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: The problem of dynamic stability of small amplitude motions on a two-fluid system with a free surface is considered. For the case of no rotation the character of the Kelvin-Helmholtz instability is remarkably different as compared to systems where the external gravitational modes are absent either through the mechanism of filtering or by imposing a rigid top. In the case of a constant rotation, it is shown that the instabilities on a wave length - shear plane consist of regions where only the gravitational modes or only the rotational modes or both independently are unstable, in addition to regions where instabilities are generated by an interaction between the gravitational and rotational modes. (Author)

Instability of Rotational and Gravitational Modes of Oscillation