Background Density Gradient Research Articles

Charged magnetosonic solitons propagating in gentle density gradients and wave breaking

A class of nonrelativistic magnetosonic soliton, where the charge-separation electric field can be as large as the background magnetic field, is discovered in a strongly magnetized cold plasma, where the electron cyclotron frequency is much larger than the electron plasma frequency. We study how the Mach number of such a soliton is changed by the presence of a gentle background density gradient. An effective Hamiltonian for the soliton trajectory is derived, with which one can show that the soliton Mach number increases as the soliton travels to a background of increasing density, or equivalently, decreasing Alfven speed. The soliton can generally exchange its energy, momentum, and mass with the background plasmas. Our results also show that the soliton may undergo wave breaking at a finite background Alfven speed.

Internal waves and tides in shallow water

The well-known Garrett and Munk description of the internal wave spectrum synthesizes many observations into a spectral model that reproduces the general features of the mid-latitude, deep-ocean internal wave field. The general applicability of this ‘‘kinematic’’ spectral model is related to the dynamic balance of the internal wave field, but the model itself includes no dynamics and is meant to represent only the average or steady-state spectrum, away from the direct influence of sources, sinks, or boundaries. In shallow water, the kinematic model is typically not appropriate, since some or all of the simplifying assumptions about the wave field may be invalidated. Variable topography, strong tidal currents, fronts, and ice cover (at high latitudes) are the principal reasons for these complications, and result in an internal wave field which varies both spatially and temporally from the steady-state kinematic description. The most straightforward way to address the inadequacy of steady-state models for shallow water acoustics experiments is direct observation of the internal wave field at the site. Profiles sufficient to define the ‘‘mean’’ or background density gradient along with time series of temperature and horizontal velocity are the most common observations.

The effects of a vertical contraction on turbulence dynamics in a stably stratified fluid

We have experimentally studied the effects of mean strain on the evolution of stably stratified turbulence. Grid-generated turbulence ($Re_{\lambda \leqslant 25}$) in a stable linear mean background density gradient was passed through a two-dimensional contraction, contracting the stream only in the vertical direction. This induces an increase in stratification strength, which reduces the largest vertical overturning scales allowed by buoyancy forces. The mean strain through the contraction causes, on the other hand, stretching of streamwise vortices tending to increase the fluctuation levels of the transverse velocity components. This competition between buoyancy and vortex stretching dominates the turbulence dynamics inside and downstream of the contraction. Comparison between non-stratified and stratified experiments shows that the stratification significantly reduces the vertical velocity fluctuations. The vertical heat flux is initially enhanced through the contraction. Then, farther downstream the flux quickly reverses, leading to very strong restratification coinciding with an increase in the vertical velocity fluctuations. The vertical heat flux collapses much more rapidly than in the stratified case without an upstream contraction and the restratification intensity is also much stronger, showing values of normalized flux as strong as −0.55. Velocity spectra show that the revival of vertical velocity fluctuations, due to the strong restratification, starts at the very largest scales but is then subsequently transferred to smaller scales. The distance from the turbulence-generating grid to the entrance of the contraction is an important parameter which was varied in the experiments. The larger this distance, the larger the integral length scale can grow, approaching the limit set by buoyancy, before entering the contraction. The evolution of the various turbulence length scales is described. Two-point measurements of velocity and temperature transverse integral scales were also performed inside the contraction. The emergence of ‘zombie’ turbulence, for large buoyancy times, is in good quantitative agreement with the numerical simulations of Gerz & Yamazaki (1993) for stratification number larger than 1.

Boundary mixing in stratified reservoirs

We consider the steady flow driven by turbulent mixing in a benthic boundary layer along a sloping boundary in the general case of a non-uniform background density gradient. The velocity and density fields are decomposed into barotropic and baroclinic components, and a solution is obtained by taking an expansion in the small parameter A, the aspect ratio of the boundary layer defined as the thickness divided by the alongslope length. The flow in the boundary layer is governed by a balance between alongslope baroclinic and barotropic density fluxes. A number of flow regimes can exist, and we show that in the regimes relevant to lakes and reservoirs, the barotropic flow is divergent and drives an exchange flow between the boundary layer and the interior. This leads to changes in the interior density gradient which are significant when compared to field observations.

Resistive drift wave and interchange turbulence in a cylindrical plasma with magnetic and velocity shear

By solving numerically the two-field nonlinear model equations for the potential and density fluctuations in the presence of a density gradient, magnetic curvature with shear, and poloidal velocity shear, turbulent spectra and diffusion rates are studied. When the adiabatic parameter (Ωe/νe)(ρs2/R2)/(κρs) is small, a trend of a dual cascade, normal cascade of the density fluctuations, and an inverse cascade of the potential fluctuations, is seen in the wave number spectra, producing a large particle flux proportional to νe1/3. Here R is the major radius, ρs is the ion Larmor radius at the electron temperature, Ωe is the electron cyclotron frequency, νe is the electron ion collision frequency, and κ is an inverse scale length of the background density gradient. Parallel wave numbers are represented by 1/R. For large (Ωe/νe)(ρs2/R2)/(κρs), the electrons become adiabatic, with a significantly reduced particle flux proportional to νe. In the presence of an externally imposed radial electric field with a negative (positive) polarity, Er<0 (Er≳0), the poloidal velocity shear in the E×B drift motion suppresses (enhances) the fluctuation level in the growth phase; however, these effects practically disappear in the saturated state. The radial electric field produced by the inverse cascade due to the convective nonlinearity is also studied; however, its effect on the particle transport is mild.

Formation of a spatially ordered structure in a finite- beta edge plasma.

A three-dimensional inhomogeneous magnetohydrodynamic equation is investigated numerically. It is found that a spatially ordered structure is formed at a saturated energy level by the excitation of the convective cell modes due to the three-dimensional nonlinear mode coupling. It is shown that the saturated energy level and radial plasma flux are proportional to the magnitude of the background density gradient. The experimental observation of a self-organized coherent structure in a finite-..beta.. collisional edge plasma is expected.

Resonance absorption in inhomogeneous plasma with randomly rippled critical surface

The two-dimensional resonance absorption problem is considered for a wave incident obliquely upon an inhomogeneous plasma with a linear density gradient perturbed by random irregularities which are modulated in the direction perpendicular to both the plasma background density gradient and to the magnetic component of the incident wave. The net coefficient of plasma reflectivity is obtained in the form of a sum of the regular coefficient of reflectivity and the coefficient of anomalous reflectivity. The latter is due to conversion of coherent light into incoherent light by scattering off the random plasma density irregularities.

Internal waves around a body moving in a compressible density-stratified fluid

A body is started from rest and moves on an arbitrary path in an inviscid isothermal compressible atmosphere. The phase configuration of the internal waves and the gravity-modified acoustic waves which are generated by the body is studied using small amplitude wave theory. When the body moves at supersonic speeds and the background density gradient approaches zero, it is shown how the wave solutions approach the pure acoustic wave solutions of Lilleyet al.(1953).