Reformulation of the parabolic approximation for waves in stratified moving media
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Mcaninch, Gerry L.↗
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Acoustic propagation in a thermally stratified atmosphere
Acoustic propagation in an atmosphere with a specific form of a temperature profile has been investigated by analytical means. The temperature profile used is representative of an actual atmospheric profile and contains three free parameters. Both lapse and inversion cases have been considered. Although ray solutions have been considered, the primary emphasis has been on solutions of the acoustic wave equation with point source where the sound speed varies with height above the ground corresponding to the assumed temperature profile. The method used to obtain the solution of the wave equation is based on Hankel transformation of the wave equation, approximate solution of the transformed equation for wavelength small compared to the scale of the temperature (or sound speed) profile, and approximate or numerical inversion of the Hankel transformed solution. The solution displays the characteristics found in experimental data but extensive comparison between the models and experimental data has not been carried out.
Vanmoorhem, W. K.↗
On the prediction of the behavior of the velocity, temperature and humidity fields above a thermally stratified air-water interface
A turbulent kinetic energy-dissipation (k-epsilon) model is employed to numerically simulate the behavior of the mean velocity, temperature and humidity fields, along with such second-order statistics as Reynolds stresses, turbulent heat and mass transfer correlation, and bulk transfer coefficients in the boundary layer above wind-generated laboratory waves. The k and epsilon equations have been properly modified to account for thermal stratification, the presence of free surface, and favorable pressure gradient effects. Predictions are compared with available data.
Papadimitrakis, Yiannis A.↗
Stratified charge rotary engine - Internal flow studies at the MSU engine research laboratory
High-speed visualization and laser Doppler velocimetry (LDV) systems consisting of a 40-watt copper vapor laser, mirrors, cylindrical lenses, a high speed camera, a synchronization timing system, and a particle generator were developed for the study of the fuel spray-air mixing flow characteristics within the combustion chamber of a motored rotary engine. The laser beam is focused down to a sheet approximately 1 mm thick, passing through the combustion chamber and illuminates smoke particles entrained in the intake air. The light scattered off the particles is recorded by a high speed rotating prism camera. Movies are made showing the air flow within the combustion chamber. The results of a movie showing the development of a high-speed (100 Hz) high-pressure (68.94 MPa, 10,000 psi) fuel jet are also discussed. The visualization system is synchronized so that a pulse generated by the camera triggers the laser's thyratron.
Hamady, F.↗
The stability of a compressible stratified shear layer
The stability of a shear layer under the effect of gravity is investigated using the compressible magnetohydrodynamic (MHD) equations, including an effective gravity term to represent the curvature effects of the flow and magnetic field line geometry. A general eigenmode equation is derived for a two-dimensional MHD fluid, and an energy-principle analysis to explain the effect of compressibility on the critical Richardson number is presented. For the case of a hyperbolic tangent shear flow and exponential density profile, it was found that, in the Boussinesq approximation, the compressibility raises the critical Richardson number from 1/4 to as much as 1/2, with the exact value depending on the value of the magnetic field at infinity. Under approximation of a strong asymptotic magnetic field, without invoking the Boussinesq approximation, it is shown both analytically and numerically that the density gradient terms cause the shear instability to be dispersive. The long-wavelength stability boundary for the Richardson number J = 0 is characterized by a normalized phase velocity c =
Wang, Z.↗
Numerical investigation of the spreading of self-excited stratified jets
The structure and evolution of self-excited subsonic periodic arrays of jets of constant and variable density are studied using spectral-element direct numerical simulations. The governing equation of motion is presented, and a method based on spectral element discretizations appropriate for simulating arbitrarily complex geometry jets and large density variations for subsonic flows is developed. Variable density fields are found to be more unstable than the corresponding uniform density fields with much higher rms values; as a result, their spreading is also considerably larger. There is a dramatic increase in spreading after a few pairings occur. Findings presented for low and high side-momentum flux reveal a shifting of the origin of instability from the near-field to the far-field, respectively, and suggest possible routes of stabilization.
