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An analysis of some exact solutions for stratified wind-stress flows with centripetal effects

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Abstract

In this paper, we present an exact purely azimuthal solution for the governing equations of three-dimensional wind-stress geophysical stratified flows over an impermeable flat bed and with a flat surface, with centripetal effects at arbitrary latitude. In general stratification (depending on the depth and latitude but not on the azimuthal direction), we consider the governing equation in the \(\beta\)-plane approximation. For the special two-layer model (due to the strong stratification), we analyze the problem in the f-plane approximation. Moreover, in the two-layer flows, we prove some monotonicity results with respect to the strength of the wind speed near the ocean’s surface.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, China

    Yanjuan Yang

  2. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Xun Wang

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  1. Yanjuan Yang
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  2. Xun Wang
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Correspondence to Yanjuan Yang.

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This work was supported by the China Postdoctoral Science Foundation (Grant No. 2021M702037) and the Shandong Provincial Natural Science Foundation (Grant No. ZR2021QA048).

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Yang, Y., Wang, X. An analysis of some exact solutions for stratified wind-stress flows with centripetal effects. Annali di Matematica 201, 2663–2676 (2022). https://doi.org/10.1007/s10231-022-01213-x

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