General Formulation of a Perturbation Theory for Unsteady Cavity Flows

[+] Author and Article Information
D. P. Wang, T. Yao-Tsu Wu

California Institute of Technology, Pasadena, Calif.

J. Basic Eng 87(4), 1006-1010 (Dec 01, 1965) (5 pages) doi:10.1115/1.3650791 History: Received March 08, 1965; Online November 03, 2011


The problem of a two-dimensional cavity flow of an ideal fluid with small unsteady disturbances in a gravity free field is considered. By regarding the unsteady motion as a small-perturbation of an established steady cavity flow, a fundamental formulation of the problem is presented. It is shown that the unsteady disturbance generates a surface wave propagating downstream along the free cavity boundary, much in the same way as the classical gravity waves in water, only with the centrifugal acceleration owing to the curvature of the streamlines in the basic flow playing the role of an equivalent gravity effect. As a particularly simple example, the surface waves in a hollow potential vortex flow is calculated using the present theory.

Copyright © 1965 by ASME
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