Background Density Profile Research Articles

Baroclinic instability and eddy tracer transport across sloping bottom topography: How well does a modified Eady model do in primitive equation simulations?

Theoretical tracer diffusivities given by linear Eady theory that accounts for non-zero bottom slopes are compared with diffusivities diagnosed from primitive equation simulations of thermally forced flows over an idealized continental slope. The behavior is discussed in terms of a bottom slope parameter δ ¯ , the ratio of the bottom slope to an expression roughly representing the depth-averaged isopycnal slope. The theoretical diffusivities, scaled by the total thermal wind shear and the first internal deformation radius, agree qualitatively with diagnosed diffusivities for δ ¯ ≲ 0 , the parameter regime appropriate for buoyant boundary currents flowing over continental slopes. But whereas Eady theory would suggest maximum diffusivities for moderate positive slopes, δ ¯ ≃ 0.5 , the diagnosed diffusivities are highest for δ ¯ = 0 , i.e. for flat bottoms. Finally, whereas Eady diffusivities should drop to zero for δ ¯ ≳ 1 , i.e. when the bottom becomes steeper than the mean isopycnal slope, the diagnosed diffusivities do not. Similarities and differences are discussed in terms of more general linear stability theory applied to the background density profile over the central slope region. It is found that interior potential vorticity gradients, neglected by Eady theory, both cause significant modification to the Eady mode and also enable non-Eady instabilities that are responsible for the non-zero diffusivities for δ ¯ ≳ 1 . Furthermore, estimates of kinetic energy spectral fluxes suggest that an inverse kinetic energy cascade is present, and it is speculated that this is responsible for the diagnosed maximum diffusivity for flat bottoms.

Available potential energy diagnosis in a direct numerical simulation of rotating stratified turbulence

Review of three studies devoted to the available potential energy (APE) leads to the proposal of a diagnosis for APE, well-suited for rotating stratified flows within the primitive equations (PE) framework in which anharmonic effects (due to large vertical displacements of isopycnals) are permitted. The chosen diagnosis is based on the APE definition of Holliday & McIntyre (J. Fluid Mech., vol. 107, 1981, pp. 221–225) and uses the background stratification of Winters et al. (J. Fluid Mech., vol. 289, 1995, pp. 115–128). Subsequent evaluation of the APE in a PE direct simulation (1/100°, 200 levels) of oceanic mesoscale turbulence indicates that anharmonic effects are significant. These effects are due to large vertical displacements of the isopycnals and the curvature of the background density profile.

Transition from drift to interchange instabilities in an open magnetic field line configuration

The transition from a regime dominated by drift instabilities to a regime dominated by pure interchange instabilities is investigated and characterized in the simple magnetized toroidal device TORPEX [TORoidal Plasma EXperiment, A. Fasoli et al., Phys. of Plasmas 13, 055906 (2006)]. The magnetic field lines are helical, with a dominant toroidal component and a smaller vertical component. Instabilities with a drift character are observed in the favorable curvature region, on the high field side with respect to the maximum of the background density profile. For a limited range of values of the vertical field they coexist with interchange instabilities in the unfavorable curvature region, on the plasma low field side. With increasing vertical magnetic field magnitude, a gradual transition between the two regimes is observed on the low field side, controlled by the value of the field line connection length. The observed transition follows the predictions of a two-fluid linear model.

Internal wave tunnelling through non‐uniformly stratified shear flow

We examine the transmission of internal gravity waves through a non‐uniformly stratified fluid with vertically varying background shear. To quantify wave transmission we show that the appropriate measure is the ratio of the flux of transmitted to incident pseudoenergy, T. We derive an analytic prediction of T for the transmission of waves through a piecewise‐linear shear flow in two cases. In both, the fluid is unstratified over the depth of the shear and uniformly stratified elsewhere. In one study, the density profile is continuous. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number, Ri, becomes large. In the limit of an infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland and Yewchuk (2004). In weak shear, incident waves can transmit weakly, even if the phase speed matches the flow speed within the shear layer (a critical level). However, no transmission occurs when the phase speed of incident waves exactly matches the flow speed on the opposite flank of the shear. In strong shear, with Ri ⋍ 1, a transmission peak occurs where the incident wavenumber and frequency are close to, but different from, those associated with unstable modes. In a second study, the background density profile is discontinuous and representative of a well‐mixed patch within a once uniformly stratified fluid. In this case, no transmission occurs for incident waves with phase speed matching the speed of the flow within the shear layer. However, a transmission spike occurs if the incident waves are resonant with interfacial waves that flank the shear.

