Laboratory Study of Low-Frequency Waves Induced by Random Gravity Waves on Sloping Beaches

Low-frequency waves induced by the shoaling of random gravity waves (the primary waves) on sloping beaches were studied experimentally. Incident primary waves with a Pierson-Moskowitz (PM) spectrum were mechanically generated at a water depth of 0.7 m and propagated toward beaches with three different slopes (1/20, 1/30, and 1/40) in separate experiments. Four wave conditions with significant wave heights ranging from 0.078 to 0.125 m were used. The time series of surface elevations were simultaneously recorded at various water depths along the beach. Low-frequency waves were obtained from the data with a low-pass filter. Our results show that the spectra of low-frequency waves on beaches are dramatically changed by the beach slope and the wave height of incident primary waves. The cross-correlation of low-frequency waves with the surface-elevation envelope of the primary waves shows that the incident bound long waves are dominant. Free low-frequency waves propagate in the offshore direction with very low amplitudes due to high energy dissipation on the beach. The energy ratio between the low-frequency and the primary waves in the shoaling region outside the surf zone strongly correlates to the local surface skewness. For a given water depth, the low-frequency wave energy is proportional to m03/2, where m0 is the primary wave energy, in agreement with the field observations.