the north of the African easterly jet along 15°N convection remains in southerly flow throughout the waves’ trajectory. Along 10°N over West Africa, the location of convection is consistent with the adiabatic dynamical forcing implied by the advection of perturbation vorticity by the mean thermal wind in the zonal direction, as in the companion paper. Offshore, and along 15°N, the relationship between the convection and dynamics is more complex, and not as easily explained in terms of dynamical forcing alone.

A Barotropic Envelope Rossby Soliton Model for Block–Eddy Interaction. Part IV: Block Activity and Its Linkage with a Sheared Environment

Abstract In this paper, a basic-state flow that has a linear, weak meridional shear is used as a mean flow condition to see if the blocking activity is related to the state of the zonal mean flow based upon the envelope soliton theory proposed in Part I. It is found that an isolated coherent structure similar to a dipole block can arise from the resonant interaction between preexisting planetary- and synoptic-scale waves, but its asymmetry, intensity, and persistence depend strongly upon the horizontal shear of the basic-state flow prior to block onset. The cyclonic shear of the basic-state flow not only plays an important role in preventing the eastward spread of block energy, but also provides a strong diffluent flow as a precursor of block flow. In such an environment, a high amplitude dipole anomaly is maintained and the deformed synoptic-scale eddies tend to deflect northward. But the anticyclonic shear of a basic-state flow plays a reverse role, which causes deformed eddies to deflect southward. It is also found that positive westerly wind anomalies at both high and low latitudes and negative anomalies at middle latitudes are maintained by synoptic-scale eddies through the self-interaction of block. In this case, the zonal mean westerly wind is accelerated at high and low latitudes, and decelerated at middle latitudes. Only for a basic state with cyclonic shear is the meridional profile of the zonal mean wind during the onset of a dipole block in agreement with observations. In addition, it can be shown by computing scatter diagrams of potential vorticity against streamfunction in different sheared environments that an eddy-induced isolated block can exhibit a local free-mode characteristic. Two approximately linear functional relationships between potential vorticity and streamfunction are found to be probably attributed to synoptic eddies.

Perturbation Growth in Baroclinic Waves

Abstract Floquet theory is applied to the stability of time-periodic, nonparallel shear flows consisting of a baroclinic jet plus a neutral wave. This configuration is chosen as an idealized representation of baroclinic waves in a storm track, and the stability analysis may be helpful for understanding generic properties of the growth of forecast errors in such regions. Two useful attributes of Floquet theory relevant to this problem are that the period-average mode growth rate is norm independent, and the t→ ∞ stability limit is determined by the stability over one period. Exponentially growing Floquet modes are found for arbitrarily small departures from parallel flows. Approximately 70% of Floquet-mode growth in energy is due to barotropic conversion, with the remainder due to zonal heat flux. Floquet-mode growth rates increase linearly with neutral wave amplitude (i.e., the “waviness” of the jet) and also increase with neutral wave wavelength. Growth rates for meridionally localized jets are approximately 40% smaller than for comparable cases with linear vertical shear (the Eady jet). Singular vectors for these flows converge to the leading Floquet mode over one basic-state period, and the leading instantaneous optimal mode closely resembles the leading Floquet mode. Initial-value problems demonstrate that the periodic basic states are absolutely unstable, with Floquet modes spreading faster than the basic-state flow both upstream and downstream of an initially localized disturbance. This behavior dominates the convective instability of parallel-flow jets when the neutral baroclinic wave amplitude exceeds a threshold value of about 8–10 K. This result suggests that forecast errors in a storm track may spread faster, and affect upstream locations, for sufficiently wavy jets.

