Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities
Abstract
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 ρ1 and ρ2 and viscosities μ1 and μ2. 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 η(t) evolves according to η(t)/η(0)=1+(ΔvA/2kν)(1-e-2k2νt) where Δv is the jump velocity imparted by the shock, A=(ρ2-ρ1)/(ρ2+ρ1), ν=(μ1+μ2)/(ρ1+ρ2), k=2π/λ is the wave number of the perturbation, and t is time. We also consider the turbulent energy in accelerating fluids and calculate the reduction in Eturbulent as a function of ν, and propose experiments to measure the effect of viscosity on RT and RM instabilities.
- Publication:
-
Physical Review E
- Pub Date:
- January 1993
- DOI:
- 10.1103/PhysRevE.47.375
- Bibcode:
- 1993PhRvE..47..375M
- Keywords:
-
- 47.20.-k;
- 52.35.Py;
- 47.40.Nm;
- Flow instabilities;
- Macroinstabilities;
- Shock wave interactions and shock effects