Velocity profiles and surface roughness under breaking waves

Abstract

Recent measurements under wave‐breaking conditions in the ocean, lakes, and tanks reveal a layer immediately below the surface in which dissipation decays as depth to the power −2 to −4 and downwind velocities are approximately linear with depth. This behavior is consistent with predictions of a conventional, one‐dimensional, level 2.5 turbulence closure model, in which the influence of breaking waves is parameterized as a surface source of turbulent kinetic energy. The model provides an analytic solution which describes the near‐surface power law behavior and the deeper transition to the “law of the wall.” The mixing length imposed in the model increases linearly away from a minimum value, the roughness length, at the surface. The surface roughness emerges as an important scaling factor in the wave‐enhanced layer but is the major unknown in the formulation. Measurements in the wave‐affected layer are still rare, but one exceptional set, both in terms of its accuracy and proximity to the surface, is that collected by Cheung and Street [1988] in the Stanford wind tunnel. Their velocity profiles first confirm the accuracy of the model, and, second, allow estimation, via a best fit procedure, of roughness lengths at five different wind speeds. Conclusions are tentative but indicate that the roughness length increases with wind speed and appears to take a value of approximately one sixth the dominant surface wavelength. A more traditional wall‐layer model, which ignores the flux of turbulent kinetic energy, will also accurately reproduce the measured velocity profiles. In this case, enhanced surface turbulence is forced on the model by the assumption of a large surface roughness, three times that required by the full model. However, the wall‐layer model cannot predict the enhanced dissipation near the surface.