Dynamic Balances in a Wavy Boundary Layer

Abstract

Abstract The authors analyze the influence of waves on the budgets of momentum flux and kinetic energy in the atmospheric flow over sea surface waves and use the findings to reinterpret the results from the earlier empirical studies on the subject. This analysis employs the framework of wave–mean flow interaction and experimental data collected recently over the open ocean. From a minimal set of plausible assumptions, limited to small-slope waves and uncorrelated turbulent and wave-induced motions in the wind, this study demonstrates that the budgets apply separately to the turbulent and the wave-induced flows. The explicit forms of the wave-supported fluxes of momentum and kinetic energy favor wave spectra ∝ ω−β, 4 ≤ β ≤ 5 for wind–wave equilibrium. These explicit forms also show that in common conditions at heights above one significant wave height from the unperturbed surface, the wave-supported fluxes are a small fraction of the total, of the order of 5%. The wave influence on the kinetic energy budget and on the shape of the wind profile is therefore also small at these heights and thus difficult to identify experimentally next to influences from nonstationarity or horizontal inhomogeneity. Consequently, the predictions of Monin–Obukhov phenomenology show little sensitivity to wave effects. This makes the phenomenology as valid over the ocean as it is over land, but a poor instrument for studying wind–wave interaction. Describing the wind–wave interaction through the dynamics and statistics of the wave-induced motion remains a viable and productive alternative.