The stability of a stratified shear layer

Abstract

The stability of a stratified shear layer is investigated using an exponential density profile and a laminar shear flow with a continuous velocity distribution. It is shown that an exact stability boundary can be obtained for an inhomogeneous inviscid fluid under the action of gravity without the need to impose the Boussinesq approximation. The stability boundary is given by J=k̂2(1−β2/4−k̂2), where β is the ratio of the velocity and density gradient scale sizes, J is the Richardson number, and k̂ is the perpendicular wavenumber normalized to the velocity gradient scale size; this reduces to the stability boundary derived by Drazin [J. Fluid Mech. 4, 214 (1958)] in the limit β=0. The solution allows for c=β/2, where c is the normalized phase velocity.

Collisional shear instability in the equatorial F region ionosphere

“…and and are then identical to and derived by Keskinen et al [1988] for the particular density and velocity profiles they chose to analyze but are otherwise somewhat more general. Upon combining with , we arrive at the following dispersion relation: In the collisionless limit where the plasma density is also taken to be constant, this reduces to which is the standard dispersion relation for the transverse Kelvin Helmholtz instability [e.g., Mikhailovskii , 1974; Satyanarayana et al , 1987a]. This instability has been studied exhaustively and is known to emerge in regions where has a vanishing second derivative.…”

“…which is the standard dispersion relation for the transverse Kelvin Helmholtz instability [e.g., Mikhailovskii, 1974;Satyanarayana et al, 1987a]. This instability has been studied exhaustively and is known to emerge in regions where v has a vanishing second derivative.…”

Nonlinear saturation of Rayleigh-Taylor instability and generation of shear flow in equatorial spread-F plasma

“…Most of the research for nonlinear RT mode in the ionosphere has been restricted to collisional domain, although it has been shown that inertial effects are important in the high-latitude ionosphere. The influence of transverse velocity shear on Rayleigh-Taylor instability has been well investigated in the linear theory by various authors, especially, Guzdar, Satyanarayana, and their collaborators (Guzdar et al, 1982;Satyanarayana et al, 1987). They have found that a sheared velocity flow can substantially reduce the growth rate of a Rayleigh-Taylor instability in the short wavelength regime.…”

“…Linear and nonlinear studies on the RT instability have been carried out in recent years by Flaherty, Finn, and others (Flaherty et al, 1999;Finn et al, 1992). In the past, it has been shown by many authors (Guzdar et al, 1982;Satyanarayana et al, 1987) that RT instability of a magnetized plasma may be saturated by the external imposition of velocity shear. Recently, in a complementary investigation, Finn (1993) has demonstrated by numerical simulations that the velocity shear may be self consistently generated since the RT vortices are themselves unstable to formation of velocity shear.…”

Collisional Rayleigh-Taylor instability and shear-flow in equatorial Spread-F plasma

“…The influence of transverse velocity shear on RayleighTaylor instability has been well investigated in the linear theory by various authors (Guzdar et al, 1982;Satyanarayana et al, 1984Satyanarayana et al, , 1987Chaturvedi and Ossakow, 1977). It is found that a sheared velocity flow can substantially reduce the growth rate of a Rayleigh-Taylor instability in the short wavelength regime.…”