Sea surface waves significantly affect the wind energy input to the Ekman layer in the upper ocean. In the study, we first incorporated the wave-induced Coriolis-Stokes forcing, the reduction of wind stress caused by wave generation, and wave dissipation into the classical Ekman model to investigate the kinetic energy balance in the wave-affected Ekman layer. Then, both the theoretical steady-state solution for the idealized condition and the non-steady state solution for the realistic ocean were derived. Total energy input to the wave-affected Ekman layer includes the wind stress energy input and the wave-induced energy input. Based on the WAVEWATCH III model, the wave spectra were simulated to represent realistic random directional wave conditions. The wind stress energy input and the wave-induced energy input to the wave-affected Ekman layer in the Antarctic Circumpolar Current (ACC) in the period from 1988 to 2010 were then calculated. The annual mean total energy input in the ACC region was 402.5 GW and the proportions of the wind stress energy input and the wave-induced energy input were respectively 85% and 15%. Particularly, total energy input in the ACC in the wave-affected Ekman layer model was 59.8% lower than that in the classical Ekman model. We conclude that surface waves play a significant role in the wind energy input to the Ekman layer.

Supplement to: Zhang, Yuming; Song, Zhaoyang; Wu, Kejian; Shi, Yongfang (2019): Influences of random surface waves on the estimates of wind energy input to the Ekman layer in the Antarctic circumpolar current region. Journal of Geophysical Research: Oceans