Batcho, P. F.↗
Post-glacial relaxation of a viscously stratified compressible mantle
The postglacial relaxation phenomenon of a viscously compressible nonself-gravitating spherical-shell model is investigated. Analytical solutions to an exponentially depth-dependent viscosity are developed with various types of compressible density models such as those with an exponential dependence of the radius and an algebraic-root dependence of the radius. The solutions of a viscously compressible multilayered model with constant thermodynamic properties and viscosity are developed by the propagator matrix method. The results show that inferences of deep mantle viscosity from postglacial rebound would be hampered by mantle compressibility for long-wavelength harmonics because of the smaller excitation of compressible eigenfunctions in the lower mantle. The relaxation times and velocity fields are more sensitive to higher viscosity contrast for the exponentially varying viscosity than for models with discrete jumps in the viscosity structure.
Wu, J.↗
Numerical simulations of thermal instabilities in stratified gases. II - Exploration of the parameter space
The temporal evolution of density perturbations in an initially hydrostatic isothermal atmosphere consisting of an optically thin radiating compressible plasma is studied. Numerical techniques are used to describe the nonlinear evolution of the perturbations, and the relative equilibrium between dynamic and thermal instabilities as governed by three independent control parameters are examined, namely, the initial density contrast of the perturbation, the ratio of the local buoyancy oscillation period to the local radiative cooling time, and the ratio of the perturbation radius to the local scaleheight. Four orders of magnitude of initial density contrasts and ratios of buoyancy and cooling times, and one order of magnitude of the bubble dimensions are explored. Well-defined oscillations were found to occur in a limited parameter range, and thermal instability to occur even within secondary condensations deriving from the bubble fragmentation.
Reale, F.↗
Nonlinear stratified flow over localized topographic obstacles on Mars
The current dynamical influence of the Martian atmosphere on the surface is clearly revealed by dark surface albedo features which are associated with localized topographic relief and were described in detail and classified as Type I(d) wind streaks. The contrast of the streaks diminishes or disappears during the global dust storms, and the streaks are observed to quickly reform after the termination of the storms; the streaks remain stable after L(sub S) = 0 deg until the next dust storm. These observations, together with the ragged edges of the streaks, were used to infer that the dark streaks are formed by the removal of bright dust from a darker substrate.
Magalhaes, J. A.↗
Dynamically stratified Monte Carlo forecasting
A new method for performing Monte Carlo forecasts is introduced. The method, called dynamic stratification, selects initial perturbations based on a stratification of the error distribution. A simple implementation is presented in which the error distribution used for the stratification is estimated from a linear model derived from a large ensemble of 12-h forecasts with the full dynamic model. The stratification thus obtained is used to choose a small subsample of initial states with which to perform the dynamical Monte Carlo forecasts. Several test cases are studied using a simple two-level general circulation model with uncertain initial conditions. It is found that the method provides substantial reductions in the sampling error of the forecast mean and variance when compared to the more traditional approach of choosing the initial perturbations at random. The degree of improvement, however, is sensitive to the nature of the initial error distribution and to the base state. In practice the method may be viable only if the computational burden involved in obtaining an adequate estimate of the error distribution is shared with the data-assimilation procedure.
Schubert, Siegfried↗
On the use of forbidden lines as density diagnostics in stratified media
The influence of density and ionization gradients on the observed density-sensitive forbidden-line ratios from a spatially unresolved source is investigated by means of a simple model. In order to assess the role played by the source geometry, both spherical and cylindrical systems where all spatial dependences are given by power laws are considered. It is shown that the present ratios can be used to estimate the spatial dependence of density and ionization as well as the source geometry.
Safier, Pedro N.↗
Dynamo action in stratified convection with overshoot
Results are presented from direct simulations of turbulent compressible hydromagnetic convection above a stable overshoot layer. Spontaneous dynamo action occurs followed by saturation, with most of the generated magnetic field appearing as coherent flux tubes in the vicinity of strong downdrafts, where both the generation and destruction of magnetic field is most vigorous. Whether or not this field is amplified depends on the sizes of the magnetic Reynolds and magnetic Prandtl numbers. Joule dissipation is balanced mainly by the work done against the magnetic curvature force. It is this curvature force which is also responsible for the saturation of the dynamo.
