Stabilization of the Rayleigh--Taylor instability by convection in smooth density gradient: Wentzel--Kramers--Brillouin analysis

Journal Article · Sun Nov 01 04:00:00 EST 1992 · Physics of Fluids B; (United States)

DOI:https://doi.org/10.1063/1.860357· OSTI ID:6995978

Bud'ko, A B; Liberman, M A ^[1]

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1. Department of Technology, Uppsala University, Box 534, S-75 121, Uppsala (Sweden)

A self-consistent analytical model based on the Wentzel--Kramers--Brillouin (WKB) approximation is developed to investigate the suppression of the Rayleigh--Taylor (RT) instability by the combined effect of the convective mass flow and structured profiles both, in subsonic and supersonic flow regimes. The eigenvalue problem for the instability growth rates {sigma} is reduced to the problem of solving the system of algebraic equations. In static stratified plasma the eigenvalues spectrum {sigma}{sub {ital n}}({ital k}) ({ital n}=0,1,2,...) is found for any density profile. In the presence of steady-state mass flow the growth rate is obtained as an implicit function of the transverse wave number and as a functional of the unperturbed profiles. The cutoff wave number is expressed explicitly as the function of the unperturbed variables. Applicability of the WKB approach implies Fr={ital v}{sup 2}/{ital gL}{much lt}1 (Fr is the local Froude number, {ital L} is the stratification length scale), still it yields satisfactory agreement with numerical solutions of the boundary value problem for the RT growth rates in the ablatively accelerated plasma of larger targets with sharp density gradient (Fr{similar to}1).

• OSTI ID: 6995978
• Journal Information: Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 4:11; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700340* -- Plasma Waves
Oscillations
& Instabilities-- (1992-)
ABLATION
CONVECTION
ENERGY TRANSFER
EQUILIBRIUM
FLUID FLOW
FROUDE NUMBER
HEAT TRANSFER
INSTABILITY
INSTABILITY GROWTH RATES
LASER-PRODUCED PLASMA
MASS TRANSFER
MHD EQUILIBRIUM
PLASMA
RAYLEIGH-TAYLOR INSTABILITY
STABILIZATION
SUBSONIC FLOW
SUPERSONIC FLOW
WKB APPROXIMATION