Necessary conditions for spatial inviscid instability

Abstract

Rayleigh's inflection point theorem and Fjortoft's theorem provide necessary conditions for inviscid temporal instability of a plane parallel flow. Although these theorems have been assumed to hold in the spatial framework also, a rigorous theoretical basis for such an application is not available in the literature. In this paper, we provide such a basis by carrying out a formal analysis of the Rayleigh equation. We prove that, under certain conditions satisfied by a wide class of flows, the Rayleigh and Fjortoft theorems are applicable to the spatial stability problem also. This work thus fills the lacuna in the spatial stability theory with regard to these classical theorems.