Comment on Enhanced TKE Dissipation under Breaking Waves

It is noted that the results of recent experiments on the enhancement of turbulent kinetic energy (TKE) dissipation below surface waves can be stated as follows. TKE dissipation is enhanced by a factor 15Hws/z at depths 0.5Hws < z < 20Hws with respect to the wall-layer result ǫ = u ∗w/κz, where u∗w is the friction velocity in water and Hws is the significant windsea wave height. For open ocean conditions, this reduces in most cases to an enhancement factor 10u ∗w/gz ≈ U 2 10/gz. Recently, a group of experimentalists and theorists has succeeded in measuring and interpreting how turbulent kinetic energy dissipation is much enhanced below surface waves in the WAVES experiment (Agrawal et al. 1992, Terray et al. 1996) and also in the SWADE experiment (Drennan et al. 1996). In Fig. 1a, their results are shown for the enhancement of TKE dissipation ǫ with respect to to the wall-layer result ǫwall = u 3 ∗w/κz as a function of dimensionless depth gz/u 2 ∗w. Here u∗w is the friction velocity in water. A general enhancement is clear, but there is no clear relationship between the enhancement factor and the dimensionless depth. Moreover, WAVES and SWADE data appear to be different. Terray et al. 1996 point out that there are two important scaling variables for wave-enhanced TKE dissipation: windsea wave height Hws and energy dissipation of surface waves. The latter will be equal to the energy input F from the wind to surface waves. Using these variables, they find a clear relation: ǫHws/F = 0.3(Hws/z) 2 for WAVES. The SWADE data (Drennan et al. 1996) satisfy the very same relation as the WAVES data (Fig. 1b). To estimate enhanced TKE dissipation, the relation of Terray et al. has the drawback that one has to estimate somehow the wind input F . But this is not really necessary. An equally good fit can be obtained by using u ∗w instead of F , with the added advantage that the result can be written as an enhancement factor times the wall-layer result. This is shown in Fig. 1c. The straight line corresponds to ǫ = 15 H z u ∗w κz (1) Note that Fig. 1 is a log-log plot and that the uncertainty in the factor 15 is quite large. The fit of Fig. 1b is only slightly better than the fit of Fig. 1c; a slightly better fit than that of Fig. 1b can be obtained using u ∗wcp instead of F (not shown), with cp the wave velocity at the windsea peak frequency. Aproaching the surface, TKE dissipation should not grow without bound. Using that TKE dissipation integrated over depth should equal the wind-input F , Terray et al. 1996 arrived at a