Observations of nonlinear interactions in directionally spread shoaling surface gravity waves

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Abstract
Shoaling wave fields generated in laboratory experiments were analyzed to determine the sensitivity of nonlinear interactions to the directional distributions of incident waves. Peaks in the directional spectra observed in shallow water were consistent with near‐resonant, quadratic interactions between two primary waves transferring energy to a third wave with the sum frequency and vector sum wavenumber of the primary waves. Directionally colinear waves forced a higher‐frequency wave propagating in the same direction as the primary waves, while directionally spread (i.e., noncolinear) primary waves forced a higher‐frequency wave that propagated in a direction between those of the interacting primary waves. Deepwater wave fields with similar frequency spectra but different directional spectra evolved to different shallow‐water directional spectra, yet their shallow‐water frequency spectra were remarkably similar. This result suggests that the shape of the directional spectrum of the incident wave field has only a small effect on the magnitudes of nonlinear energy transfers during shoaling. The principal effect of directionality in the incident wave field is on the directions, not the amplitudes, of the nonlinearly generated waves. The laboratory data demonstrate clearly the importance of triad interactions between noncolinear and colinear shoaling waves.