The instability of jets of arbitrary exit geometry

This paper describes a calculation technique to determine the linear instability characteristics of jets of arbitrary exit geometry. In particular, elliptic and rectangular jets are considered. The numerical procedure involves both a conformal transformation between the computational domain and the physical plane and a solution of the transformed stability equation in the computational domain. Modern, efficient, conformal mappings are used for both simply and doubly connected domains. The numerical solution is based on a hybrid finite difference/pseudospectral discretization of the stability equation. The technique is validated by comparison with previous stability calculations for circular and elliptic jets. Calculations are performed for the stability characteristics of elliptic and rectangular jets of aspect ratio 2:1. Growth rates, phase velocities, and pressure eigenfunctions are presented.