Constant Density Gradient Research Articles

Estimating the In Situ Stratification via Remotely Sensed Internal Wave Speeds

Abstract This work tests a methodology for estimating the ocean stratification gradient using remotely sensed, high temporal and spatial resolution field measurements of internal wave propagation speeds. The internal wave (IW) speeds were calculated from IW tracks observed using a shore-based, X-band marine radar deployed at a field site on the south-central coast of California. An inverse model, based on the work of Kar and Guha, utilizes the linear internal wave dispersion relation, assuming a constant vertical density gradient is the basis for the inverse model. This allows the vertical gradient of density to be expressed as a function of the internal wave phase speed, local water depth, and a background average density. The inputs to the algorithm are the known cross-shore bathymetry, the background ocean density, and the remotely sensed cross-shore profiles of IW speed. The estimated density gradients are then compared to the synchronously measured vertical density profiles collected from an in situ instrument array. The results show a very good agreement offshore in deeper water (∼50–30 m) but more significant discrepancies in shallow water (20–10 m) closer to shore. In addition, a sensitivity analysis is conducted that relates errors in measured speeds to errors in the estimated density gradients. Significance Statement The propagation speed of ocean internal waves inherently depends on the vertical structure of the water density, which is termed stratification. In this work, we evaluate and test with real field observations a technique to infer the ocean density stratification from internal wave propagation speeds collected from remote sensing images. Such methods offer a way to monitor ocean stratification without the need for extensive in situ measurements.

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S = αN/f, where α, N, and f are the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases with S, asymptotically matching Lentz and Chapman for S < 1. When the solution conserves interior potential vorticity, the momentum transport is proportional to S2 for S < 1 and is in better agreement with numerical simulations.

Theoretical and Experimental Study of Joint Osmotic and Electroosmotic Water Transfer through a Cation-Exchange Membrane.

Using the previously developed cell model of a charged membrane and the principles of linear thermodynamics of irreversible processes (the Onsager approach), exact and approximate (in the case of an ideally selective membrane) analytical formulae for calculating the osmotic and electroosmotic permeability of the membrane in aqueous solutions of 1:1 electrolyte at constant electric current density and concentration gradient were suggested. The formulae have been successfully verified by our own experimental data for the extrusion cation-exchange membrane MF-4SC p.29 in NaCl solution up to concentrations of 3 M. The contribution of electroosmotic and osmotic water fluxes to the total water transport through the mentioned individual perfluorinated ion-exchange membrane under conditions close to the process of electrodialysis concentrating was experimentally estimated. The cases of co- and counter-directed osmotic and electroosmotic water fluxes are studied. A good correspondence between theoretical and experimental results was obtained, which made it possible to determine the physicochemical parameters of the electromembrane system (the diffusion coefficients of individual ions and the coefficient of equilibrium distribution of electrolyte molecules in the membrane matrix, the characteristic exchange capacity of the cell model). The achieved results make it possible to fully characterize existing and promising types of ion-exchange membranes based on the developed cell model of a charged membrane.

Three-Dimensional, Submicron Porous Electrode with a Density Gradient to Enhance Charge Carrier Transport.

Rapid charging capability is a requisite feature of lithium-ion batteries (LIBs). To overcome the capacity degradation from a steep Li-ion concentration gradient during the fast reaction, electrodes with tailored transport kinetics have been explored by managing the geometries. However, the traditional electrode fabrication process has great challenges in precisely controlling and implementing the desired pore networks and configuration of electrode materials. Herein, we demonstrate a density-graded composite electrode that arises from a three-dimensional current collector in which the porosity gradually decreases to 53.8% along the depth direction. The density-graded electrode effectively reduces energy loss at high charging rates by mitigating polarization. This electrode shows an outstanding capacity of 94.2 mAh g-1 at a fast current density of 59.7 C (20 A g-1), which is much higher than that of an electrode with a nearly constant density gradient (38.0 mAh g-1). Through these in-depth studies on the pore networks and their transport kinetics, we describe the design principle of rational electrode geometries for ultrafast charging LIBs.

