ACOUSTIC RAYS IN 2-DIMENSIONAL ROTATING FLOWS

The differential equation of acoustic rays in two dimensional rotating flows is derived, and is integrated for the cases of rigid body rotation and the potential vortex, with a point acoustic source. In the case of rigid body rotation, the rays are bent in the direction of rotation, resulting in defocusing on the side of the acoustic source near the center of rotation and focusing on the opposite side. In the case of the potential vortex, a number of rays are trapped by the vortex and spiral towards the center. Other rays at first appear to be trapped, but then reach a turning point and leave the vortex. These rays are substantially deflected and defocused. In addition, with a circulation corresponding to a Mach number of 0.5 at the acoustic source, a caustic is formed. However, with one half that circulation, the caustic does not appear. © 1969, Acoustical Society of America. All rights reserved.