Numerical experiments on transition triggering off in a two-dimensional shear flow

Transition triggering off in a mixing layer with a hyperbolic tangential velocity profile is studied using a two-dimensional numerical simulation. The simulation involves solving time-dependent two-dimensional Navier-Stokes equations using a finite-difference scheme. The Navier-Stokes equations are formulated in terms of the stream function and vorticity and discretized over a grid of square meshes. The vorticity advection is approximated by an implicit second-order scheme which conserves both vorticity and square vorticity. Numerical realizations are compared, in terms of the streamwise growth of momentum thickness and vorticity, with the results of Winant and Browand's experiments (1974).