A Discrete Wavelet Analysis of Freak Waves in the Ocean

In the past few years, wavelet methods have been applied in coastal and ocean current data analysis [2, 5, 6]. These new tools have better performance than the traditional Fourier techniques. They localize the information in the time-frequency space and are capable of trading one type of resolution for the other, which renders them suitable for the analysis of nonstationary signals. It was first introduced in [5, 6] that the wavelet transform is a powerful tool for coastal and ocean engineering studies. An analysis of applying continuous wavelet transform spectrum analysis to the result of laboratory measurement of landslide-generated impulse waves was presented in [2]. In fact, the measured results are understandably unsteady, nonlinear, and nonstationary, hence the application of timelocalized wavelet transform analysis is shown to be a suitable as well as a useful approach. The analysis of correlating the time-frequency wavelet spectrum configurations in connection with the ambient parameters that drive the impulse wave process, with respect to time and space, leads to interesting and stimulating insights not previously known. In [7], an analysis of a set of available freak wave measurements gathered from several periods of continuous wave recordings made in the Sea of Japan during 1986–1990 by the Ship Research Institute of Japan was presented. The analysis provides an ideal opportunity to catch a glimpse of the incidence of freak waves. The results show that a well-defined freak wave can be readily identified from the wavelet spectrum, where strong energy density in the spectrum is instantly surged and seemingly carried over to the high-frequency components at the instant the freak wave occurs. Thus for a given freak wave, there appears a clear corresponding signature shown in the time-frequency wavelet spectrum.