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Explicit solution of atmospheric Ekman flows with some types of Eddy viscosity

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Abstract

In this paper, we study the standard problem of the wind in the steady atmospheric Ekman layer with classical boundary conditions. We consider the system with varying eddy viscosity coefficients that are small perturbation of a constant. We derive the explicit solution by using a different argument in the previous works. For two layers, the eddy viscosity is constant in the upper layer, while is only continuous with height in the lower layer, we transform the system to a first order Riccati equation with a suitable initial value and derive the solution for piecewise-constant eddy viscosity.

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Authors and Affiliations

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

    Yi Guan & JinRong Wang

  2. School of Mathematical and Information Sciences, Guiyang University, Guiyang, 550005, Guizhou, China

    Yi Guan

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

    Michal Fečkan

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

    Michal Fečkan

  5. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    JinRong Wang

Authors
  1. Yi Guan
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  2. Michal Fečkan
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  3. JinRong Wang
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Corresponding author

Correspondence to JinRong Wang.

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Communicated by Adrian 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), Department of Science and Technology of Guizhou Province (Fundamental Research Program [2018]1118), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), Natural Science Foundation of Guizhou Province ([2020]090), the Slovak Research and Development Agency under the Contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20.

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Guan, Y., Fečkan, M. & Wang, J. Explicit solution of atmospheric Ekman flows with some types of Eddy viscosity. Monatsh Math 197, 71–84 (2022). https://doi.org/10.1007/s00605-021-01551-7

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  • DOI: https://doi.org/10.1007/s00605-021-01551-7

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