A New Method for Measuring the Directional Wave Spectrum. Part I. Description

Abstract

A new method for measuring the directional wave spectrum is introduced, and the usefulness of the method is examined through numerical analysis of synthetic wave fields. The principle of the method consists of the direct application of the fast Fourier transform technique to the two-dimensional spectrum estimation. Unlike other known methods, the procedure is not based explicitly on the evaluation of the cross-covariance function or the cross spectrum. Two examples of wave gage arrangement for the method have been presented. The first army (Array A) consists of a set of twelve wave detectors equally spaced around a circle, and the second (Army B) consists of eight detectors on an outer circle and four detectors on an inner circle with half the radius of the outer. Denoting the nondimensional scale of the wave detector array by = 2r/L [where r is the radius of the (outer) wave detector circle and L the wavelength], the ranges in which the method is useful turn out to be 1.0 ≤ ≤ 1.18 and 1.25 ≤ ≤ 1.60 for Array A and 0.6 ≤ ≤ 1.7 for Array B. In this method, the use of an improper dispersion relation for actual wind waves is a possible factor in methodological error. Many of the spurious estimates obtained can be ascribed to the use of improper dispersion relations. Using this fact, it is possible to determine a reasonable dispersion relation for actual wind waves.