Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities
- University of California, Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
We consider the effect of viscosity on Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities by deriving a moment equation for fluids with arbitrary density and viscosity profiles, including surface tension. We apply our result to the classical case of two semi-infinite fluids with densities [rho][sub 1] and [rho][sub 2] and viscosities [mu][sub 1] and [mu][sub 2]. Treating a shock as an instantaneous acceleration we find that perturbations at the interface undergo damped oscillations when viscosity and surface tension are both present. For pure viscosity the amplitude [eta]([ital t]) evolves according to [eta]([ital t])/[eta](0)=1+([Delta][ital vA]/2[ital k][nu])(1[minus][ital e][sup [minus]2[ital k]2][nu][ital t]) where [Delta][ital v] is the jump velocity imparted by the shock, [ital A]=([rho][sub 2][minus][rho][sub 1])/([rho][sub 2]+[rho][sub 1]), [nu]=([mu][sub 1]+[mu][sub 2])/([rho][sub 1]+[rho][sub 2]), [ital k]=2[pi]/[lambda] is the wave number of the perturbation, and [ital t] is time. We also consider the turbulent energy in accelerating fluids and calculate the reduction in [ital E][sub turbulent] as a function of [nu], and propose experiments to measure the effect of viscosity on RT and RM instabilities.
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 6897723
- Journal Information:
- Physical Review E; (United States), Journal Name: Physical Review E; (United States) Vol. 47:1; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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