The rotation of a sedimenting spheroidal particle in a linearly stratified fluid

We derive analytically the angular velocity of a spheroid, of an arbitrary aspect ratio$\kappa$, sedimenting in a linearly stratified fluid. The analysis demarcates regions in parameter space corresponding to broadside-on and edgewise settling in the limit$Re, Ri_v \ll 1$, where$Re = \rho _0UL/\mu$and$Ri_v =\gamma L^3\,g/\mu U$, the Reynolds and viscous Richardson numbers, respectively, are dimensionless measures of the importance of inertial and buoyancy forces relative to viscous ones. Here,$L$is the spheroid semi-major axis,$U$an appropriate settling velocity scale,$\mu$the fluid viscosity and$\gamma \ (>0)$the (constant) density gradient characterizing the stably stratified ambient, with the fluid density$\rho_0$taken to be a constant within the Boussinesq framework. A reciprocal theorem formulation identifies three contributions to the angular velocity: (1) an$O(Re)$inertial contribution that already exists in a homogeneous ambient, and orients the spheroid broadside-on; (2) an$O(Ri_v)$hydrostatic contribution due to the ambient stratification that also orients the spheroid broadside-on; and (3) a hydrodynamic contribution arising from the perturbation of the ambient stratification whose nature depends on$Pe$;$Pe = UL/D$being the Péclet number with$D$the diffusivity of the stratifying agent. For$Pe \ll 1$, this contribution is$O(Ri_v)$and orients prolate spheroids edgewise for all$\kappa \ (>1)$. For oblate spheroids, it changes sign across a critical aspect ratio$\kappa _c \approx 0.41$, orienting oblate spheroids with$\kappa _c < \kappa < 1$edgewise and those with$\kappa < \kappa _c$broadside-on. For$Pe \ll 1$, the hydrodynamic component is always smaller in magnitude than the hydrostatic one, so a sedimenting spheroid in this limit always orients broadside-on. For$Pe \gg 1$, the hydrodynamic contribution is dominant, being$O(Ri_v^{{2}/{3}}$) in the Stokes stratification regime characterized by$Re \ll Ri_v^{{1}/{3}}$, and orients the spheroid edgewise regardless of$\kappa$. Consideration of the inertial and large-$Pe$stratification-induced angular velocities leads to two critical curves which separate the broadside-on and edgewise settling regimes in the$Ri_v/Re^{{3}/{2}}$–$\kappa$plane, with the region between the curves corresponding to stable intermediate equilibrium orientations. The predictions for large$Pe$are broadly consistent with observations.

Microscopic theory of plasmon-enabled resonant terahertz detection in bilayer graphene

The electron gas hosted in a two-dimensional solid-state matrix, such as a quantum well or a two-dimensional van der Waals heterostructure, supports the propagation of plasma waves. Nonlinear interactions between plasma waves, due to charge conservation and current convection, generate a constant density gradient which can be detected as a dc potential signal at the boundaries of the system. This phenomenon is at the heart of a plasma-wave photodetection scheme which was first introduced by Dyakonov and Shur for electronic systems with a parabolic dispersion and then extended to the massless Dirac fermions in graphene. In this work, we develop the theory of plasma-wave photodetection in bilayer graphene, which has the peculiarity that the dispersion relation depends locally and dynamically on the intensity of the plasma wave. In our analysis, we show how quantum capacitance effects, arising from the local fluctuations of the electronic dispersion, modify the intensity of the photodetection signal. An external electrical bias, e.g. induced by top and bottom gates, can be used to control the strength of the quantum capacitance corrections, and thus the photoresponse.

Solutions for Subtidal Flow in Channels and Estuaries Under Different Integral Constraints

AbstractThis study builds on Huntley and Ryan (2018, https://doi.org/10.1002/2017JC012748) and related prior works on channels and estuaries by considering solutions for the same subtidal dynamics but with alternative integral flow constraints. Prior solutions do not have a truly two‐dimensional (2‐D) flow field, as axial changes in the axial flow are implied. Three constraint types are considered: the Constant case with spatially constant density gradients constrained with section‐integrated flow (as in prior works), Semi‐Variable case with a constant axial density gradient and laterally variable lateral density gradient constrained with depth‐integrated lateral flow, and Variable case with spatially variable density gradients in both directions constrained with depth‐integrated axial and lateral flows. The Semi‐Variable and Variable cases can produce solutions with truly 2‐D flow if the depth‐integrated lateral flow is set to zero everywhere. Differences among solutions are illustrated with idealized and realistic applications from Huntley and Ryan (2018, https://doi.org/10.1002/2017JC012748). For the idealized application, the Constant case and the Semi‐Variable case with 2‐D flow have clear differences in axial velocity and stark contrasts in lateral flow (and density gradients). For the Nares Strait application, the Variable case with observed depth‐averaged axial and lateral velocities is best able to represent the fastest observed down‐channel velocities, the weak reversed flow on one side of the channel, and the observed lateral flow structure. Overall, selecting different integral constraints on flow conspicuously changes the subtidal flow, opens up new possibilities for truly 2‐D flow solutions, and provides additional flexibility for representing observed conditions in realistic situations.

