Wave transformation across the inner surf zone

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Abstract
Sea and swell wave heights observed on transects crossing the mid and inner surf zone on three beaches (a steep concave‐up beach, a gently sloped approximately planar beach, and a beach with an approximately flat terrace adjacent to a steep foreshore) were depth limited (i.e., approximately independent of the offshore wave height), consistent with previous observations. The wave evolution is well predicted by a numerical model based on the one‐dimensional nonlinear shallow water equations with bore dissipation. The model is initialized with the time series of sea surface elevation and cross‐shore current observed at the most offshore sensors (located about 50 to 120 m from the mean shoreline in mean water depths 0.80 to 2.10 m). The model accurately predicts the cross‐shore variation of energy at both infragravity (nominally 0.004 < f < 0.05 Hz) and sea swell (here 0.05 < f ≤ 0.18 Hz) frequencies. In models of surf zone hydrodynamics, wave energy dissipation is frequently parameterized in terms of γs, the ratio of the sea swell significant wave height to the local mean water depth. The observed and predicted values of γs increase with increasing beach slope β and decreasing normalized (by a characteristic wavenumber k) water depth kh and are well correlated with β/kh, a measure of the fractional change in water depth over a wavelength. Errors in the predicted individual values of γs, are typically less than 20%. It has been suggested that infragravity motions affect waves in the sea swell band and hence γs, but this speculation is difficult to test with field observations. Numerical simulations suggest that for the range of conditions considered here, γs is insensitive to infragravity energy levels.

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