Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 4

Constant vorticity atmospheric Ekman flows in the modified $\beta$-plane approximation

Pages: 311 – 321

DOI: https://dx.doi.org/10.4310/DPDE.2022.v19.n4.a4

Authors

Yi Guan (Department of Mathematics and Department of Mathematics & Information Science, Guizhou University, Guiyang, Guizhou, China)

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

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

Abstract

In this paper, we study the classical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. The full nonlinear governing equations with the general boundary conditions are considered in the sense of modified $\beta$‑plane approximation. Under the assumption of a flat surface and constant vorticity vector, we show that the flow has one nonvanishing component, a result that differs from that valid within the framework of the standard $\beta$‑plane approximation.

Keywords

Ekman layer, constant vorticity, modified $\beta$-plane approximation

2010 Mathematics Subject Classification

Primary 35Q31. Secondary 35J60, 76B15.

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1fundingThis work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), Youth Science and Technology Talents Growth Project of Guizhou Provincial Education Department ([2020]090), the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 2/0153/16 and No. 1/0078/17.

Received 27 September 2021

Published 14 December 2022