Kelvin-Helmholtz instabilities of supersonic shear layers

Journal Article · Wed Aug 01 04:00:00 EDT 1984 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/162311· OSTI ID:6045490

Choudhury, S R; Lovelace, R V.E.

A study is made of the stability of finite-thickness compressible shear layers, v = zv/sub z/(x). Two different velocity profiles are investigated in detail using the analogy between the pressure perturbation, deltap = f(x) exp (i(k/sub y/y+k/sub z/z-..omega..t)), and the bound and scattering wave states of the one-dimensional Schroedinger equation. By analytical and numerical methods, fairly complete contour maps have been generated for the real and imaginary parts of the wave frequency (..omega../sub r/ and ..omega../sub i/) as a function of the two free dimensionless parameters, the ''reduced Mach number,'' Aequivalentk/sub z/v/sub z/m/(kc/sub s/), and the wavenumber, BequivalentkL. Here, v/sub z/(x = +- infinity) = +- v/sub z/m, (k/sub y//sup 2/ +k/sub z//sup 2/)/sup 1/2/, c/sub s/ is the adiabatic sound speed, and L is a length characterizing the thickness of the shear layer. Two distinct regimes of instability are delineated in the (A,B)-plane. In one regime there are unstable standing waves which are analogous to the well-known Kelvin- Helmholtz warping instability of a vortex sheet (where v/sub z/(x) is a step function). In the second regime, there are unstable traveling wave modes which are absent in the case of a vortex sheet.

• Research Organization: Department of Electrical Engineering, Cornell University
• OSTI ID: 6045490
• Journal Information: Astrophys. J.; (United States), Journal Name: Astrophys. J.; (United States) Vol. 283:1; ISSN ASJOA
• Country of Publication: United States
• Language: English

Related Subjects

640450* -- Fluid Physics-- Superfluidity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
COMPRESSION
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
FLUID MECHANICS
FUNCTIONS
HELMHOLTZ INSTABILITY
HYDRODYNAMICS
INSTABILITY
MECHANICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
PLASMA WAVES
SCHROEDINGER EQUATION
SHEAR
STANDING WAVES
SUPERSONIC FLOW
TRAVELLING WAVES
WAVE EQUATIONS
WAVE FUNCTIONS