General properties of a multilayer stratified fluids system

Linearized Euler equations of a general stationary multiple layer stratified system for both compressible and incompressible inviscid fluids are analyzed. The main result is that many features of a multilayer system are universal, in the sense they do not depend on such details as the number of layers, their thicknesses, equations of state for the fluids, and equilibrium density distributions. Necessary and sufficient conditions of stability are determined. For compressible fluids, it is possible for the system to be unstable even if there is no density inversion anywhere. It is shown that a compressible system is always more unstable than the corresponding incompressible one. A universal upper bound for the growth rate for a given perturbation wave number is given. General Rayleigh–Taylor unstable modes are characterized, and the range of unstable wave numbers is determined. Properties of stable modes are discussed. Numerical algorithms for solving the eigenvalue problem of the set of linearized Euler equations are given.