Resonant Interactions for Waves Breaking on a Beach

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Abstract
A laboratory and theoretical study of the transition from strongly reflected surging to dissipative plunging breakers on a relatively steep plane beach (1:8) has revealed the following: (1) The run-up and offshore variation of sea surface elevation of surging waves are well predicted by linear theory. (2) The fluctuating part of the run-up (related to the amplitude of the reflected incident wave) reaches a maximum value; a further increase in incident progressive wave energy results in increased dissipation. (3) Subharmonic edge waves (the growing instabilities of surging waves) are driven primarily by the swash motion, which does not increase with increasing incident breaking wave height. However, the turbulence accompanying incident wave breaking, and the effective eddy viscosity, rapidly increases with increasing breaker height. As a result, subharmonic resonances do not occur with spilling or steep plunging waves; very strong viscous effects suppress the nonlinear instabilities. (4) edge waves generated by a surging incident wave can be suppressed by superimposing an additional breaking wave of different frequency on the incident wave field. Thus, any excited edge waves are likely to have length scales at least the order of a surf zone width.

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