Viscous nonlinear theory of Richtmyer-Meshkov instability

We propose a quantitative prediction of the effect of viscosity on the weak ly nonlinear impulsive Richtmyer-Meshkov instability between two fluids of arbitrary density and viscosity. This theory is based on an asymptotic anal ysis of the Navier-Stokes equations using singular perturbation techniques. The law obtained for interface deformation does not agree with former theo retical predictions of the effect of viscosity [K. O. Mikaelian, Phys. Rev. E 47, 375 (1993)], but compares very well with direct numerical simulation s we performed using a front-tracking code developed in our laboratory. App lication of this law to typical experimental parameters gives a formal demo nstration of the relevance of inviscid models for the description of typica l shock-tube experiments; at the same time, however, it shows that care sho uld be taken with regard to viscosity in the case of impulsive experiments performed with liquids. (C) 2001 American Institute of Physics.