Stability and mix in spherical geometry

We consider a spherical system composed of N concentric fluid shells having perturbations of amplitude ${\mathrm{\eta }}_{\mathit{i}}$ at interface i, i=1,2,...,N-1. For arbitrary implosion-explosion histories ${\mathit{R}}_{\mathit{i}}$(t), we present the set of N-1 second-order differential equations describing the time evolution of the ${\mathrm{\eta }}_{\mathit{i}}$ which are coupled to the two adjacent ${\mathrm{\eta }}_{\mathit{i}\pm 1}$. We report analytical solutions for the N=2 and N=3 cases. We also present a model to describe the evolution of a turbulent mixing layer in spherical geometry when the interface between two fluids undergoes a constant acceleration or a shock.