Open-boundary Hamiltonian adaptive resolution. From grand canonical to non-equilibrium molecular dynamics simulations.

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume, and chemical potential. In practice, following the Hamiltonian adaptive resolution strategy, the system is partitioned into a domain of interest and a reservoir of non-interacting, ideal gas particles. An external potential, applied only in the interfacial region, balances the excess chemical potential of the system. To ensure that the size of the reservoir is infinite, we introduce a particle insertion/deletion algorithm to control the density in the ideal gas region. We show that it is possible to study non-equilibrium phenomena with this open-boundary molecular dynamics method. To this aim, we consider a prototypical confined liquid under the influence of an external constant density gradient. The resulting pressure-driven flow across the atomistic system exhibits a velocity profile consistent with the corresponding solution of the Navier-Stokes equation. This method conserves, on average, linear momentum and closely resembles experimental conditions. Moreover, it can be used to study various direct and indirect out-of-equilibrium conditions in complex molecular systems.

Stably stratified exact coherent structures in shear flow: the effect of Prandtl number

We examine how known unstable equilibria of the Navier-Stokes equations in plane Couette flow adapt to the presence of an imposed stable density difference between the two boundaries for varying values of the Prandtl number $Pr$, the ratio of viscosity to density diffusivity, and fixed moderate Reynolds number, $Re=400$. In the two asymptotic limits $Pr \to 0$ and $Pr \to \infty$, it is found that such solutions exist at arbitrarily high bulk stratification but for different physical reasons. In the $Pr \to 0$ limit, density variations away from a constant stable density gradient become vanishingly small as diffusion of density dominates over advection, allowing equilibria to exist for bulk Richardson number $Ri_b \lesssim O(Re^{-2}Pr^{-1})$. Alternatively, at high Prandtl numbers, density becomes homogenised in the interior by the dominant advection which creates strongly stable stratified boundary layers that recede into the wall as $Pr\to\infty$. In this scenario, the density stratification and the flow essentially decouple, thereby mitigating the effect of increasing $Ri_b$. An asymptotic analysis is presented in the passive scalar regime $Ri_b \lesssim O(Re^{-2})$, which reveals $O(Pr^{-1/3})$-thick stratified boundary layers with $O(Pr^{-2/9})$-wide eruptions, giving rise to density fingers of $O(Pr^{-1/9})$ length and $O(Pr^{-4/9})$ width that invade an otherwise homogeneous interior. Finally, increasing $Re$ to $10^5$ in this regime reveals that interior stably stratified density layers can form away from the boundaries, separating well-mixed regions.

The unitary elasticity property in a monocentric city with negative exponential population density

The central prediction of the monocentric city model is that real estate prices, density of development, population density, and land rent decline with the distance from urban center. The spatial pattern follows a negative exponential under the conditions derived by Brueckner (1982) and McDonald and Kim (1987). Research has demonstrated that these exponential density gradients have flattened over time due to rising income and falling transportation costs. This paper identifies a heretofore unknown property in a monocentric city with negative exponential population density, the “unitary elasticity property (UEP).” If a city is characterized by a constant density gradient, even if the slope of that gradient is changing over time, the sum of the elasticity of central density and the elasticity of land area with respect to population change will be approximately equal to unity. When this new prediction is tested, it fits US cities fairly well. Further analysis demonstrates that topographic barriers and age of housing stock are the key factors explaining the deviation from the UEP.

Error analysis of supersonic air-to-air ejector schlieren pictures

The scope of this article is focused on general analysis of errors and uncertainties possibly arising from CFD-to-schlieren pictures matching. Analysis is based on classic analytical equations. These are firstly evaluated with the presumption of constant density gradient along the ray course. In other words, the deflection of light-ray caused by density gradient is negligible in compare to the cross size of constant gradient area. It is the aim of this work to determine, whether this presumption is applicable in case of supersonic air-to-air ejector. The colour and black and white schlieren pictures are carried out and compared to CFD results. Simulations had covered various eddy viscosities. Computed pressure gradients are transformed into deflection angles and further to ray displacement. Resulting computed light- ray deflection is matched to experimental results

