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Article Dans Une Revue European Journal of Mechanics - B/Fluids Année : 2002

The effect of viscosity, surface tension and non-linearity on Richtmyer–Meshkov instability

Résumé

A weakly non-linear theoretical model of the Richtmyer–Meshkov instability between two viscous fluids with surface tension is proposed. The model is based on the application of singular perturbations techniques to the incompressible Navier–Stokes equations written for two superposed immiscible fluids. A simple analytical law of interface deformation is obtained, in which the effects of viscosity, surface tension and non-linearities appear under the form of independent terms. The model gives also access to the velocity and pressure distribution in the fluids, which can be of interest for estimating vorticity diffusion in the fluids. A comparison with accurate direct numerical simulations confirms the validity of the proposed theory. The interface deformation law is then applied to typical experimental configurations in order to estimate the relative influence of surface tension, viscosity and non-linearities on the growth of perturbations for each of the chosen cases.

Dates et versions

hal-01453037 , version 1 (02-02-2017)

Identifiants

Citer

Stéphane Popinet, Pierre Carlès. The effect of viscosity, surface tension and non-linearity on Richtmyer–Meshkov instability. European Journal of Mechanics - B/Fluids, 2002, 21 (5), pp.511-526. ⟨10.1016/S0997-7546(02)01199-8⟩. ⟨hal-01453037⟩
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