Internal Wave Tunnelling Through Non-uniformly Stratified Shear Flow

Abstract We examine the transmission of internal gravity waves through a non‐uniformly stratified fluid with vertically varying background shear. To quantify wave transmission we show that the appropriate measure is the ratio of the flux of transmitted to incident pseudoenergy, T. We derive an analytic prediction of T for the transmission of waves through a piecewise‐linear shear flow in two cases. In both, the fluid is unstratified over the depth of the shear and uniformly stratified elsewhere. In one study, the density profile is continuous. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number, Ri, becomes large. In the limit of an infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland and Yewchuk (2004). In weak shear, incident waves can transmit weakly, even if the phase speed matches the flow speed within the shear layer (a critical level). However, no transmission occurs when the phase speed of incident waves exactly matches the flow speed on the opposite flank of the shear. In strong shear, with Ri ⋍ 1, a transmission peak occurs where the incident wavenumber and frequency are close to, but different from, those associated with unstable modes. In a second study, the background density profile is discontinuous and representative of a well‐mixed patch within a once uniformly stratified fluid. In this case, no transmission occurs for incident waves with phase speed matching the speed of the flow within the shear layer. However, a transmission spike occurs if the incident waves are resonant with interfacial waves that flank the shear.

Gyrofluid Turbulence Modelling of the Linear Device VINETA

The two-moment version of the three-dimensional gyrofluid code GEM3 has been adapted for the simulation of drift-wave turbulence in the linear device VINETA [1]. In the modified GEM3 code gyrofluid equations for the density and parallel velocity of electrons and ions are solved for the cylindrical annulus. Computations are done for the electrostatic case using an exponential background density profile observed experimentally. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonuniqueness of Conjugate Flows

The problem of weakly stratified flows conjugate to a uniform flow with a prescribed density distribution over its depth is considered. The sufficient condition of existence and uniqueness of the conjugate flow is obtained for a smooth generic background density profile. If the condition obtained is violated, it is shown that the number of branches of conjugate flows and their asymptotic behavior near the bifurcation point are determined by the fine structure of stratification.

Classical mode conversion description of neutrino oscillations in dense magnetized plasmas

Neutrino oscillations in dense magnetized plasmas, similar to those found in supernovas, are described. The adopted model is similar to the classical mode conversion problems examined in fluid dynamics and plasma physics. This approach allows for the derivation of analytical results for the neutrino conversion probability for different combinations of background density profile and magnetic field profile.

Imaging radar observations and nonlocal theory of large-scale plasma waves in the equatorial electrojet

Abstract. Large-scale (l ~ 1 km) waves in the daytime and night-time equatorial electrojet are studied using coherent scatter radar data from Jicamarca. Images of plasma irregularities within the main beam of the radar are formed using interferometry with multiple baselines. These images are analyzed according to nonlocal gradient drift instability theory and are also compared to nonlinear computer simulations carried out recently by Ronchi et al. (1991) and Hu and Bhattacharjee (1999). In the daytime, the large-scale waves assume a non-steady dynamical equilibrium state characterized by the straining and destruction of the waves by shear and diffusion followed by spontaneous regeneration as predicted by Ronchi et al. (1991). At night, when steep plasma density gradients emerge, slowly propagating large-scale vertically extended waves predominate. Eikonal analysis suggests that these waves are trapped (absolutely unstable) or are nearly trapped (convectively unstable) and are able to tunnel between altitude regions which are locally unstable. Intermediate-scale waves are mainly transient (convectively stable) but can become absolutely unstable in narrow altitude bands determined by the background density profile. These characteristics are mainly consistent with the simulations presented by Hu and Bhattacharjee (1999). A new class of large-scale primary waves is found to occur along bands that sweep westward and downward from high altitudes through the E-region at twilight.Key words. Ionosphere (equatorial ionosphere; ionospheric irregularities; plasma waves and instabilities)

Propagation of electromagnetically generated wake fields in inhomogeneous magnetized plasmas

Generation of wake fields by a short electromagnetic pulse in a plasma with an inhomogeneous background magnetic field and density profile is considered, and a wave equation is derived. Transmission and reflection coefficients are calculated in a medium with sharp discontinuities. Particular attention is focused on examples where the longitudinal part of the electromagnetic field is amplified for the transmitted wave. Furthermore, it is noted that the wake field can propagate out of the plasma and thereby provide information about the electron density profile. A method for reconstructing the background density profile from a measured wake field spectrum is proposed and a numerical example is given.

Effect of poloidal shear flow on local flattening of density profile due to nonlinear resistive interchange mode

When resistive interchange modes (RIMs) are unstable in aStellarator/Heliotron device, they may change the pressure profile even forβ values lower than the ideal β limit. The nonlinear RIM withn/m = 2/3 modifies the density profile in the vicinity of the resonantsurface with ι = 2/3 easily under the assumption of constanttemperature. Here m(n) is a poloidal (toroidal) mode number andι is a rotational transform. Also poloidal shear flow is generatedthere, which limits the region of density profile modificationsubstantially. The sign of the density gradient becomes positive at theresonant surface. A quasi-stationary profile is obtained forlow-collisional plasmas. When the collision frequency is high, localhumps are produced in the background density profile, and they have atendency to move to the resonant surface. It is also shown that thedensity profile including humps is correlated with the poloidal velocityshear profile. Here the typical shearing rate of the poloidal flow at thesaturated state exceeds the linear growth rate of the (m,n) = (3,2) mode.