Instabilities in hurricane-like boundary layers

Recent advances in observational technology have led to a more detailed knowledge of the low-level flow in hurricanes. In particular, quasi-streamwise rolls on a variety of scales have been observed. Some of these rolls have radial wavelengths of 4–10 km, which is comparable to rolls associated with instabilities inherent to Ekman-type boundary layers. The evolution and stability of the swirling boundary layer underneath a hurricane-like vortex is studied using both a nonlinear model and linearized stability analysis. The nonlinear model is an axisymmetric model of incompressible fluid flow, which is used to simulate the development of boundary layers underneath vortices with hurricane-like wind profiles. Axisymmetric rolls appear in these boundary layers, which have some similarities to the observed rolls in hurricanes. The axisymmetric flow is also used as the basic-state for a linearized stability analysis. The analysis technique allows for arbitrary variation in the radial and vertical directions for both the basic-state flow and the perturbations. Thus, the strong radial variations and curvature effects common to strong vortices are part of the analysis. The analysis finds both symmetric and asymmetric instabilities that are similar to those in the nonlinear simulations and in observations. The instabilities acquire some of their energy from the vertical shear associated with a reversal of the radial inflow at the top of the boundary layer, and some of their energy from vertical shear of the azimuthal flow. The radial flow energy conversion tends to increase for flows with less inertial stability and for modes oriented across the low-level shear; the azimuthal flow conversion increases for larger inertial stability and for modes aligned with the low-level shear.

Finite-time normal mode disturbances and error growth during Southern Hemisphere blocking

The structural organization of initially random errors evolving in a barotropic tangent linear model, with time-dependent basic states taken from analyses, is examined for cases of block development, maturation and decay in the Southern Hemisphere atmosphere during April, November, and December 1989. The statistics of 100 evolved errors are studied for six-day periods and compared with the growth and structures of fast growing normal modes and finite-time normal modes (FTNMs). The amplification factors of most initially random errors are slightly less than those of the fastest growing FTNM for the same time interval. During their evolution, the standard deviations of the error fields become concentrated in the regions of rapid dynamical development, particularly associated with developing and decaying blocks. We have calculated probability distributions and the mean and standard deviations of pattern correlations between each of the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. The mean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases with increasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but not always, gives the largest mean pattern correlation with error fields. Corresponding pattern correlations with the fast growing normal modes of the instantaneous basic state flow are significant but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increase further when the time interval is increased beyond six days.

A balanced approach to modelling rotating stably stratified geophysical flows

We describe a new approach to modelling three-dimensional rotating stratified flows under the Boussinesq approximation. This approach is based on the explicit conservation of potential vorticity, and exploits the underlying leading-order geostrophic and hydrostratic balances inherent in these equations in the limit of small Froude and Rossby numbers. These balances are not imposed, but instead are used to motivate the use of a pair of new variables expressing the departure from geostrophic and hydrostratic balance. These new variables are the ageostrophic horizontal vorticity components, i.e. the vorticity not directly associated with the displacement of isopycnal surfaces. The use of potential vorticity and ageostrophic horizontal vorticity, rather than the usual primitive variables of velocity and density, reveals a deep mathematical structure and appears to have advantages numerically. This change of variables results in a diagnostic equation, of Monge–Ampère type, for one component of a vector potential is proportional to the displacement of isopycnal surfaces. This diagnostic equation makes transparent the conditions for both static and inertial stability, and may change form from (spatially) elliptic to (spatially) hyperbolic even when the flow is statically and inertially stable. A numerical method based on these new variables is developed and used to examine the instability of a horizontal elliptical shear zone (modelling a jet streak). The basic-state flow is in exact geostrophic and hydrostratic balance. Given a small perturbation however, the shear zone destabilizes by rolling up into a street of vortices and radiating inertia–gravity waves.

The Influence of Atmospheric Blocking on the Rossby Wave Propagation in Southern Hemisphere Winter Flows.

