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Ocean Science An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/os-2020-31
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/os-2020-31
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 27 May 2020

Submitted as: research article | 27 May 2020

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This preprint is currently under review for the journal OS.

The Ekman spiral for piecewise-uniform diffusivity

David G. Dritschel1, Nathan Paldor2, and Adrian Constantin3 David G. Dritschel et al.
  • 1School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
  • 2The Fredy & Nadin Herrman Institue of Earth Sciences, The Hebrew University, Jerusalem 9190401, Israel
  • 3Department of Mathematics, University of Vienna, Vienna 1090, Austria

Abstract. We re-visit Ekman's (1905) classic problem of wind-stress induced ocean currents to help interpret observed deviations from Ekman's theory, in particular from the predicted surface current deflection of 45 degrees. While previous studies have shown that such deviations can be explained by a vertical eddy viscosity varying with depth, as opposed to the constant profile taken by Ekman, analytical progress has been impeded by the difficulty in solving Ekman's equation. Herein, we present a solution for piecewise-constant eddy viscosity which enables a comprehensive understanding of how the surface deflection angle depends on the vertical profile of eddy viscosity. For two layers, the dimensionless problem depends only on the depth of the upper layer and the ratio of layer viscosities. A single diagram then allows one to understand the dependence of the deflection angle on these two parameters.

David G. Dritschel et al.

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David G. Dritschel et al.

David G. Dritschel et al.

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Short summary
Ekman's (1905) solution for how wind affects ocean surface currents is revisited and extended analytically for a piecewise-constant profile of vertical diffusion. This allows a comprehensive understanding of how the surface current deflection angle relative to the wind direction varies with the profile of vertical diffusion.
Ekman's (1905) solution for how wind affects ocean surface currents is revisited and extended...
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