An Experimental Study of the Statistical Properties of Wind-Generated Gravity Waves
Statistical properties of wind-generated waves are studied under laboratory conditions. The properties studied include distributions of various zero crossings; crest, trough, and wave amplitudes; local maxima and minima; group length and number of waves per group; and the joint probability distribution of amplitude and period. The results indicate that all the distribution functions are in qualitative agreement with the theoretical expressions derived by Longuet-Higgins in the late 1950s and early 1960s; however, systematic deviations from the results based on a joint Gaussian distribution are apparent. The most likely dynamical reasons for the deviations are: the nonlinear mechanism causing the unsymmetric crest and trough shape, and the breaking of waves. Both of these reasons for deviations are found to be controlled by a single internal variable, the significant slope, defined as the ratio of the rms wave height to the wavelength corresponding to the waves at the spectral peak. The significant slope is also found to be the controlling factor in determining the spectral shape and evolution. Thus, the present set of detailed observational data could be used as the base to link the dynamics and the statistical properties of the wind wave field.
KeywordsWave Field Wind Wave Joint Probability Distribution Fourth Moment Group Length
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