Studies of two-dimensional vortex streets

Abstract

Periodic vortex streets, often considered as a model for the organized structures observed in the wake of two-dimension al (2D) bluff bodies, are revisited. After the generation of the shear layers the formation of the vortices is mainly an inviscid process. An intrinsic scaling for the formation of vortex streets is found based on the invariants of motion for 2D inviscid flows; namely the kinetic energy, impulse, circulation and the translational velocity of the vortex system. We show that in the frame of reference of the invariants of motion the intrinsic shedding Strouhal number St defined based on the invariants of motion and the aspect ratio of the vortex street K (the ratio of the lateral distance to the streamwise distance between the centers of vortices) are literally the same. The formation of the vortex street is a manifestation of Kelvin's variational principle. Using the computational results from Saffman and Schatzman1 for the inviscid vortex streets of vortex patches we estimate values of the nondimensional energy and circulation of the vortex system for a wide class of vortex patches. A relaxational explanation of the vortex shedding is also offered. In this picture the bluff body is considered as a source of providing the system with invariants of motion. After the formation of the shear layers the system will relax toward its final equilibrium state where the formation of a vortex street is mandated by the invariants of motion for the two-dimensional Euler equations. Similar to the vortex ring pinch-off process it is speculated that the characteristics of the vortex system can be modified by modification in the rate of generation of invariants of motion. The two main methods for modifying a vortex system are the dynamical changing of the speed and the lateral spacing of the generated shear layers during the formation of circulation regions. This is often achieved by periodic streamwise and lateral oscillations of the bluff body.