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. "the law of the wall." Despite the apparently obvious difference between the free surface layer and, say, the bottom boundary Paper number 95JC03220. 0148-0227/96/95CJ-03220505.00 layer in the ocean or atmosphere, past measurements immediately below the water surface have tended to indicate a logarithmic velocity profile for wind-driven flow. This is true in tank experiments [e.g., Shemdin, 1972, 1973; Wu, 1975], in lakes [e.g., Churchill and Csanady, 1983; Csanady, 1984], and in the ocean [e.g., Richman e! al., 1987; Jones, 1985]. In each of these sets of measurements the influence of wave breaking appears not to have been detected either because winds were not sufficiently strong or because observations were not sufficiently close to the surface. A notable exception is Csanady [1984], who noticed a sublayer very close to the surface, within which the velocity profile was linear and which, he suggested, was due to breaking waves. Only recently have innovative techniques enabled measurements into the wave-affected layer. Both Kitaigorodskii e! al. [1983], using "drag spheres" mounted on a tower in Lake Ontario, and Thorpe [1984], using underwater acoustic reflections from bubbles in Loch Ness, postulated a wav...

The Effect of Wave Breaking on Surf-Zone Turbulence and Alongshore Currents: A Modeling Study*

“…By assuming a well-developed sea where the energy input by the wind balances that dissipated by wave breaking, ⑀ w is related to the wind friction velocity cubed. Such models have success in predicting enhanced dissipation in the surface layer (Craig and Banner 1994) and in reproducing (Terray et al 1999;Burchard 2001) the observed open-ocean dissipation depth scaling (Anis and Moum 1995;Drennan et al 1996). In contrast, in the surf zone the cross-shore gradient of onshore wave energy flux F x supplies turbulence to the water column; that is, for an alongshore uniform beach dF x /dx ϭ ⑀ w , which is estimated either by crossshore differencing F x measurements (e.g., Elgar et al 1997;Trowbridge and Elgar 2001) or from a wave transformation model (e.g., Thornton and Guza 1983).…”

“…To examine these issues, a one-dimensional (1D) vertical mean flow and turbulence model is developed (section 2) that incorporates the effect of breakingwave-generated turbulence through a time-dependent surface flux extending the steady approach often used in open-ocean modeling (Craig and Banner 1994;Burchard 2001). Model parameters are constrained by the literature and are not tuned to improve model-data agreement.…”

“…Turbulence in the open-ocean under breaking waves has been modeled using a steady surface flux of TKE (e.g., Craig and Banner 1994;Terray et al 1999;Burchard 2001), that is,…”

Effects of waves on coastal water dispersion in a small estuarine bay

“…Effects of wave breaking on vertical turbulence are taken into account through the surface boundary conditions for (A18) and (A19), which were adapted from Craig and Banner [1994], Craig [1996] by Burchard [2001]. The surface boundary conditions for q 2 =2 and are, respectively, given by …”

Description of the Navy Coastal Ocean Model Version 1.0

“…Since z s and z 0 are usually fairly small relative to the vertical grid resolution, the effect of this change is not usually significant. However, in the case of strong winds and breaking waves at the surface, the surface roughness can significantly increase the mixing in the surface mixed layer (Craig and Banner 1994;Craig 1996). The density p, which is used to calculate the vertical buoyancy gradient in the TKE equation, must not include the effect of local changes in pressure on the density; otherwise, the vertical stability will be overestimated.…”