Oceanographic wave buoy motion as a 3D-vector field: Spectra, linear components and bound harmonics

This study analyses time history data measured by a widely used type of oceanographic buoy. The motion of the buoy is recorded as a three-component displacement vector with one vertical and two horizontal components. Focusing on the average shapes of the large events in the time series, we investigate the linear and nonlinear structure of the displacements and their inherent relationships. All three displacements show clear evidence of both linear and second-order contributions. Two types of nonlinear contributions are identified: the difference term representing slow oscillation on the mooring system, and the sum term oscillating at roughly twice the frequency of the linear waves. These terms are small vertically but larger horizontally. We examine the coupled structure of the vertical and horizontal motions with a conditioning analysis. The averaged time histories associated with large waves are found to obey a simple reciprocal relationship, and the average shape of the motion in space associated with large waves in the sea-state resembles that in a localised steep wave-group. The power spectrum of the vertical motion can be transformed into those in the horizontal plane. This work demonstrates that, as well as providing accurate spectral information of the sea state, oceanographic wave buoys can provide internally consistent time series for the vector displacement field with little observable distortion from the mooring system.