Wave structures in jets of arbitrary shape. II. Application of a generalized shooting method to linear instability analysis

Abstract

The shooting method, used in the linear instability analysis of plane shear layers, is generalized so as to be applicable to the case of straight three-dimensional, inviscid, compressible jets of arbitrary mean flow profile. A jet is assumed to have a core region of constant flow W0 bounded by curve C, and an outer-flow boundary C̃ outside of which the flow is negligible. The instability eigenmodes are determined by using the Helmholtz surface integral relations between the incremental pressure and its normal derivative on C and C̃, together with finite difference approximate solutions of the Rayleigh differential equation in one region between C and C̃. Calculations typically require about 50 times less computer time than do equivalent integral-equation methods. Numerical results are presented for incompressible jets with circular and elliptic core regions and several azimuthal variations of momentum thickness.