Kinematics Prediction by Stokes and Fourier Wave Theories

Abstract

Recent laboratory measurements of wave kinematics indicate that the horizontal velocity under the crest is smaller than that under the trough in the range of intermediate to deep water waves. The mathematically correct fifth‐order Stokes and Fourier wave theories can better predict the measured behavior if a zero uniform coflowing mass transport velocity is included in the solution algorithms. This is contrary to the conclusions made by Engevik and by Gudmestad and Connor. Horizontal velocity predictions from the Stokes and Fourier wave theories are in general more accurate than the deep‐water Green function method of Engevik and the second order stretching method of Gudmestad and Connor. The necessary correction procedure when using the Stokes and Fourier wave theories with a specified Eulerian current to predict the wave kinematics in a close flume with zero net flow over depth is also discussed in this paper.