Free-surface oscillations of a liquid relative to an equilibrium state of uniform rotation about the vertical of an axisymmetric container are considered for small α = ω ²a|g , where ω is the angular velocity of rotation and a the cylinder radius. A variational approximation is used to obtain explicit results, with an error of O(α2), for axisymmetric gravity and inertial waves in a flat-bottomed circular cylinder; these results are found to be in agreement with observations reported by Fultz (1962). The first-order (in ω) effects of rotation on asymmetric waves in a circular cylinder also are determined.
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John W. Miles (1964) studied this question.
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