Numerical simulations of a shock interacting with a compressible vortex are presented for shocks and vortices of various relative strengths. The simulations show the effects of the vortex on the shock structure and the structure of the acoustic field generated by the shock–vortex interaction. A relatively weak vortex perturbs the transmitted shock only slightly, whereas a strong vortex leaves the transmitted shock with a structure corresponding to either a regular or Mach reflection. The acoustic wave generated by the interaction consists of two components: a ‘‘quadrupolar’’ component produced by the initial shock–vortex interaction and the complex reflected shock system. When these waves merge, they form the asymmetric structure seen in experiments.

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In this paper we discuss the mechanisms responsible for the formation of the acoustic wave when a shock interacts with a vortex. Experimental measurements have shown that this interaction produces a primarily quadrupolar acoustic wave with a strong compression attached to the shock front. We review earlier work which shows that this strong compression is due to the distortion of the shock. The origin of the quadrupolar component is examined by comparing twodimensional computations of the shock-vortex interaction to those of an isolated elliptical vortex. The elliptical vortex is similar to the compressed vortex produced when a shock interacts with an initially circular vortex. We concentrate on interactions in which the shock transit time is short. The pressure field of the shock-vortex interaction is compared to that of an analogous isolated elliptical vortex for three cases: a weak shock interacting with a weak vortex, a strong shock interacting with a weak vortex, and a strong shock interacting with a strong vortex. Our results indicate that both shock distortion and vortex compression are important to the formation of the acoustic wave.

Experimental, theoretical, and computational research has shown that the interaction of a shock with a vortex produces a quadrupolar acoustic wave. Although the theoretical basis for this has been accepted for some time, there has not been a detailed comparison of the predictions for the pressure variation around and through the acoustic wave to the pressure ÿelds obtained from numerical simulations. In this paper, Ribner's theory is used to predict the acoustic pressure ÿeld evolving from a shock interacting with either a Rankine (or inÿnite) vortex or with a composite (or ÿnite) vortex. A comparison of these theoretical results indicates the importance of vortex geometry on the acoustic wave. Then the theoretical results are compared to the results of detailed computations. The computational results were obtained by solving the two-dimensional conservation equations for mass, momentum, and energy for a compressible, inviscid uid using the Flux-Corrected Transport algorithm. These results show that there is good qualitative agreement between the theory and the computation.