A MODEL FOR CHARACTERIZATION OF A VORTEX PAIR FORMED BY SHOCK PASSAGEOVER A LIGHT-GAS INHOMOGENEITY

This work investigates the two-dimensional flow of a shock wave over a circular light-gas inhomogeneity in a channel with finite width. The pressure gradient from the shock wave interacts with the density gradi ent at the edge of the inhomogeneity to deposit vorticity around the p erimeter, and the structure rolls up into a pair of counter-rotating v ortices. The aim of this study is to develop an understanding of the s caling laws for the flow field produced by this interaction at times l ong after the passage of the shock across the inhomogeneity. Numerical simulations are performed for various initial conditions and the resu lts are used to guide the development of relatively simple algebraic m odels that characterize the dynamics of the vortex pair, and that allo w extrapolation of the numerical results to conditions more nearly of interest in practical situations. The models are not derived directly from the equations of motion but depend on these equations and on intu ition guided by the numerical results. Agreement between simulations a nd models is generally good except for a vortex-spacing model which is less satisfactory.