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Resonance phenomena for water waves in channels of arbitrary cross-section

This article studies the evolutionary problem for linear gravity waves on the surface of water in a uniform, symmetric channel which is excited by an antisymmetric pressure force of frequency ω at the free surface. It is shown that there is a countably infinite set of frequencies {ω0, ω1, …} which give rise to resonance phenomena: the amplitude of the wave motion grows like t1/2 as t∞ in a sense which is precisely specified. Under pressure forcing at any other frequency the solution obeys the principle of limiting amplitude. These results are obtained by combining methods developed for problems in acoustic waveguides with regularity theory for elliptic boundary-value problems in non-smooth domains. Copyright © 1999 John Wiley & Sons, Ltd.