Viscous nonlinear theory of Richtmyer–Meshkov instability

Pierre Carlès (1) , Stéphane Popinet (1)

1 LMM - Laboratoire de modélisation en mécanique

We propose a quantitative prediction of the effect of viscosity on the weakly nonlinear impulsive Richtmyer–Meshkov instability between two fluids of arbitrary density and viscosity. This theory is based on an asymptotic analysis of the Navier–Stokes equations using singular perturbation techniques. The law obtained for interface deformation does not agree with former theoretical predictions of the effect of viscosity [K. O. Mikaelian, Phys. Rev. E 47, 375 (1993)], but compares very well with direct numerical simulations we performed using a front-tracking code developed in our laboratory. Application of this law to typical experimental parameters gives a formal demonstration of the relevance of inviscid models for the description of typical shock-tube experiments; at the same time, however, it shows that care should be taken with regard to viscosity in the case of impulsive experiments performed with liquids.

Domaines: Mécanique des fluides [physics.class-ph]

Pierre Carlès, Stéphane Popinet. Viscous nonlinear theory of Richtmyer–Meshkov instability . Physics of Fluids, 2001, 13 (7), pp.1833-1836. ⟨10.1063/1.1377863⟩. ⟨hal-01453024⟩