Articles | Volume 16, issue 5
https://doi.org/10.5194/os-16-1089-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/os-16-1089-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| Highlight paper
| 
18 Sep 2020
Research article | Highlight paper |
| 18 Sep 2020
| 18 Sep 2020
The Ekman spiral for piecewise-uniform viscosity
David G. Dritschel
CORRESPONDING AUTHOR
School of Mathematics and Statistics, University of St Andrews,
St Andrews KY16 9SS, UK
Nathan Paldor
The Fredy & Nadine Herrmann Institute of Earth Sciences,
The Hebrew University, Jerusalem 9190401, Israel
Adrian Constantin
Department of Mathematics, University of Vienna, Vienna 1090,
Austria
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Cited
31 citations as recorded by crossref.
- Exact solutions of the Beaufort Gyre in the presence of ice W. Zhang & H. Zhang https://doi.org/10.1063/5.0279592
- The surface current of Ekman flows with time-dependent eddy viscosity L. Roberti https://doi.org/10.3934/cpaa.2022064
- Boundedness of atmospheric Ekman flows with two-layer eddy viscosity Y. Guan https://doi.org/10.1063/5.0142172
- Atmospheric Ekman Flow Varying With Latitude in the Northern Hemisphere Y. Guan et al. https://doi.org/10.1155/jom/6652604
- A Unifying Perspective on Transfer Function Solutions to the Unsteady Ekman Problem J. Lilly & S. Elipot https://doi.org/10.3390/fluids6020085
- Explicit Solution and Boundedness Analysis of Atmospheric Ekman Flows with a Three-Layer of Eddy Viscosity J. Feng et al. https://doi.org/10.1007/s12346-025-01244-8
- Explicit solutions of atmospheric Ekman flow with some cases of eddy viscosities Y. Guan & J. Wang https://doi.org/10.1007/s00605-023-01854-x
- The atmospheric Ekman flows with time-dependent eddy viscosity Y. Guan https://doi.org/10.1016/j.dynatmoce.2024.101496
- Constant Vorticity Ekman Flows in the $$\beta $$-Plane Approximation J. Wang et al. https://doi.org/10.1007/s00021-021-00612-z
- Local and Global Analysis for Discontinuous Atmospheric Ekman Equations J. Wang et al. https://doi.org/10.1007/s10884-021-10037-x
- Sensitivity of boundary layer features to depth-dependent baroclinic pressure gradient and turbulent mixing in an ocean of finite depth V. Llorente et al. https://doi.org/10.1016/j.ocemod.2024.102359
- Variable Eddy Viscosities in the Atmospheric Boundary Layer from Ageostrophic Wind-Speed Profiles T. Lyons https://doi.org/10.1007/s00021-021-00575-1
- Nonlinear wind-drift ocean currents in arctic regions A. Constantin https://doi.org/10.1080/03091929.2021.1981307
- A boundary-value problem arising in the modelling of equatorial wind-drift currents K. Marynets https://doi.org/10.1007/s00605-021-01552-6
- Regenerative Orr mechanism yielding large non-modal perturbation energy growth in a viscosity stratified plane shear flow S. Jose https://doi.org/10.1016/j.ijmultiphaseflow.2024.105001
- Perturbation Analysis for the Surface Deflection Angle of Ekman-Type Flows with Variable Eddy Viscosity L. Roberti https://doi.org/10.1007/s00021-021-00586-y
- An exact solution representing equatorial wind-drift currents with depth-dependent continuous stratification L. Fan & R. Liu https://doi.org/10.1007/s00605-022-01759-1
- Ekman-inertial instability N. Grisouard & V. Zemskova https://doi.org/10.1103/PhysRevFluids.5.124802
- Nonlinear dynamics of wind-drift currents at mid-latitudes C. Puntini https://doi.org/10.1016/j.nonrwa.2025.104557
- The Ekman spiral for piecewise-constant eddy viscosity L. Roberti https://doi.org/10.1080/00036811.2021.1896709
- Atmospheric Ekman-type solutions with some eddy viscosities in ellipsoidal coordinates T. Yang et al. https://doi.org/10.1080/00036811.2022.2147068
- Explicit solution of atmospheric Ekman flows with some types of Eddy viscosity Y. Guan et al. https://doi.org/10.1007/s00605-021-01551-7
- Stability analysis of the boundary value problem modelling a two-layer ocean K. Marynets https://doi.org/10.3934/cpaa.2022083
- The Ekman spiral for two types of eddy viscosities Y. Guan et al. https://doi.org/10.1080/00036811.2022.2044026
- On flow simplification occurring in viscous three-dimensional water flows with constant non-vanishing vorticity C. Martin https://doi.org/10.1016/j.aml.2021.107690
- Analytical Atmospheric Ekman-Type Solutions with Height-Dependent Eddy Viscosities D. Ionescu-Kruse https://doi.org/10.1007/s00021-020-00543-1
- Existence and stability results for steady atmospheric Ekman flows in ellipsoidal coordinates T. Yang et al. https://doi.org/10.1016/j.cjph.2025.03.009
- The deflection angle between a wind-forced surface current and the overlying wind in an ocean with vertically varying eddy viscosity A. Constantin et al. https://doi.org/10.1063/5.0030473
- Influence of Stratification and Bottom Boundary Layer on the Classical Ekman Model V. Santander-Rodríguez et al. https://doi.org/10.3390/jmse10101388
- The atmospheric Ekman spiral for piecewise-uniform eddy viscosity E. Stefanescu https://doi.org/10.1088/1402-4896/ad6d1b
- Ekman-type solutions of surface ocean currents with vertically varying eddy viscosity W. Zhang & H. Zhang https://doi.org/10.1007/s00605-024-02040-3
31 citations as recorded by crossref.
