A simple method for calculating the velocity field beneath irregular waves: Fid-Bau Portal

A simple method for calculating the velocity field beneath irregular waves

Donelan, M.A. / Anctil, F. / Doering, J.C.

AbstractThe need for estimating water velocities beneath ocean waves for engineering calculations has produced ad hoc methods that are based on the relation between sea surface elevation and the velocity potential given by linear theory. These methods depend on some assumptions, which are, in general, clearly inappropriate for ocean waves. In this paper, we present a new, theoretically consistent method of superposition for a spectrum of linear waves and examine its characteristics with respect to several existing methods. Numerical simulations and laboratory data, collected using a surface-following device and an acoustic current meter, are used to test the relative accuracy of the new method and four existing methods of predicting wave-induced velocities. The results show that linear methods can provide reasonably accurate predictions of wave-induced velocities both at depth and near the free surface. In particular, predictions obtained using coordinate stretching and modified stretching methods as well as the new superposition method are in close agreement with measurements, while those given by the methods of extrapolation and direct linear theory grossly overpredict the near surface crest velocities. Rms errors indicate that, overall, the proposed method of superposition provides the most accurate predictions of wave-induced velocities. In addition, the new method satisfies Laplace's equation and also predicts correctly both the Eulerian and Lagrangian drift velocities under irregular waves, whereas the stretching methods fail in both these regards.