On effect of surface tension in the Rayleigh–Taylor problem of stratified viscoelastic fluids

Abstract

In this article, we investigate the effect of surface tension in the Rayleigh-Taylor (RT) problem of stratified incompressible viscoelastic fluids. We prove that there exists an unstable solution to the linearized stratified RT problem with a largest growth rate Λ under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold ϑ c). Moreover, for this instability condition, the largest growth rate Λ ϑ decreases from a positive constant to 0, when ϑ increases from 0 to ϑ c , which mathematically verifies that the internal surface tension can constrain the growth of the RT instability during the linear stage.