The influence of blocking systems on the propagation of planetary Rossby waves is investigated over the South Pacific. Two episodes of blocked flow observed during the winter of 1995 in the Southern Hemisphere were selected for this purpose. Rossby wave activity is analyzed with the aid of a barotropic model linearized around zonally and meridionally varying basic states obtained from the National Centers for Environmental Prediction Center (NCEP)/National Center for Atmospheric Research (NCAR) Reanalysis Project data. Basic state flows corresponding to the blocking events, and to the seven-day period immediately prior to (after) their onset (decay) were used. The forcing, represented by an anomalous divergence pattern, is placed in two different regions—tropics and subtropics. Numerical results are discussed based on the linear theory for Rossby wave propagation. Fields of stationary wavenumber (Ks) for barotropic Rossby waves are computed for the basic state flows. Wave activity fluxes are calculated for the perturbation fields. The spatial distribution of Ks showed the jet streams as potentially efficient waveguides, as indicated by the agreement between the position of the jet stream axes and the relative maxima of Ks. A tendency for increasing values of Ks in the high latitudes (south of 65°S) was obtained along the poleward flank of the longitudinal zone where the blocking systems were positioned. This suggests a possible enhancement on Rossby wave activity along sub-polar regions during these blocking events. In contrast, for the periods preceding and subsequent to the blocking systems, values of Ks at high latitudes did not show a tendency to increase, characterizing a normal situation in which local maximum values of Ks are confined to the mid- and subtropical latitudes. The numerical results suggest that the planetary Rossby wave propagation can be influenced by this alteration in the latitudinal distribution of higher values of Ks during the life cycle of the blocking systems. A transition, from subtropical to sub-polar, of the main sector of wave propagation was obtained between the pre-blocking and blocking situations, and with the subtropical Rossby wave activity regaining importance after the decay of the blocking events. Moreover, for situations preceding the blocking systems, a region of maximum values on wave activity flux was obtained on the longitudinal zone where the blocking patterns would develop subsequently, indicating a possible participation of stationary Rossby wave propagation on the onset of the blocking episodes.

VHF radar measurements and model simulations of mountain waves over Wales

AbstractVery high frequency (VHF) radar measurements of mountain waves over Aberystwyth, Wales, during 29 November 1997 are presented and compared with the predictions made by a three‐dimensional numerical model which is based on the linearized equations of motion. The radar height–time plot of vertical velocity reveals a wave field in the troposphere and lower stratosphere which changes significantly throughout the day. Four separate radiosonde soundings taken during the day are used to represent the steady background flow in the numerical model. In this case the steady‐state model wave fields are shown to compare qualitatively well with the radar measurements and the three‐dimensional information provided by the model is used to help explain the changes in the wave field observed by the radar throughout the day.The radiosonde profiles are interpolated in time to provide approximate basic‐state data at two‐hour intervals. Model steady‐state vertical‐velocity fields, based on each of these 13 approximate basic‐state profiles are used to generate a model time–height vertical‐velocity plot which is qualitatively similar to that obtained from the radar measurements, indicating that, to a reasonable approximation, the evolving wave field can be regarded as a sequence of independent steady states. This is generally true if the basic‐state flow remains steady over the time taken for wave packets to propagate over several wavelengths. Group‐velocity arguments are used to show that, for typical mountain waves in the troposphere, such time‐scales are generally less than one hour.Model simulations in which the basic‐state flow is allowed to vary in time continually (based on either the interpolated radiosonde soundings or the radar horizontal‐wind measurements) are conducted. In this case the simulated wave fields are always unsteady; the waves show a tendency to drift in response to changes in the basic‐state wind field. For example, during instances when the wind speed at a given level decreases (whilst the wind direction remains the same) the waves show an upwind phase propagation with a typical phase speed of the order of 1 m s−1. The consequence of this unsteadiness for the propagation of the waves is discussed. Copyright © 2002 Royal Meteorological Society.

Capillary flow in interior corners: The infinite column

Capillary flow of a sinusoidally perturbed liquid column in an interior corner of infinite extent is solved using lubrication theory. Due primarily to the length scales selected to nondimensionalize the momentum equation, an analytic time scale governing the settling of the perturbation is determined. The time scale, which is shown to be independent of a steady base state flow, proves useful in rapidly predicting transients for surface settling in certain liquid-bearing tanks of spacecraft employing interior corners for fluids management purposes. The asymptotic analysis is extended to address flows along interior corners whose faces are slightly nonplanar. The generalized formulation is presented for the case of a perfectly wetting fluid in a second-order polynomial corner. A leading-order analytic solution for small corner angles is provided. It is shown that a “convex corner” decreases the response time of the liquid and increases the capillary flow rate along the corner by increasing both the driving force and cross-sectional area of the flow. Gravity acting normal to the corner axis along the bisector of the corner angle is also considered and is found to accelerate, decelerate, or destabilize such flows depending on its sign and magnitude.

