A new class of instabilities of rotating flows

The stability of flows which are the sum of a linear flow with circular or elliptic streamlines and a transverse standing wave is examined. A coordinate transformation annihilating the linear component of the how is made, and the stability of the transformed flow is studied via two complementary methods. First, the stability with respect to local small scale perturbations is analyzed by virtue of the short wavelength stability method of Eckhoff and Lifschitz & Hameiri and it is found that all transformed flows are unstable with respect to such perturbations. Second, the corresponding linearized problem is studied via appropriately modified classical methods and global instabilities are found. It is shown that the growth rate of the global instabilities increases with their wavenumber and asymptotically approaches the value predicted by the short wavelength stability method. It is argued that the observed instabilities play an important role in transitions from laminar two-dimensional flows to turbulent three-dimensional ones. (C) Elsevier, Paris.