Numerical simulation of the formation of vortex streets in a compressible fluid

The mechanism of the formation of vortex streets in the wake of a bluff body can be studied by considering the interaction of two infinite vortex sheets which are initially a fixed distance apart. This idea was conceived by Abernathy and Kronauer who, by this consideration succeeded in explaining essential features of the mechanism in an inviscid incompressible fluid. In this paper, we take up this idea in order to study the formation of vortex streets in a compressible fluid at different Mach numbers. This done by direct numerical simulations based on the two-dimensional compressible Navier-Stokes equations. To follow the development of the vortex sheets we combined the numerical simulation of the flow field with a marker particle algorithm At the beginning of our calculations the vortex sheets are marked by a set of particles. They are advected during the calculation in a Lagrangean fashion according to the calculated flow field. The formation of the vortex street is then visualized by graphically displaying these marker particles, similar to streaklines in experiments. While in practice flows usually develop streamwise, in our numerical calculations we assume two infinite vortex sheets which are periodically disturbed in space and the results show the development of vortex streets in time. This flow model enables us to perform large-scale computations with good resolution and the solution does not leave the computational domain