Flow of a fluid near its density maximum in a differentially rotating cylinder

A numerical study is made of the basic-state flow field of a fluid with a density maximum in a differentially rotating cylinder. The fluid density reaches a maximum ρ m at temperature T m, and a quadratic ( ρ– T) relationship is used to model the fluid behavior near T m. The temperature at the bottom (top) endwall disk is T B (T T ) , with ΔT≡ T T− T B>0, and T m lies between T B and T T. The rotation rate of the bottom (top) endwall disk is Ω B (Ω T ) , with ε≡(Ω T −Ω B )/Ω B ≪1 . Numerical solutions were obtained of the Navier–Stokes equations for large rotational Reynolds number and large Rayleigh number. Detailed flow and density fields are portrayed to be strongly dependent on the density inversion factor γ≡( T m− T B)/( T T− T B). When γ=0, the results are qualitatively similar to those of a usual Boussinesq fluid with a linear ( ρ– T) relationship. It is shown that a modified thermal wind relation prevails in the interior, in which the vertical shear of azimuthal velocity is balanced by the radial gradient of density. As γ increases, the overall strength of meridional circulation grows. The vertical profiles of azimuthal velocity are plotted as γ varies. The Ekman layer suction is intensified as γ increases. The behavior of average Nusselt number Nu at the bottom disk with varying γ is discussed and physical rationalizations are given.

Baroclinic Instability in an Euler Equations–Based Column Model: The Coexistence of a Deep Synoptic-Scale Mode and Shallow Subsynoptic-Scale Modes

Abstract The authors provide a detailed analysis of a shallow mode of subsynoptic-scale baroclinic instability by analyzing a one-dimensional column model in which the assumption of balance is applied to the basic-state flow but in which nongeostrophic unbalanced effects are retained in the description of the evolution of the perturbation under the Boussinesq approximation. This model is employed to analyze the stability of a meridionally confined mean state that is based upon hydrodynamic fields extracted from the central columns of a tropospheric cross section of the midlatitude jet stream. Numerical solutions are obtained at very high resolution through application of a sparse matrix method for solution of the corresponding cubic eigenvalue problem. Thereby the existence of a deep synoptic-scale mode and boundary-confined subsynoptic-scale modes is confirmed. The spatial scale and phase speed of these modes agree with those previously obtained on the basis of both nonseparable stability analysis and so...

Climatology of intrusions into the tropical upper troposphere

Regions of upper tropospheric equatorial westerly winds, observed over the Pacific and Atlantic Oceans during northern fall to spring, are important for extratropical‐tropical interactions. This paper focuses on one feature of these “westerly ducts” that has received relatively little attention to date: the occurrence of Rossby wave breaking events that transport tongues of extratropical air deep into the tropics, mix tropical and subtropical air, and can affect deep convection. A climatology of these “intrusion” events formed from 20 years of meteorological analyses shows a strong dependence on the basic‐state flow. Notably, intrusion events are found to occur almost exclusively within westerly ducts, with more events in the presence of stronger equatorial westerlies. It is also found that there is strong interannual variability in the frequency of Pacific events, with fewer events during the warm phases of ENSO (consistent with the changes in the basic flow). Since these intrusion events laterally mix trace constituents and have been linked to tropical convection, their spatial and temporal variability may cause related variability in the distribution of trace constituents and tropical convection.

Stationary Wave Accumulation and the Generation of Low-Frequency Variability on Zonally Varying Flows

Abstract A potent mechanism for the generation of low-frequency atmospheric variability on vortex basic states consisting of a single potential vorticity jump, or contour, separating two regions of uniform equivalent barotropic potential vorticity is described. Such basic states represent in a simple manner the potential vorticity distribution of the extratropical upper troposphere. It is shown that the group velocity for stationary waves propagating on such states can vanish for realistic zonal variations in the basic-state flow along the vortex edge, leading to local exponential disturbance growth due to the accumulation of wave action. Further, pseudo-energy stability criteria are derived that suggest that exponentially growing global disturbances are possible for sufficiently strong zonal variations in the flow along the vortex edge. These predictions are examined using linear and nonlinear initial value problem calculations. For wavenumber-1 flow variations in the basic-state zonal flow along the vor...