Laboratory experiments on mountain‐induced rotors

AbstractIn this article we present some laboratory experiments on stratified flows over isolated obstacles which were aimed at the simulation of atmospheric rotors as induced by the interaction of mountain waves and the boundary layer. For this purpose we modified the classical tank experiments on mountain waves performed with constant density gradients by introducing an elevated density inversion above the obstacle height. This kind of inversion seems to favour very much the development of mountain‐induced rotors as was shown in recent numerical simulations. In fact our experimental set‐up was guided by the simulations of Vosper, which provided systematically the upstream conditions under which mountain rotors are expected. We were able to confirm the results from these numerical simulations over a wide range of parameters. Detailed analyses of flow structures for some selected cases, as obtained by particle image velocimeter analysis, are presented. Copyright © 2010 Royal Meteorological Society

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt numberScis 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale,Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale asRa1/2Sc1/2, and the Reynolds number would scale asRa1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with theRa1/2scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check theScscaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Flow Convergence Caused by a Salinity Minimum in a Tidal Channel

Residence times of dissolved substances and sedimentation rates in tidal channels are affected by residual (tidally averaged) circulation patterns. One influence on these circulation patterns is the longitudinal density gradient. In most estuaries the longitudinal density gradient typically maintains a constant direction. However, a junction of tidal channels can create a local reversal (change in sign) of the density gradient. This can occur due to a difference in the phase of tidal currents in each channel. In San Francisco Bay, the phasing of the currents at the junction of Mare Island Strait and Carquinez Strait produces a local salinity minimum in Mare Island Strait. At the location of a local salinity minimum the longitudinal density gradient reverses direction. This paper presents four numerical models that were used to investigate the circulation caused by the salinity minimum: (1) A simple one-dimensional (1D) finite difference model demonstrates that a local salinity minimum is advected into Mare Island Strait from the junction with Carquinez Strait during flood tide. (2) A three-dimensional (3D) hydrodynamic finite element model is used to compute the tidally averaged circulation in a channel that contains a salinity minimum (a change in the sign of the longitudinal density gradient) and compares that to a channel that contains a longitudinal density gradient in a constant direction. The tidally averaged circulation produced by the salinity minimum is characterized by converging flow at the bed and diverging flow at the surface, whereas the circulation produced by the constant direction gradient is characterized by converging flow at the bed and downstream surface currents. These velocity fields are used to drive both a particle tracking and a sediment transport model. (3) A particle tracking model demonstrates a 30 percent increase in the residence time of neutrally buoyant particles transported through the salinity minimum, as compared to transport through a constant direction density gradient. (4) A sediment transport model demonstrates increased deposition at the near-bed null point of the salinity minimum, as compared to the constant direction gradient null point. These results are corroborated by historically noted large sedimentation rates and a local maximum of selenium accumulation in clams at the null point in Mare Island Strait.

Mixing in a stably stratified medium by horizontal shear near vertical walls

Stratified environmental flows near boundaries can have a horizontal mean shear component, orthogonal to the vertical mean density gradient. Vertical transport, against the stabilizing force of gravity, is possible in such situations if three-dimensional turbulence is sustained by the mean shear. A model problem, water with a constant mean density gradient flowing in a channel between parallel vertical walls, is examined here using the technique of large eddy simulation (LES). It is found that, although the mean shear is horizontal, the fluctuating velocity field has significant vertical shear and horizontal vorticity, thereby causing small-scale vertical mixing of the density field. The vertical stirring is especially effective near the boundaries where the mean shear is large and, consequently, the gradient Richardson number is small. The mean stratification is systematically increased between cases in our study and, as expected, the buoyancy flux correspondingly decreases. Even so, horizontal mean shear is found to be more effective than the well-studied case of mean vertical shear in inducing vertical buoyancy transport as indicated by generally larger values of vertical eddy diffusivity and mixing efficiency.

On the inadequacies of Long's model for steady two-dimensional stratified flows

Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief. 1This aspect was dramatically evident in the experiments of Long (1955) and Davis (1969), in which the upstream effects become prominent when the lee waves began to break internally and become strongly turbulent. The wave breaking and turbulence created a body of fluid essentially at rest with respect to the obstacle which then acted to block the upstream flow in a source-like manner. On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 (1969)).

