Fractals and Nonlinearity of Ocean Waves

Abstract

From observations using secondary field data and dimension calculations, ocean waves exhibit fractals. Fractals are also hypothesized to have a direct relation with the degree of the waves nonlinearity. We took secondary data of 40 time series of wave record taken from Grays Harbor Wave Refraction Experiment, Washington in 1999. The data are divided into two groups, one group being data taken from the water depth of 25 meters and second group being data taken from water depth of 12 meters. The selection of data is in such a way that the second group is the waves traveling from the first group. We use rescaled range analysis to calculate the fractal dimension of the waves and Goda nonlinearity parameter as a measure of the waves nonlinearity. From the results, we confirm that fractals are a function of waves nonlinearity.

Keywords

• Fractals; nonlinear; Waves; Rescaled range analysis; Benoit; Fractal dimension; Nonlinearity Parameter; Skewness.