Wave structures in jets of arbitrary shape. I. Linear inviscid spatial instability analysis

Abstract

Green function methods are used to give a practical form of the Rayleigh linear inviscid instability analysis for jets of arbitrary mean flow profile. Simple illustrations of the general methodology are given for vortex-sheet and continuous-velocity-profile shear layers. Some of the numerical results for elliptic jets are compared with those previously obtained from solutions of Mathieu’s equation in elliptic cylindrical coordinates.