Reynolds stress closure in jet flows using wave models

Numerical methods were developed that will form the computational part of the turbulence closure scheme. A wave model was developed for the two-dimensional shear layer. This configuration is being used as a test case for the closure schemes. Various numerical schemes were examined to give efficient solutions of the Rayleigh equation for this geometry. These include both spectral and finite difference methods. Secondly, numerical methods are under development to solve the non-separable Rayleigh equation. This solution is required for the closure scheme in more complex geometries. A model problem was used to assist in the algorithm development. Two-dimensional spectral methods and a hybrid spectral/finite difference technique were developed. An analytic solution of the Rayleigh equation for a basic elliptic flow was obtained. This will be used to verify the stability codes developed for arbitrary geometries. Other numerical methods for solving the Rayleigh equation based on the boundary element technique were also examined. These solutions are forming the basis of a model for the shock structure in jets of arbitrary geometry.