Dynamics of ring vortices impinging on planar shock waves

In the present paper the encounter of vortex rings with planar shock waves is studied in a three-dimensional environment, with the objective to assess the influence of shock and vortex strength and vortex orientation on the dynamics of the process. The study relies on numerical simulations performed by means of a state-of-the-art hybrid compact/WENO (weighted essentially nonoscillatory) shock-capturing algorithm to solve the Euler equations of gas dynamics. The study focuses on the characterization of the interaction in terms of the evolution of the geometrical parameters of the vortex and the mean flow properties such as kinetic energy and enstrophy. The vortex is compressed as it passes through the shock, and its characteristic dimensions decrease; at the same time its axis is deflected and the ring follows a complex dynamic evolution, even though a nearly steady state is reached for the global quantities. In particular, it has been found that the total vortex kinetic energy is generally nonincreasing after the interaction, while the enstrophy always increases. A simple theory is developed here to shed some light onto the physical phenomena involved, which is found to compare reasonably well with the results of the computations. Some final comments are made regarding the extension of the results reported in the present study to the analysis of shock-compressed turbulence.