The influence of double-diffusive processes on the melting of ice in the Arctic Ocean: laboratory analogue experiments and their interpretation

This study has been motivated by two oceanographic observations: an increased rate of melting of sea ice in the Arctic Ocean, and the advance of an anomalously warm tongue of Atlantic water across the Arctic below the halocline over the last few decades. A series of laboratory experiments has been carried out in order to explore the physical principles underlying these phenomena, and the possibility that the extra heating at depth is responsible for the enhanced melting rate. A tank was filled with salt solution having various constant vertical density gradients. A block of ice one third of the length of the tank was floated on the surface at one end, and the rest of the surface and the walls of the tank were insulated. When no extra heat was supplied the melting rate (loss of weight of the ice in 1 h) systematically decreased as the stratification was changed from homogeneous fluid to increasingly large density gradients, while keeping the salinity of the solution in contact with the ice constant. An analogue of the intruding Atlantic water was produced by heating the lower portion of the vertical end wall at the end of the tank opposite to the ice end, keeping its temperature constant, and using the same range of salinity gradients as in the unheated experiments. Again the melting rate decreased as the density gradient was increased, but for low gradients it was larger than that in the unheated experiments. Above a certain intermediate gradient there was no significant difference in melting rate between the unheated and heated runs. The melting data were supplemented by photographs and vertical temperature and salinity profiles. The upward transfer of heat from the body of the fluid to melt the ice was clearly double-diffusive: overturning layers, separated by ‘diffusive’ interfaces, were visible on shadowgraphs, and the thickness of the layers decreased as the density gradient increased. The mean thickness of the layers through the depth of the tank also systematically decreased as the density gradient increased. With weak gradients an extra heat flux to the ice came from the intruding heated layer, but at large gradients this tongue of warm water at depth did not add to the flux near the surface. Though they were obtained in a simple, arbitrary and fixed geometry, we believe that the results of these experiments can be used as the basis for a better physical understanding of the melting rates of ice in the Arctic under various conditions.

Traversal times and charge confinement for spatially dependent effective masses within semiconductor heterostructures: the quantum potential approach

The classical traversal time is a well-defined functional of the carrier trajectory and in graded heterostructures acquires significant corrections due to the position-dependent effective mass. The quantum potential corrections for pure states and the corrections to quantum Monte Carlo for mixed states are derived using the Wigner formalism. Application to graded SiGe shows additional transport corrections, including enhanced charge confinement, which are of the same order as the conventional constant mass density gradient corrections.

Nonlinear Study of Stratified Fluid Through Porous Media

An analysis is presented to describe the effects of Darcy resistance, fluid inertia, and horizontal density gradient on a heterogeneous Boussinesq fluid saturated porous medium in the presence of the vertical gravitational field using the Forchheimer-Lapwood extended Darcy (DLF) equation. The fluid is initially at rest, and sets in motion owing to two forms of the initial density gradients. One is the constant initial horizontal density gradient and the other is the piecewise constant density gradient. In the case of the uniform initial horizontal density gradient a purely horizontal motion develops satisfying the nonlinear Forchheimer extended Darcy (FD) equation. Analytical solution of this equation is obtained and limiting solutions valid for the Darcy regime and for a nonviscous fluid in the absence of porous media are derived. A measure of the stability of the flow is discussed briefly using the Richardson number. A comparison between the nature of solutions satisfying the nonlinear and linear initial value problems is made. We found that the vertical density gradient varies continuously both with space z and time t but the horizontal density gradient remains unchanged. In the case of a piecewise constant initial density gradient with continuous distribution of density, stream function formulation is used and the solutions are obtained using time-series analysis. In this case the solution shows crowding of the density profiles in the lower half of the channel, reflecting an increase in density gradient and incipient frontogenesis there, because of the increase in circulation of the flow due to the piecewise initial density gradient. Copyright © 2001 by Begell House, Inc.

K-1706 物質拡散に関する分子動力学的研究(J08-2 熱流体現象の原子・分子論的アプローチ(2))(J08 熱流体現象の原子・分子論的アプローチ)

The mutual diffusion under the condition of a constant density gradient of two kinds of Lennard-Jonse (L-J) liquids is studied by means of two dimensional molecular dynamics method. It is found that the diffusion velocity depends on the number density. In order to know the driving force for the mutual diffusion, the resultant force acting on particles in a region is divided into four kinds of forces. It is found that the diffusion velocity is affected strongly by two resultant forces out of four forces. The average values of resultant force with respect to the number of particles has a remarkable relation with the diffusion velocity.