Application of Walsh Function to Multi-Directional Ocean Wave Simulation

Abstract

Irregular ocean waves are usually represented as the summation of the sinusoidal functions which have orthogonal characteristics. In order to save much computational time in ocean wave simulation, the Walsh function is very useful instead of the sinusoidal function.The Walsh function is a rectangular waveform taking only two amplitude value ±1. The Walsh function satisfies orthogonality and is a complete function set. The Walsh function is similar to sin-cos function. The frequency of sinusoidal function corresponds to the sequency of the Walsh function. Fourier transformation and FFT correspond to Walsh transformation and FWR (Fast Walsh Transformation) respectively.In this paper the authors show the procedure to generate Walsh function. Then they derive the procedure to transform the ocean wave spectrum in frequency domain to that in sequency domain. And they simulate irregular ocean waves based on the Walsh function which correspond to the wave spectrum in sequency domain. Finally they discuss the computational time of this simulation comparing with that of the sinusoidal function.They conclude the Walsh function is useful to reduce the computational time for the ocean wave simulation.