Current Development in Theory and Applications of Wavelets
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Abstract: This paper concerns the evolution of groupiness of
irregular waves on a mild slope beach using both the continuous and discrete
wavelet transforms. Two cases of mechanically generated random waves based on Jonswap
spectra are used in this study. Waves for both cases propagate a
relatively long distance on the beach before breaking. The groupiness factor and mean run length are used to measure the degree of
wave groupiness. The results show that changes in wave groupiness occur outside
the surf zone and that groupiness decreases sharply across the surf zone. The
variations in wave groupiness are closely related to the changes of group
structures of the first harmonic of the waves And the process of uniformity of
the first harmonic energy along time, which is mainly caused by breaking, leads
to the decrease of groupiness in surf zone. Using a multi-resolution analysis
based on the discrete wavelet transform (DWT), the variations in wave groupiness
in the region where wave breaking is not predominant are mainly due to the
changes in the difference frequencybetween the peak
frequencies of the two series, whose energies are dominant in the waves, at two
time scales of DWT.
Keywords and phrases: wavelet transform, irregular waves, wave groupiness, nonlinearity.
