Abstract
We consider the linear stability problem of inviscid, incompressible swirling flows with radius-dependent density with respect to two-dimensional disturbances. Some results of Miles on the parallel flow stability theory are extended to the swirling flow stability theory. In particular, series solutions for the stability equation for swirling flows are obtained and these solutions are used in the study of the variation of the Reynolds stress. For singular neutral modes it is shown that the Reynolds stress varies like the inverse square of the radial distance in agreement with the homogeneous flow result of Maslowe & Nigam. It is also proved that singular neutral modes do not exist whenever the value of the Richardson number at the critical layer exceeds one quarter.
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