Experimental investigation on three-dimensional structures of wind wave surfaces

Abstract

This study experimentally investigated the three-dimensional features of wind wave surfaces in a laboratory. Free surfaces of wind waves under five types of wind velocities at four wind fetches were reconstructed by a stereo camera system. The dispersion law of wind waves was obtained from the spatio–temporal spectrum and showed a Doppler shift owing to the drift current. The wavenumber spectrum in the crosswind and wind direction follow the same power law of k−3 in the equilibrium range. Dynamic mode decomposition (DMD) was used to investigate the three-dimensional structures of the wave surface. Two different modes—the parallel mode and the net mode—were defined to characterize the structure of the wave surface. The parallel mode represents the average wave behavior over time, whereas the net mode represents the three-dimensional characteristics of the wind waves. The ratio of the wave number in the crosswind to the wind direction decreases with increasing wind fetch and converges to approximately 0.5. The wind wave spectrum in the wavenumber space had an elliptical distribution. Using the dispersion law, the wind wave spectrum in the (ω,k) domain can be predicted by a quartic surface.