Study of Rayleigh-Taylor instability in viscosity-stratified fluid layers

Abstract

The Rayleigh-Taylor instability in viscosity varying fluid layers is studied. A heavier fluid layer is superimposed on a lighter fluid layer. Both the fluid layers are bounded between two parallel isothermal horizontal walls. Out of the two walls, one wall is isothermally heated, while the other wall is isothermally cooled. The Rayleigh-Taylor instability is studied for axisymmetric configuration. Viscosities of both the fluids are considered to be varying with temperature. The effect of viscosity ratio, temperature ratio, heating location, Prandtl number and Weber number on the instability is studied. When the viscosity of fluid layers vary with temperature, the configuration becomes more unstable compared to that for constant viscosity fluid layers. For varying viscosity fluid layers the spike undergoes large deformations. At lower viscosity ratios, mushroom shaped spike is formed with elongated skirt structure. Whereas, at higher viscosity ratios, spike with fluid column structure is formed. It is found that increasing viscosity ratio shows stabilizing effect. Increasing temperature ratio is found to show destabilizing effect with complex spike structure formation at high temperature ratios. In top wall heating configuration, formation of mushroom shaped spike and skirt of the spike occurs earlier in a thinner and elongated form compared to that of bottom wall heating configuration. Prandtl number showed insignificant effect on the instability. For the parameter values of the study, when Weber is lower than 55 the configuration is stable and does not undergo instability. Overall, surface tension has shown stabilizing effect on the instability.