Effects of viscosity and elasticity on Rayleigh–Taylor instability in a cylindrical geometry

Abstract

In this paper, we present a linear analysis of the Rayleigh–Taylor instability (RTI) in cylindrical geometry to investigate the effects of viscosity and elasticity on growth rates using a decomposition method. This method decomposes the fourth-order differential equations into two coupled second-order differential equations to easily obtain the dispersion relations. The motions of the interfaces are analyzed for the instability at liquid/liquid, solid/liquid, and solid/solid interfaces, and the results retrieve those previously obtained for inviscid fluids. Generally, the planar growth rates recover those in the cylindrical geometry when the dimensionless radius Br or mode number n is large enough. The RTI for different cylindrical geometries is particularly investigated to study the effects of viscosity, elasticity, and curvature. It is found that the n = 1 mode will always survive and dominate the motion of the interfaces when the dimensionless radius is significantly small. We believe that this method will provide the possibility of investigating the behaviors of different types of interfaces based on their driven conditions. Furthermore, this will help to find a way to study the evolution of low-mode asymmetries that is essential for controlling the integrity of a fusion target under study during implosion processes in high energy-density physical experiments. This method provides basic guidance for exploration of Bell–Plesset effects and of the transition from elasticity to plasticity in cylindrical geometry.

Converging-diverging shock-driven instabilities along soft hydrogel surfaces

“…A detailed order parameter study which includes Refs [49][50][51][52][53][54][55][56]. is provided in the Supplemental Material and underscores this finding[42].According to our analysis, cylindrical Rayleigh-Taylor or parametric instabilities as reported in Refs [15,[57][58][59]. may develop regardless of the scale of the hydrostatic stress because these instabilities do not require nonlinear volumetric material response, but the instability reported in this paper requires sufficiently large pressures and wave dispersion upon shock reflection.…”

“…According to our analysis, cylindrical Rayleigh-Taylor or parametric instabilities as reported in Refs. [15,[57][58][59] may develop regardless of the scale of the hydrostatic stress because these instabilities do not require nonlinear volumetric material response, but the instability reported in this paper requires sufficiently large pressures and wave dispersion upon shock reflection. Richtmyer-Meshkov instabilities do require a nonlinear equation of state but develop due to baroclinic effects induced by compressive shock waves.…”