Laboratory Simulation of Multidirectional Spectra of Ocean Waves
Authors: Chakrabarti Subrata K. , Snider Robert H. 
Published: October 2008

ABSTRACT
A method of obtaining the multidirectional components of an ocean wave and the directional distribution of its energy is developed. The theoretical development, based on real time wave records collected simultaneously at three or more adjacent wave staffs, uses the relative time of arrival of wave crests from one staff to another.
The directional distribution technique was verified through computer simulated wave data and was found to be accurate to within one degree of the true angle of wave propagation.
A four gauge system arranged in an equilateral triangular pattern with one gauge located at the center was used as the recording array in a wave tank. Variation of wave direction in relation to the gauge pattern was obtained by rotating this array within the tank. The data from these runs are combined to simulate multidirectional ocean waves. The experimental results demonstrate the applicability of this technique to design problems, using data recorded at the intended job site.

INTRODUCTION
Until recently, the design of offshore structures was based on the representation of the sea waves by a single sinusoid. While in some instances the simplification may be satisfactory, the wind-generated waves in the ocean cannot be represented adequately by a single sine wave. Consequently, the wave energy spectrum is becoming increasingly important in the design of submerged or semi-submersible structures. In addition to knowing the total energy in the wave, it is also desirable, for design purposes, to know the relative directional energy distribution. This distribution of energy with respect to wave direction is commonly known as the directional spectrum. The directional spectrum is equally essential to the wave forecaster in his study of wave generation and propagation and to the engineer in his study of coastlines and harbors.
Of the many techniques developed and employed in obtaining the directional spectrum of waves, the use of an array of wave staffs to record the wave profiles continuously has received the most attention (1-2, 4-9). One of the pioneers in this area was Barber (1-2). Stevens (9) measured the directional spectra by employing a linear array of detectors. Moberek (7) studied the wind generated wave in the laboratory in order to obtain the directional spectra. Borgman (4) utilized the method of co- and quad-spectra obtained from wave staff records to determine the directional distribution of energy. Borgman and Panicker (5, 8) later applied this theory to the field test data obtained from a wave gauge array off Point Mugu, California.
In the present study, the sea wave is represented by the summation of a finite number of single sinusoidal waves (e.g., 9). Thus, while others calculate the co- and quad-spectral densities of the actual wave profiles and then use an approximate representation, the theory developed here initially assumes a truncated Fourier series representation of the wave.
This paper is a generalization of the previous work by the senior author (6) on the unidirectional wave.