Summary: We consider a spherical system composed of \(N\) concentric fluid shells having perturbations of amplitude at interface \(\eta_ i\), \( i=1, 2,\cdots , N-1\). For arbitrary implosion-explosion histories \(R_ i(t)\), we present the set of \(N-1\) second-order differential equations describing the time evolution of the \(\eta_ i\) which are coupled to the two adjacent \(\eta_ {i\pm 1}\). 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.