Effect of viscosity and shear flow on the nonlinear two fluid interfacial structures

A nonlinear formulation is presented to deal with the combined action of Rayleigh-Taylor and Kelvin-Helmholtz instabilities as well as combined Ricthmyer-Meshkov and Kelvin-Helmholtz instabilities at the two fluid interface under the influence of viscosity and consequent shear flow. Using Layzer's model, the development of the interfacial structures like bubbles is investigated analytically and numerically. It is found that the growth and normal velocity of the structures are dependent on the relative velocity shear and the kinematic coefficient of viscosity of both the fluids. Both the bubble growth and growth rate are reduced significantly for fluids of higher viscosity coefficient with small velocity shear difference. It is also observed that, for viscous fluids, the transverse velocity of the perturbed interface becomes slower under certain conditions.