Nonlinear Rayleigh–Taylor Instability of a Cylindrical Interface in Explosion Flows

Abstract

The nonlinear growth of instabilities of an outward propagating, but decelerating, cylindrical interface separated by fluids of different densities is investigated. Single mode perturbations are introduced around the contactsurface, and their evolution is studied by conducting inviscid 2D and 3D numerical simulations. In the past, a significant amount of work has been carried out to model the development of the perturbations in a planar context where the contact surface is stationary or in a spherical context where a pointsource blast wave is initiated at the origin. However, for the finitesource cylindrical blastwave problem under consideration, there is a need for a framework which includes additional complexities such as compressibility, transition from linear to nonlinear stages of instability, finite thickness of the contact interface (CI), and timedependent deceleration of the contact surface. Several theoretical potential flow models are presented. The model which is able to capture the above mentioned effects (causing deviation from the classical Rayleigh–Taylor Instability (RTI)) is identified as it compares reasonably well with the DNS results. Only for higher wavenumbers, the early development of secondary instabilities (Kelvin–Helmholtz) complicates the model prediction, especially in the estimation of the highdensity fluid moving into lowdensity ambient.