Wave energy input into the Ekman layer

Abstract

This paper is concerned with the wave energy input into the Ekman layer, based on 3 observational facts that surface waves could significantly affect the profile of the Ekman layer. Under the assumption of constant vertical diffusivity, the analytical form of wave energy input into the Ekman layer is derived. Analysis of the energy balance shows that the energy input to the Ekman layer through the wind stress and the interaction of the Stokes-drift with planetary vorticity can be divided into two kinds. One is the wind energy input, and the other is the wave energy input which is dependent on wind speed, wave characteristics and the wind direction relative to the wave direction. Estimates of wave energy input show that wave energy input can be up to 10% in high-latitude and high-wind speed areas and higher than 20% in the Antarctic Circumpolar Current, compared with the wind energy input into the classical Ekman layer. Results of this paper are of significance to the study of wave-induced large scale effects. Ekman layer, wind energy input, wave energy inputSince the surface mixed layer plays an important role in the coupling between the atmosphere and ocean, energetics of ocean circulation associated with wind energy flux to the surface mixed layer have taken on community interests in the past. Faller [1] first discussed the energetics of ocean circulation from wind stress, tidal dissipation and other sources. The global wind energy flux to inertial motions was estimated at 0.47-0.7 TW by Watanabe and Hibiya [2] and Alford [3] . Wunsch [4] and Huang et al. [5] made an estimate of the wind energy to geostrophic current at 1 TW. Wang and Huang [6] employed the classical Ekman model to estimate global wind energy input to the subinertial motions as 2.3-2.4 TW. Attempt to estimate the wind energy flux to surface waves has also been made recently by Wang and Huang [7] (60 TW). However, in the above-mentioned studies, energy inputs to currents and surface waves were discussed independently. Whether or not the surface waves could have influences on wind energy input to the currents remains unclear.The classical Ekman theory, assuming a balance between Coriolis force and the divergence of momentum transfer by turbulence stress, predicted a perfect current profile of Ekman spiral. However, observational evidence did not directly support the classical Ekman model. There are three features that cannot be predicted by the Ekman model. Firstly, the surface current lies at an angle between 10° and 45° to the surface wind stress [8] .Cushman-Roisin [9] documented a smaller angle ranging from 5° to 10°. Secondly, at a depth between 5 and 20 m the current is deflected by approximately 75° from the wind stress [10] . Thirdly, the current is rapidly attenuated below the surface [10] .Advances have been made recently in tackling the above-mentioned discrepancies between theory and observations. Recent studies show that the key to understanding the observed Ekman current profiles is the influence of surface wave motion via the Stoke...

Some aspects of the Coriolis‐Stokes forcing in the oceanic momentum and energy budgets

“…Has it a similar impact on the mean energy? This has been the subject of some recent studies [see e.g., Liu et al ., ; Wu and Liu , ; Wu et al ., ; Polton , ; Liu et al ., ].…”

“…There has been a number of studies to consider the effect of the CS force on the kinetic energy of the mean flow [see e.g., Liu et al ., ; Wu and Liu , ; Wu et al ., ; Polton , ; Liu et al ., ]. The general conclusion is that the CS force acts as a direct source term in the kinetic energy equation.…”