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RESEARCH PAPERS

Surface Oscillations of a Rotating Liquid

[+] Author and Article Information
J. W. Miles

University of California, Los Angeles, Calif.

B. A. Troesch

Space Technology Laboratories, Inc., Los Angeles, Calif.

J. Appl. Mech 28(4), 491-496 (Dec 01, 1961) (6 pages) doi:10.1115/1.3641773 History: Received November 15, 1960; Online September 16, 2011

Abstract

The free oscillations of a fluid in a rotating, axially symmetric container are investigated under the assumption that the equilibrium motion of the fluid be a rigid-body rotation. Gravitational forces are neglected. The resulting boundary-value problem leads to an elliptic or hyperbolic partial differential equation, depending on the frequency/angular velocity ratio. The problem is solved for a cylindrical container and discussed exhaustively. Due to the Coriolis force, there exist modes with the radial velocity component vanishing inside the fluid (“nodal cylinders”), besides the usual nodes in axial and azimuthal direction. The oscillations in the neighborhood of critical container dimensions are analyzed. Numerical results are presented in graphs.

Copyright © 1961 by ASME
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