On the incipient breaking of small scale waves

Abstract

It is shown that the surface wind drift in the ocean substantially reduces the maximum wave height ξ_xand wave orbital velocity that can be attained before breaking. Ifqis the magnitude of the surface drift at the point where the wave profile crosses the mean water level andcis the wave speed, then\[ \zeta_{\max} = \frac{c^2}{2g}\bigg(1-\frac{q}{c}\bigg)^2. \]Incipient breaking in a steady wave train is characterized by the occurrence of stagnation points at wave crests, but not necessarily by discontinuities in slope. After breaking, there is in the mean flow a stagnation point relative to the wave profile near the crest of the broken wave, on one side of which the water tumbles forward and behind which it recedes more smoothly to the rear. Some simple flow visualization studies indicate the general extent of the wake behind the breaking region.