A Correction to the Baroclinic Pressure Gradient Term in the Princeton Ocean Model

Abstract An error in the calculation of the baroclinic pressure gradient term in the Princeton Ocean Model (POM) was identified while modeling the M2 tidal current near its critical latitude in the southern Weddell Sea. The error arises from the present calculation of density, which involves the subtraction of a background density profile from the density field calculated at each internal time step. The small displacement of sigma surface depths relative to the surface, as surface elevation changes, causes a slight error in the calculation of the vertical and horizontal gradients of potential density. The error is largest at the seabed over rapidly changing bathymetry such as the continental slope. The baroclinic pressure gradient error is typically much smaller than the Coriolis term in the momentum equations and, therefore, usually unimportant. Close to the critical latitude, however, near-resonance between the error and Coriolis terms can cause an energetic and spatially complex spurious inertial mode ...

Internal gravity waves: Analysis using the periodic, inverse scattering transform

Abstract. The discrete periodic inverse scattering transform (DPIST) has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV) equation - (1) linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2) nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s) * (ε/μ2), where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.

Wave propagation in one-dimensional inhomogeneous random media with an application to lower hybrid waves in fusion plasmas

Wave propagation in a one-dimensional stratified medium, whose physical parameters are subject to random fluctuations, is considered. The complex-valued reflection coefficient obeys, as a function of the slab width L, a stochastic Riccati differential equation, associated with an initial-value problem. Using this fact, solving first the boundary-value problem satisfied by the field on [0,L] is avoided. The reflection coefficient can be computed numerically by a Monte-Carlo-type procedure by the generation of suitable sequences of random numbers aimed at constructing realizations of the stochastic processes that enter the refractive index. An application is made to the propagation of ‘‘lower hybrid waves’’ in thermonuclear (fusion) plasmas for realistic models of the deterministic density profile using available experimental data for the statistics of the random fluctuations. Several functional forms of the density profile are considered, and the relevant physical approximations are discussed. This work generalizes a previous analysis that did not include the inhomogeneous background density profile. Results show that the reflected power is a sensitive function of the form of the density profile.

Statistical ray tracing in plasmas with random density fluctuations.

The propagation of light rays in a plasma is considered for small density fluctuations superimposed upon a given background density profile. The lowest-order angular spreading, focusing, and drift effects are calculated in the geometrical-optics limit using a statistical random-walk approach. This method is an economical semianalytic alternative to a purely numerical ray-trace approach and is of particular but not exclusive interest in describing the propagation of laser light in laser-produced plasmas. The model is applied to a simple fluctuation spectrum characterized by an rms amplitude and by a correlation length. Results are presented for the evolution of the intensity profiles of beams incident on a plane-parallel linear-profile plasma slab as a function of the angle of incidence. Comparisons of these results with numerical Monte Carlo ray-trace solutions show good agreement. Density fluctuations as small as a few percent of the critical density can, for example, produce significant angular broadening in the specularly reflected beam and reduce the sensitivity of the absorption fraction to the incidence angle, particularly near normal incidence.

Selective Withdrawal Through A Point Sink And Pycnocline Formation In A Linearly Stratified Flow

Experiments were carried out on selective withdrawal through a point sink in the endwall of a rectangular tank containing a linearly stratified fluid. The results indicate that the withdrawal layer half thickness d may be expressed as d/(Q/N)1/3 = 1.02 (standard error .02), where Q is discharge through the point sink in the endwall and N is the buoyancy frequency of the fluid. This result is restricted to the inertial regime for which Q/νL>l, where ν is kinematic viscosity and L the tank length. An attempt to account for asymmetry in the withdrawal layer and in the evolving background density profile did not significantly reduce experimental scatter. The development of a sharp pycnocline in the initially linear stratification can be predicted using a kinematic approach. A solution is presented of the equations of conservation of mass and volume for an incompressible, nondiffusive fluid, using steady-state empirical relations between d, Q, N, and the velocity field in lieu of the momentum equations. Predictions based on this solution are compared with experimental results, with generally good agreement.

Generalisation of the virial theorem and related theorems for jellia with arbitrary background densities and application to special geometriees and profiles. I. General theory and application to the jellium sphere and the semi-infinite electron gas

Virial and Budd-Vannimenus theorems (1973) are generalised and derived unitarily and simplified: for a jellium with an arbitrary background density rho (r) four different but equivalent expressions of the pressure term in the virial theorem are found, containing the total energy Erho , the electrostatic potential phi rho (r), the electric field Erho (r) and the electron density nrho (r), respectively. The expression with phi rho (r) generalises the Budd-Vannimenus theorem for arbitrary geometries and background density profiles and the other expressions with Erho (r) and nrho (r) give electrostatically equivalent formulations of the Budd-Vannimenus theorem. The jellium sphere is studied especially for the limiting case of infinite radius R to infinity , yielding bulk and surface theorems. The latter involves a correction of a theorem given by Vannimenus and Budd, arising from the necessity to start with a finite system for a consistent treatment of the pressure. Also an expression given by Heinrichs (1979) is corrected.

Electric field limitation of drift dissipative wave generation in ionospheric structures

Coupled background electric fields and density profiles exist across the sides of striations and other elongated ionospheric structures. The presence of the electric field profoundly modifies the behavior of drift dissipative waves by shifting the location of the waves away from the point where the relative density gradient is a maximum, consequently inhibiting the growth of the waves.