Journal of Fluid Mechanics



On steep gravity waves meeting a vertical wall: a triple instability


MICHAEL S. LONGUET-HIGGINS a1 and DAVID A. DRAZEN a2
a1 Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0402, USA
a2 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0213, USA

Abstract

Theoretical arguments suggest that progressive gravity waves incident on a vertical wall can produce periodic standing waves only if the incident wave steepness ak is quite small, certainly less than 0.284. Laboratory experiments are carried out in which an incident wave train of almost uniform amplitude meets a vertical barrier. At wave steepnesses greater than 0.236 the resulting motion near the barrier is non-periodic. A growing instability is observed in which every third wave crest is steeper than its neighbours. The steep waves develop sharp crests, or vertical jets. The two neighbouring crests are rounded, at-topped, or of intermediate form. The instability grows by a factor of about 2.2 for every three wave periods, almost independently of the incident wave steepness.

(Received October 21 2001)
(Revised March 20 2002)



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