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Subharmonic resonance of nonlinear cross-waves

Published online by Cambridge University Press:  21 April 2006

Seth Lichter  and
Jerry Chen
Seth Lichter
Affiliation:
Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, USA
Jerry Chen
Affiliation:
Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, USA
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Abstract

The evolution equation governing wavemaker-generated cross-waves near a cutoff frequency in an infinitely deep, infinitely long channel is shown to be the nonlinear Schrödinger equation with a homogeneous boundary condition at the wavemaker. With the inclusion of an empirically determined damping coefficient, numerical results for growth rate, slow modulation period, and wave amplitude show good agreement with previous experiments. The results also describe observations of trapped and propagating solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 451 - 465
Copyright
© 1987 Cambridge University Press

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