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The Ekman spiral for piecewise-uniform viscosity

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Dritschel_2020_Ekman_spiral_OS_16_1089_2020_CC.pdf (440.1Kb)
Date
18/09/2020
Author
Dritschel, David Gerard
Paldor, Nathan
Constantin, Adrian
Funder
EPSRC
Grant ID
EP/H001794/1
Keywords
GC Oceanography
QA Mathematics
T-NDAS
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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∘. 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.
Citation
Dritschel , D G , Paldor , N & Constantin , A 2020 , ' The Ekman spiral for piecewise-uniform viscosity ' , Ocean Science , vol. 16 , pp. 1089–1093 . https://doi.org/10.5194/os-2020-31
Publication
Ocean Science
Status
Peer reviewed
DOI
https://doi.org/10.5194/os-2020-31
ISSN
1812-0784
Type
Journal article
Rights
Copyright © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License.
Description
Funding: Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1).
Collections
  • University of St Andrews Research
URL
https://os.copernicus.org/articles/16/1089/2020/
URI
http://hdl.handle.net/10023/20664

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