SPIRALS AND DISLOCATIONS IN WAVE-VORTEX SYSTEMS

The two-dimensional interaction between sound waves and a vortex is st udied. When the Mach number defined by the ratio of the typical veloci ty due to the vortex to the speed of sound is small and the ratio of t he size of the vortex to the wavelength is large, a differential equat ion for the sound waves is derived. Some classes of spiral solutions o f the equation are obtained by relating their phase function to the ba ckground flow due to the vortex. Using the analogies between the Aharo nov-Bohm effect in quantum mechanics, shallow water waves, and sound w aves, the scattering problem of an incident dislocated wave is discuss ed.