Similarity solutions of free shear flows with mean Reynolds stress turbulence models

A numerical method for modeling free shear flows is presented, and involves use of the governing equations for the mean Reynolds stress (MRS) in a similarity form. The calculations are applied to a steady, incompressible, two dimensional jet as an example, with a constraint placed on the streamwise momentum flux. Account is taken of the streamwise and cross stream velocities. The governing equations are formulated in terms of a coupled set of nonlinear parabolic partial differential equations which can be solved by a marching technique. Similarity profiles are employed to allow for the continuous expansion of the jet farther downstream, thereby permitting analytical solutions to be obtained in the similarity variable space, with the width of any region calculated in terms of an eigenvalue of the solution.