Richardson’s criterion for the stability of stratified shear flow

1986 ◽  
Vol 29 (10) ◽  
pp. 3470 ◽  
Author(s):  
John Miles
Keyword(s):  
Shear Flow ◽  
Stratified Shear Flow ◽  
The Stability

Neutral eigensolutions of the stability equation for stratified shear flow

1969 ◽  
Vol 36 (4) ◽  
pp. 673-683 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Differential Equation ◽  
Shear Flow ◽  
Analytical Form ◽  
Analytic Solutions ◽  
Stability Equation ◽  
Hypergeometric Differential Equation ◽  
Stratified Shear Flow ◽  
Parallel Shear Flow ◽  
The Stability ◽  
Simple Analytical Form

Many of the known analytic solutions of the equation for neutral disturbances to a stably stratified, inviscid, parallel shear flow are shown to belong to a wider family of solutions when a transformation to the hypergeometric differential equation is possible. Two particular cases in which the transformation can be made are examined in some detail and the solutions are expressed in a simple analytical form. A number of novel solutions are presented as examples.

The Effect of Boundaries on the Stability of Inviscid Stratified Shear Flows

1976 ◽  
Vol 43 (2) ◽  
pp. 243-248 ◽  
Author(s):  
F. Einaudi ◽  
D. P. Lalas
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Shear Flows ◽  
Infinite Domain ◽  
Hyperbolic Tangent ◽  
Stratified Shear Flow ◽  
The Stability ◽  
Exchange Of Stability

The influence of the presence and position of solid boundaries on the stability of an inviscid, stratified shear flow, is examined numerically for the case of a hyperbolic tangent velocity profile and an exponentially decreasing density. The presence of solid boundaries is shown to stabilize short wavelengths and destabilize large wavelengths. Furthermore, extra unstable modes, not present in an infinite domain, are found for large wavelengths, both for symmetric and asymmetric boundaries. Finally, the validity of the principle of exchange of stability is examined, and it is shown to be unreliable even for the case of symmetric boundaries.

On the stability of heterogeneous shear flows. Part 2

1963 ◽  
Vol 16 (2) ◽  
pp. 209-227 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Shear Flow ◽  
Wave Speed ◽  
Neutral Curve ◽  
Wave Number ◽  
Neutral Curves ◽  
Stratified Shear Flow ◽  
Neutral Mode ◽  
The Mean ◽  
The Stability ◽  
Small Disturbances

Small disturbances relative to a horizontally stratified shear flow are considered on the assumptions that the velocity and density gradients in the undisturbed flow are non-negative and possess analytic continuations into a complex velocity plane. It is shown that the existence of a singular neutral mode (for which the wave speed is equal to the mean speed at some point in the flow) implies the existence of a contiguous, unstable mode in a wave-number (α), Richardson-number (J) plane. Explicit results are obtained for the rate of growth of nearly neutral disturbances relative to Hølmboe's shear flow, in which the velocity and the logarithm of the density are proportional to tanh (y/h). The neutral curve for this configuration, J = J0(α), is shown to be single-valued. Finally, it is shown that a relatively simple generalization of Hølmboe's density profile leads to a configuration having multiple-valued neutral curves, such that increasing J may be destabilizing for some range (s) of α.

Resonant wave interactions in a stratified shear flow

1988 ◽  
Vol 190 ◽  
pp. 357-374 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Critical Level ◽  
Internal Gravity Waves ◽  
Wave Interactions ◽  
Resonant Wave ◽  
Resonant Interactions ◽  
Stratified Shear Flow ◽  
Weak Resonance ◽  
Background Shear

Resonant interactions between triads of internal gravity waves propagating in a shear flow are considered for the case when the stratification and the background shear flow vary slowly with respect to typical wavelengths. If ωn, kn(n = 1, 2, 3) are the local frequencies and wavenumbers respectively then the resonance conditions are that ω1 + ω2 + ω3 = 0 and k1 + k2 + k3 = 0. If the medium is only weakly inhomogeneous, then there is a strong resonance and to leading order the resonance conditions are satisfied globally. The equations governing the wave amplitudes are then well known, and have been extensively discussed in the literature. However, if the medium is strongly inhomogeneous, then there is a weak resonance and the resonance conditions can only be satisfied locally on certain space-time resonance surfaces. The equations governing the wave amplitudes in this case are derived, and discussed briefly. Then the results are applied to a study of the hierarchy of wave interactions which can occur near a critical level, with the aim of determining to what extent a critical layer can reflect wave energy.

A mathematical model of turbulent heat and mass transfer in stably stratified shear flow

1993 ◽  
Vol 253 (-1) ◽  
pp. 341 ◽  
Author(s):  
G. I. Barenblatt ◽  
M. Bertsch ◽  
R. Dal Passo ◽  
V. M. Prostokishin ◽  
M. Ughi
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Shear Flow ◽  
Heat And Mass Transfer ◽  
Turbulent Heat ◽  
Stratified Shear Flow ◽  
Stably Stratified Shear Flow
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