Acoustic emission by vortex–edge interaction is investigated both theoretically and experimentally. The theory of vortex sound enables us to represent the far-field pressure in terms of the vortex motion near the half-plane edge. It is found that the pressure p depends on the product of an angular factor representing directionality and a time factor representing wave profile. The pressure formula leads to the scaling law $p \propto U^{\frac{5}{2}} L^{-2}$ for the sound emitted by a vortex ring of velocity U, L being the nearest distance of the vortex path to the edge. The sound intensity is proportional to U5 and shows cardioid directionality pattern.The vortex ring used in the experiment had radius about 4.7 mm and velocity ranging from 29 to 61 m/s. The above scaling law of the pressure and the cardioid directionality of the intensity were reproduced in the experiment with reasonable accuracy. Especially notable is the agreement between the predicted and observed wave profiles. The theoretical profile is determined by the $\frac{3}{2}\,{\rm th}$ time derivative of the volume flux (through the vortex ring) of a hypothetical potential flow around the edge.
This is a detailed experimental study of the behavior of diffraction and refraction of a shock front resulting from the interaction of a shock wave and a vortex ring. A spherical shock wave impinges on a vortex ring which is traveling at a high speed in the opposite direction. The configuration of the wave front is visualized by a shadowgraph technique using a pulse dye laser. The shock front is influenced by the non-uniform flow induced by the vortex and diffracted around the vortex core. The shock front passing through the inside of the ring is decelerated by the counter-flow, and the density behind it increases. The diffracted front over the vortex ring expands spirally around the core and intersects the front passing through the inside of the ring. The intersecting circular curve converges toward the central axis of the ring. The diffracted shock in the inner part of the core forms branching waves. The branching points also focus on the central axis of the ring.
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