Nordlund, Ake↗
Sound Propagation into the Shadow Zone in a Temperature-stratified Atmosphere Above a Plane Boundary
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Pridmore-Brown, David C↗
On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations
Asymptotic regimes of geophysical dynamics are described for different Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit, of strong stratification in the Burger number of order one situation as well as in the asymptotic regime of strong stratification and weak rotation. It is shown that in both regimes horizontally averaged buoyancy variable is an adiabatic invariant for the full Boussinesq system. Spectral phase shift corrections to the buoyancy time scale associated with vertical shearing of this invariant are deduced. Statistical dephasing effects induced by turbulent processes on inertial-gravity waves are evidenced. The 'split' of the energy transfer of the vortical and the wave components is established in the Craya-Herring cyclic basis. As the Burger number increases from zero to infinity, we demonstrate gradual unfreezing of energy cascades for ageostrophic dynamics. The energy spectrum and the anisotropic spectral eddy viscosity are deduced with an explicit dependence on the anisotropic rotation/stratification time scale which depends on the vertical aspect ratio parameter. Intermediate asymptotic regime corresponding to strong stratification and weak rotation is analyzed where the effects of weak rotation are accounted for by an asymptotic expansion with full control (saturation) of vertical shearing. The regularizing effect of weak rotation differs from regularizations based on vertical viscosity. Two scalar prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure ) are obtained.
Babin, A.↗
Hydrostatic Adjustment in Vertically Stratified Atmospheres
Hydrostatic adjustment due to diabatic heat in two nonisothermal atmospheres is examined. In the first case the temperature stratification is continuous; in the second case the atmosphere is composed of a warm, isothermal troposphere and a colder, isothermal semi-infinitely deep stratosphere.In both cases hydrostatic adjustment, to a good approximation, follows the pattern found in the Lamb problem (semi-infinitely deep. isothermal atmosphere): Initially we have acoustic waves with the kinetic energy increasing or decreasing at the expense of available elastic energy. After this initial period the acoustic waves evolve into acoustic-gravity waves with the kinetic, available potential and available elastic energies interacting with each other. Relaxation to hydrostatic balance occurs within a few oscillations. Stratification in an atmosphere with a continuous temperature profile affects primarily the shape and amplitude of the disturbances. In the two-layer atmosphere, a certain amount of energy is trapped in the tropospheric waveguide as disturbances reflect off the tropopause and back into the troposphere. With each internal reflection a portion of this trapped energy escapes and radiates to infinity.
Duffy, Dean G.↗
Wake Vortex Prediction Models for Decay and Transport Within Stratified Environments
This paper proposes two simple models to predict vortex transport and decay. The models are determined empirically from results of three-dimensional large eddy simulations, and are applicable to wake vortices out of ground effect and not subjected to environmental winds. The results, from the large eddy simulations assume a range of ambient turbulence and stratification levels. The models and the results from the large eddy simulations support the hypothesis that the decay of the vortex hazard is decoupled from its change in descent rate.
Switzer, George F.↗
Validation of Radio Frequency Telemetry Concept in the Presence of Biological Tissue-Like Stratified Media
In this paper we discuss a novel radio frequency (RF) telemetry concept for biomedical applications. The concept consists of a miniaturized spiral inductor/antenna for bio-MEMS sensors and an external pick-up antenna integrated into a handheld device. The measured relative signal strength in the presence of biological phantoms ranged from 5.9 to 7.5 dB for antenna separations of 5 and 10 cm. These relative signal strengths are easily measurable, therefore validating the RF telemetry concept for biomedical applications.
Miranda, Felix A.↗
Global instability of internal waves in low-mass, stably stratified protoplanetary disks
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solar system origins planet formation↗