- Exact solutions of the Beaufort Gyre in the presence of ice W. Zhang & H. Zhang https://doi.org/10.1063/5.0279592
- The surface current of Ekman flows with time-dependent eddy viscosity L. Roberti https://doi.org/10.3934/cpaa.2022064
- Boundedness of atmospheric Ekman flows with two-layer eddy viscosity Y. Guan https://doi.org/10.1063/5.0142172
- Atmospheric Ekman Flow Varying With Latitude in the Northern Hemisphere Y. Guan et al. https://doi.org/10.1155/jom/6652604
- A Unifying Perspective on Transfer Function Solutions to the Unsteady Ekman Problem J. Lilly & S. Elipot https://doi.org/10.3390/fluids6020085
- Explicit Solution and Boundedness Analysis of Atmospheric Ekman Flows with a Three-Layer of Eddy Viscosity J. Feng et al. https://doi.org/10.1007/s12346-025-01244-8
- Explicit solutions of atmospheric Ekman flow with some cases of eddy viscosities Y. Guan & J. Wang https://doi.org/10.1007/s00605-023-01854-x
- The atmospheric Ekman flows with time-dependent eddy viscosity Y. Guan https://doi.org/10.1016/j.dynatmoce.2024.101496
- Constant Vorticity Ekman Flows in the $$\beta $$-Plane Approximation J. Wang et al. https://doi.org/10.1007/s00021-021-00612-z
- Local and Global Analysis for Discontinuous Atmospheric Ekman Equations J. Wang et al. https://doi.org/10.1007/s10884-021-10037-x
- Sensitivity of boundary layer features to depth-dependent baroclinic pressure gradient and turbulent mixing in an ocean of finite depth V. Llorente et al. https://doi.org/10.1016/j.ocemod.2024.102359
- Variable Eddy Viscosities in the Atmospheric Boundary Layer from Ageostrophic Wind-Speed Profiles T. Lyons https://doi.org/10.1007/s00021-021-00575-1
- Nonlinear wind-drift ocean currents in arctic regions A. Constantin https://doi.org/10.1080/03091929.2021.1981307
- A boundary-value problem arising in the modelling of equatorial wind-drift currents K. Marynets https://doi.org/10.1007/s00605-021-01552-6
- Regenerative Orr mechanism yielding large non-modal perturbation energy growth in a viscosity stratified plane shear flow S. Jose https://doi.org/10.1016/j.ijmultiphaseflow.2024.105001
- Perturbation Analysis for the Surface Deflection Angle of Ekman-Type Flows with Variable Eddy Viscosity L. Roberti https://doi.org/10.1007/s00021-021-00586-y
- An exact solution representing equatorial wind-drift currents with depth-dependent continuous stratification L. Fan & R. Liu https://doi.org/10.1007/s00605-022-01759-1
- Ekman-inertial instability N. Grisouard & V. Zemskova https://doi.org/10.1103/PhysRevFluids.5.124802
- Nonlinear dynamics of wind-drift currents at mid-latitudes C. Puntini https://doi.org/10.1016/j.nonrwa.2025.104557
- The Ekman spiral for piecewise-constant eddy viscosity L. Roberti https://doi.org/10.1080/00036811.2021.1896709
- Atmospheric Ekman-type solutions with some eddy viscosities in ellipsoidal coordinates T. Yang et al. https://doi.org/10.1080/00036811.2022.2147068
- Explicit solution of atmospheric Ekman flows with some types of Eddy viscosity Y. Guan et al. https://doi.org/10.1007/s00605-021-01551-7
- Stability analysis of the boundary value problem modelling a two-layer ocean K. Marynets https://doi.org/10.3934/cpaa.2022083
- The Ekman spiral for two types of eddy viscosities Y. Guan et al. https://doi.org/10.1080/00036811.2022.2044026
- On flow simplification occurring in viscous three-dimensional water flows with constant non-vanishing vorticity C. Martin https://doi.org/10.1016/j.aml.2021.107690
- Analytical Atmospheric Ekman-Type Solutions with Height-Dependent Eddy Viscosities D. Ionescu-Kruse https://doi.org/10.1007/s00021-020-00543-1
- Existence and stability results for steady atmospheric Ekman flows in ellipsoidal coordinates T. Yang et al. https://doi.org/10.1016/j.cjph.2025.03.009
- The deflection angle between a wind-forced surface current and the overlying wind in an ocean with vertically varying eddy viscosity A. Constantin et al. https://doi.org/10.1063/5.0030473
- Influence of Stratification and Bottom Boundary Layer on the Classical Ekman Model V. Santander-Rodríguez et al. https://doi.org/10.3390/jmse10101388
- The atmospheric Ekman spiral for piecewise-uniform eddy viscosity E. Stefanescu https://doi.org/10.1088/1402-4896/ad6d1b
- Ekman-type solutions of surface ocean currents with vertically varying eddy viscosity W. Zhang & H. Zhang https://doi.org/10.1007/s00605-024-02040-3
Saved (final revised paper)
Latest update: 30 May 2026
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...
