Directional Wave Spectra from Wave Sensors
The measurement of directional ocean wave spectra with in situ instruments in the ocean environment requires arrays consisting of relatively few sensors. More elaborate systems are difficult and costly to maintain.
A unified mathematical procedure to treat sparse arrays of sensors is presented. The basic starting point for the analysis is a system of integral equations which must be inverted to estimate the directional spectral density at each frequency. The system is reduced to a set of linear equations if a Fourier series for the spreading function on all or a part of the circle is introduced. Various parameterized models may be fitted using the Fourier coefficients of the series. A sequential estimate enhancement procedure involving the higher harmonics of the fitted model and the lower order harmonics included in the linear system of equations is outlined.
The formulas for a variety of particular sensor arrays are summarized in the Appendix. In addition, some sample computations showing realistic, although artificial, data are presented.
KeywordsFourier Coefficient Wave Train Coastal Engineer Directional Spectrum Sparse Array
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