Rayleigh-Taylor instability of viscoplastic liquid

The Rayleigh-Taylor instability of viscoplastic medium (VPM) is considered, which medium corresponds to real VPM or to the high-temperature limit of highly elastic-viscoplastic fluids. An effective rheological model is provided by the Bingham-Shvedov model (BSM) which is similar to the dry friction model in the mechanics of deformable solid. The main feature of BSM is the existence of yield stress corresponding to dry friction limit. Well-known in the literature is the solution for round pipe flow of BSM, in the case of which the presence of yield stress causes the emergence of a moving core at the center of flow. It is the prime objective of this study to construct a numerical model of three-dimensional flow of BSM in the gravity field, which is accompanied by a nonlinear stage of development of instability of VPM, and to analyze the correlation between the development of instability and yield stress.