ROTATING FREE-SHEAR FLOWS .1. LINEAR-STABILITY ANALYSIS

Using linear stability analysis, the instability characteristics are e xamined of both planar wakes and mixing layers subjected to rigid-body rotation with axis of rotation perpendicular to the plane of the ambi ent flow. In particular, the tendency of rotation to stabilize or dest abilize three-dimensional motions is addressed. In the inviscid limit the results are consistent with the criterion established by Pedley [J . Fluid Mech. 35, 97 (1969)] and Bradshaw [J. Fluid Mech. 36, 177 (196 9)]. Cyclonic rotation and strong anticyclonic rotation tend to stabil ize three-dimensional motions, whereas weaker anticyclonic rotation (R o > 1) acts to destabilize these motions. This latter instability is i n the form of streamwise rolls, similar to previous results obtained f or boundary layer and channel flows. It is found that this instability is stronger than the coexisting Kelvin-Helmholtz instability for roug hly the range 1. 5 < Ro < 8, and its effect is maximum for Ro congruen t-to 2. For the case of constant ambient shear, exact solutions are ob tained which give further insight into the nature of the instability.