Numerical simulations of orographic gravity waves in flows which back with height

AbstractNumerical simulations are carried out to determine the steady‐state gravity‐wave structure above a circularly‐symmetric, bell‐shaped hill when the wind backs with height. Two types of idealized basic state flow are considered; one representing the advection of a uniform baroclinic shear flow, and the other being a flow of constant speed but with a wind vector that rotates uniformly in height. of particular interest is the nature of the critical level processes that must appear at all heights due to the three‐dimensionality of the wave field and the rotation of the wind vector. As suggested by linear theory, a critical level or asymptotic wake is found downwind of the hill at any height, where ‘downwind’ refers to the wind at that level only. For small hills (where the nondimensional mountain height ≤ unity), the simulated vertical momentum flux profiles are in very good agreement with linear hydrostatic wave theory if it is assumed that wave‐component critical‐level absorption is total (i.e. no wave transmission or reflections are permitted). the vertical momentum fluxes generated by a 1 km high hill show nonlinear enhancement by a factor of about 1.5. an interesting feature of the gravity‐wave field generated by this 1 km mountain is an asymptotic wake that is dominated by a single intense shear layer in which the Richardson number is order unity.

Laminar-Turbulent Transition in a Mach 8 Elliptic Cone Flow

To examine the influence of crossflow on transition in a hypersonic boundary layer, an experimental and computational study was made of a Mach 8 flow over a sharp-nosed elliptic cone of 2:1 cross section. Extensive flow visualization was carried out experimentally, including schlieren photography and surface oil-flow visualization. Mean pressure and heat flux were measured at the wall of the wind-tunnel model. For comparison with the experiments, a computation of the basic state flow was carried out using the parabolized Navier-Stokes equations. The basic state laminar flow was found to be relatively complex, with highly skewed velocity profiles and a pair of symmetric vortices on the top centerline of the cone. Transition in the elliptic cone flow was found to be significantly different than transition in hypersonic flow over planar and axisymmetric configurations, which is driven by the second mode instability. In the elliptic cone flow the transition front was nonuniform, with early transition near the top centerline and delayed transition near the leading edge. Rope waves were observed on both the leading edge and top centerline; unusual elongated streaks were observed on the top centerline

Wind-induced variability of ocean gyres

Stochastic wind forcing of ocean gyre circulations is examined using the ideas of generalized linear stability theory applied to the barotropic vorticity equation of a idealized ocean. The barotropic vorticity equation is linearized about a time-evolving basic state flow, and the spatial patterns of stochastic surface wind stress curl that are optimal for increasing the variability of the ocean are computed. The most disruptive pattern of stochastic forcing is found to be insensitive to: measures of variance, the optimization time, the temporal decorrelation time of the stochastic forcing, the time evolution of the basic state flow, the stability of the basic state flow, basin size, gyre symmetry, and the presence of bathymetry. In addition, the most disruptive pattern of wind stress curl is reminiscent of that which would be associated with individual large-scale weather systems in the atmosphere, and changes in the amplitude of the atmospheric teleconnection patterns. The response of a nonlinear model to stochastic forcing described by the optimal patterns is examined, and the dynamics of the response discussed.

Experimental and theoretical observations of elastic instabilities in eccentric cylinder flows: local versus global instability

A theoretical and experimental investigation of the stability of the viscoelastic flow of a Boger fluid between eccentric cylinders is presented. In our theoretical study, a local linear stability analysis for the flow of an Oldroyd-B fluid suggests that the flow is elastically unstable for all eccentricities. A global solution to the stability problem is obtained by a perturbation eigenvalue analysis, incorporating the azimuthal variation of the base state flow at the same order as the streamwise variation of the stability function. A comparison between the local and global stability predictions is made. Flow visualization experiments with a solution of high molecular weight polyisobutylene dissolved in a viscous solvent clearly show the transition from a purely azimuthal flow to a secondary toroidal flow. Comparison of these experimental results with the local linear stability theory shows good agreement between the measured and predicted critical conditions for the onset of the non-inertial cellular instability at small δ, where δ is the eccentricity made dimensionless with the average gap thickness. At higher eccentricities, experiment and local linear stability theory cease to agree. Evidence will be given that this disagreement is due to a global affect, i.e. the convection of stress not included the local theory. Specifically, it is suggested that convection of polymeric stresses in the base flow as well as in the disturbance flow can stabilize the instabilities found in this geometry. Finally, the discovery of a new localized purely elastic instability associated with the recirculation flow in the co-rotating eccentric cylinder geometry is presented.

