Abstract
The classical Ekman theoretical solution for steady-state wind-driven currents of homogeneous ocean with constant eddy viscosity was obtained more than a century ago. However, it is not clear how applicable this solution is for realistic stratified ocean with depth-dependent turbulent mixing coefficient (KM). In this study, the Ekman analytical solution is compared with currents obtained by one-dimensional Mellor–Yamada turbulent ocean model (1D-MY) to assess the accuracy of the Ekman solution under various oceanic conditions. For experiments with constant density but depth-dependent KM, the Ekman solution is close to the 1D model calculation if the analytical solution uses the mean KM obtained by the 1D model for each wind speed. Inclusion in the 1D-MY model, the Craig–Banner (C-B) turbulence induced by surface breaking waves makes the surface velocity in the model more like the Ekman surface velocity; however, C-B mixing only affects current direction and speed of the upper ~ 5 m and only for strong winds. Model experiments with different mixed layer (ML) depths show abrupt decline in turbulence and vanishing currents below the ML, so model currents below the ML are weaker than the Ekman solution for an unstratified ocean. The best comparison between the model and the Ekman solutions was found when the Ekman equations use mean KM calculated from the model over the ML depth plus 10 m of the thermocline below. Sensitivity model experiments with different winds and different stratifications resulted in an empirical formula that estimates the mean KM from observed wind and ML depth, and this relation can complement the classical Ekman formula in cases where KM is unknown.
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Data availability
No external data were used in the study. The M-Y model code is publicly available at http://www.ccpo.odu.edu/POMWEB/.
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Acknowledgements
The Center for Coastal Physical Oceanography (CCPO) provided facility and computational resources. The author is also affiliated with ODU’s Institute for Coastal Adaptation and Resilience (ICAR). Two anonymous reviewers are thanked for providing useful suggestions.
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Topical Collection of the 13th International Workshop on Modeling the Ocean (IWMO), Hamburg, Germany, 27-30 June 2023.
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Ezer, T. Evaluation of the applicability of the Ekman theory for wind-driven ocean currents: a comparison with the Mellor–Yamada turbulent model. Ocean Dynamics 73, 575–591 (2023). https://doi.org/10.1007/s10236-023-01570-y
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DOI: https://doi.org/10.1007/s10236-023-01570-y