Abstract
An unsteady flow generated by a harmonically oscillating pressure distribution of frequency ω acting on the paraboloidal free surface of an inviscid, incompressible fluid rotating with uniform angular velocity Ω has been investigated. It is shown that case (i), ω>2 Ω, corresponds to the usual surface waves, and case (ii), ω<2 Ω, in contrast to the surface waves, corresponds to the inertial waves which are originated entirely due to rotation and have no counterpart in a non-rotating fluid motion. An explicit solution of the problem related to the above cases are obtained by the joint Laplace and Hankel transforms treatment in conjunction with asymptotic methods. The significant effects of the Coriolis force and the curvature of the free surface on the wave motions have been investigated. A comparison is made between the solutions of the problems with the horizontal and the paraboloidal free surface curvature. The analysis is concluded by exihibiting the characteristic features of the wave motions.
Published Version
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