Momentum fluxes due to three‐dimensional gravity‐waves: Implications for measurements and numerical modelling

AbstractA three‐dimensional wave‐action equation for linear internal gravity‐waves is derived. When the basic‐state flow does not turn with height, this equation can be used to derive the three‐dimensional version of a theorem of Eliassen and Palm. This states that, for steady flows in the absence of dissipation, the vertical flux of both horizontal components of momentum is independent of height. When the basic‐state flow exhibits turning with height, analysis of the wave‐action equation indicates that, in general, the wave field cannot be regarded as steady and the three‐dimensional Eliassen and Palm theorem does not apply. It is also shown that the wave‐action equation has serious implications for the interpretation of atmospheric measurements of the momentum flux: in order to make accurate measurements of the momentum flux arising from three‐dimensional orographically forced gravitywaves, it is necessary to average ρmu'w' (where ρm is the basic‐state density and u' and w' are the horizontal and vertical wave‐induced velocity‐perturbations respectively) on horizontal planes downstream of the orography, rather than along lines in the downstream direction (as has previously been done with aircraft measurements). Using a three‐dimensional linear numerical model, we demonstrate the importance of this in even the most simple idealized cases.

A Preliminary Investigation and Diagnosis of Weak Shear Summertime Convective Initiation for Extreme Southwest Alabama

The initiation and location of summer season convective activity, occurring between 1500 and 1800 UTC within a 100-km radius of the Mobile, Alabama, National Weather Service WSR-88D radar site, was examined on days when weak vertical wind shear environments existed. Data were collected during June and July of 1996 based on 1200 UTC analyses of upper-air charts, radar, and GOES-8 satellite imagery. Thirteen case days were selected for detailed analysis. The precise location of initiation was found to be a function of both the 0‐1-km base-state flow and the extent of the flow’s interaction with physiographic features and local sea- and bay-breeze circulations. The modified mean 1800 UTC sounding for case days was characterized by a well-mixed boundary layer, a deep moistadiabatic lapse rate, and an overall decrease in relative humidity with height. For all case days, the surface parcel was found to be the most unstable air parcel within the mixed layer. A distinct bimodal distribution was found to exist in the 0‐1-km base-state wind flow pattern with flow predominantly east-southeast or westsouthwest. Thunderstorms were observed to initiate in a ‘‘mirror image’’ pattern on either side of Mobile Bay and were focused near elevation peaks, along the sea breeze, and at or near the orthogonal intersection of the sea- and bay-breeze circulations on either side of the bay.

Effects of pressure solution and fluid migration on initiation of shear zones and faults

Constitutive relations for an isotropic poro-power-law fluid are proposed in which the effective viscosities in both shear and dilation have the same power-law dependence on the second invariant of the deviatoric stress alone, but the viscosity in dilation is 1/ ν times the viscosity in shear. The shear rate is otherwise proportional to the deviatoric stress and the dilation rate to an effective mean stress. The behavior may either involve Darcy flow of a pore fluid whose viscosity is much less than that of the solid matrix, or involve dissolution, diffusive transport, and precipitation of a soluble phase, as in pressure-solution. Linearized relations for small additional rate-of-deformation and stress superposed on a basic-state flow are obtained. These are used to treat the deformation due to a shallow, narrow indentation at the interface between a layer and an adjacent medium when both undergo bulk uniform layer-parallel shortening or extension. If the layer, the medium, or both, are nonlinear fluids with large stress exponent, shear-band like structures, extending from the indentation, and `reflecting' from any weak, slipping interface, occur in both the instantaneous velocity field and in the strain field. Since the materials considered have constant and uniform properties — e.g., they do not exhibit strain-softening — these features leave no imprint in the medium. They persist over mean strains of 10–20%, but are, like the indentation, ephemeral. It is hypothesized that localization due to an interfacial irregularity of this sort would produce bona fide shear bands if the material were strain-softening. The development of shear bands is enhanced if the adjacent medium has a large stress exponent, or if it is a poroviscous fluid with low resistance to dilation. In a poroviscous medium, dilation is concentrated in paired positive and negative lobes at the terminations of shear bands in the adjacent layer. The development of shear bands in a poroplastic layer is mildly suppressed, relative to that in an incompressible layer. Dilation is concentrated in paired loci at shear band terminations, with weaker, paired bands of positive and negative dilation on either side of the shear zone.