Observations of the Directional Characteristics of Sea Waves

Summary Simultaneous records of orbital velocity and pressure disturbance in wind generated waves have been analysed by power spectral methods, to obtain the first five angular harmonics of the directional spectrum. The observations were made at a coastal site, offshore from a gently sloping beach, where the bottom topography was sufficiently simple to permit corrections for the effects of refraction. The orbital velocities were measured by an electromagnetic flowmeter and the pressure disturbance by an N.I.O. pressure recorder. A capacitance probe was also available for recording the surface elevation. A computer program has been developed which computes the auto and cross‐spectra of the pressure and velocity components, the angular harmonics and a smoothed estimate of the directional spectrum directly from data which were recorded digitally on punched paper tape. Estimates of the mean direction and the width of the directional spectrum and its skewness, have been obtained for a wide range of frequencies and related to wind conditions in the generating area. After correction for refraction, the mean direction of the waves was found to correspond well to the mean wind direction. For waves generated by a reasonably constant wind field, the spectrum width exhibits a general tendency to increase with frequency. At low frequencies the spectrum width corrected for refraction is not inconsistent with the resonance angle given by Phillips’ theory, while at frequencies just above the transition frequency defined by the combined Miles‐Phillips theory, the spectrum is appreciably narrower than the resonance angle. The smoothed directional spectrum estimate based on five harmonics gives no indication of bimodality in the spectrum. A method of obtaining improved angular resolution using an array of three flowmeters to obtain four additional harmonics was only partially successful on account of turbulent interference generated by the pier structure to which the sea units were attached. The surface power spectrum was found to fit the equilibrium power law at high frequencies under saturation conditions. A spectrum obtained under conditions very similar to those in the swop project has been compared with the swop spectrum. Marked differences between the two suggest that bottom friction is a major influence on waves in coastal waters. The attenuation of the waves in depth was determined from the ratios of the surface elevation and pressure spectra. No significant departure from the attenuation law based on linear theory was found in any part of the spectrum where the coherency between the surface elevation and pressure was high. The ratio of the velocity and pressure spectra was also found to be consistent with linear theory, thus confirming the relation between wavelength and frequency in water of finite depth. The amount of wave energy reflected from the shore proved to be negligible. The amplitude reflection coefficient, which was deduced from the relative phase of the pressure and velocity, is of order 0.05.