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Nonlinear waves in a Kelvin-Helmholtz flow

Published online by Cambridge University Press:  29 March 2006

Ali Hasan Nayfeh
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
William S. Saric
Affiliation:
Sandia Laboratories, Albuquerque, New Mexico

Abstract

Nonlinear waves on the interface of two incompressible in viscid fluids of different densities and arbitrary surface tension are analysed using the method of multiple scales. Third-order equations are presented for the space and time variation of the wavenumber, frequency, amplitude and phase of stable waves. A third-order expansion is also given for wavenumbers near the linear neutrally stable wave-numbers. A second-order expansion is presented for wavenumbers near the second harmonic resonant wavenumber, for which the fundamental and its second harmonic have the same phase velocity. This expansion shows that this resonance does not lead to instabilities.

Type
Research Article
Copyright
© 1972 Cambridge University Press

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