Dynamics of Partial Differential Equations

Volume 20 (2023)

Number 2

Explicit solutions of atmospheric Ekman flows for some eddy viscosities in ellipsoidal coordinates

Pages: 99 – 115

DOI: https://dx.doi.org/10.4310/DPDE.2023.v20.n2.a1


Taoyu Yang (Department of Mathematics, Guizhou University, Guiyang, Guizhou, China)

Michal Fečkan (Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics & Informatics, Comenius University, Bratislava, Slovakia; and Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia)

Jinrong Wang (Department of Mathematics, Guizhou University, Guiyang, Guizhou, China)


In ellipsoidal coordinates, we study the motion of the wind in the steady atmospheric Ekman layer for the height-dependent eddy viscosities in the form of some quadratic, fourth and rational power functions. We construct the explicit solutions for these forms of the eddy viscosities by using suitable boundary conditions. Furthermore, we write down a formula of the angle between the wind vector and the geostrophic wind vector at any height.


ellipsoidal coordinates, Ekman layer, explicit solutions, variable eddy viscosity

2010 Mathematics Subject Classification

Primary 35Q35. Secondary 34A05.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Qian Ke He Ping Tai Ren Cai-YSZ[2022]002, by the Slovak Research and Development Agency under the contract No. APVV-18-0308, and by the Slovak Grant Agency VEGA No. 2/0127/20 and No. 1/0084/23.

Received 8 December 2022

Published 17 May 2023