title: Mathematical model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for viscoelastic fluids.
abstract: We extended the Goncharov model [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] for nonlinear Rayleigh-Taylor instability of perfect fluids to the case of Rivlin-Ericksen viscoelastic fluids [R. S. Rivlin and J. L. Ericksen, Rat. Mech. Anal. 4, 323 (1955)], with surface tension. For Rayleigh-Taylor instability, viscosity, surface tension, and viscoelasticity decrease the exponential growth rate predicted by linear stability analysis. In particular, we find that viscosity and surface tension decrease the terminal bubble velocity, whereas viscoelasticity is found to have no effect. All three properties increase the saturation height of the bubble. In Richmyer-Meshkov instability, the decay of the asymptotic velocity depends on the balance between viscosity and surface tension, and viscoelasticity tends to slow the asymptotic velocity decay.
authors: Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors: Bertrand
authors: B
authors: Rollin
authors: Malcolm J
authors: MJ
authors: Andrews