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Constant Vorticity Ekman Flows in the \(\beta \)-Plane Approximation

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Abstract

In this paper, we study the classical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. Three dimensional Ekman flows with constant vorticity is considered in the \(\beta \)-plane approximation. It is remarkable that we explore a totally new approach, which is much different from procedure in (Martin J Fluid Mech 865:762–774, 2019; Chu and Yang J Differ Equ 269:9336–9347, 2020), to show that any Ekman flow with a flat surface and constant vorticity vector is the stationary flow with vanishing velocity field.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    JinRong Wang & Yi Guan

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

  4. Department of Mathematics and Information Science, Guiyang University, Guiyang, 550005, Guizhou, China

    Yi Guan

Authors
  1. JinRong Wang
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  2. Michal Fečkan
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  3. Yi Guan
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Correspondence to JinRong Wang.

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The authors declare that they have no conflict of interest.

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Communicated by A. Constantin.

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This work is partially supported by the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), Discipline and Master’s Site Construction Project of Guiyang University by Guiyang City Financial Support Guiyang University [2021-xk04], the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA Nos. 1/0358/20 and 2/0127/20.

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Wang, J., Fečkan, M. & Guan, Y. Constant Vorticity Ekman Flows in the \(\beta \)-Plane Approximation. J. Math. Fluid Mech. 23, 85 (2021). https://doi.org/10.1007/s00021-021-00612-z

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