A new class of instabilities of rotating fluids

Standing waves in a rotating ideal fluid are considered. It is shown that all of them are unstable with respect to short-wavelength perturbations. Moreover, it is demonstrated that the growth rate of the corresponding instabilities tends to infinity when either the amplitude of the standing wave increases or its spatial scale decreases without bound. It is suggested that the observed instabilities are akin to the Hadamard instabilities. (C) 1996 American Institute of Physics.