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

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 σ is reduced to the problem of solving the system of algebraic equations. In static stratified plasma the eigenvalues spectrum σn(k) (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=v2/gL≪1 (Fr is the local Froude number, 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∼1).