Approximate method of solving the problem of characteristic oscillations of a liquid in cavities of revolution (Q1057132)

A method proposed earlier by the second author [Calculation of the characteristic oscillations of a liquid in fixed vessels, in: Dynamics of elastic and rigid bodies interacting with liquids, Izd. Tomsk. Un., Tomsk (1978) on pp. 157-162 ] is developed, the velocity potential being sought in the form of a sum of two potentials. The first (base) potential is a solution to the problem of the characteristic oscillations of a liquid in a cavity whose free surface coincides with the free surface of the original cavity, and the second (correcting) potential is chosen in the form of a system of harmonic functions, this system being complete and orthogonal on the wetted surface of the cavity. Cavities of revolution are analyzed as examples, and a detailed investigation of numerical results is made for a spherical cavity.