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A cylindrical coordinates approach concerning azimuthal geophysical flows

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Abstract

In this paper, we devise a new exact and partially explicit solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible azimuthal flow with a discontinuous density distribution that varies with both depth and latitude and subjected to forcing terms in terms of cylindrical coordinates. An analysis allows us to draw qualitative and quantitative results about the interface and the free surface of the azimuthal flow. Moreover, a particular example is considered to show that the interface can be determined explicitly. Finally, we obtain the expected monotonicity properties between the surface pressure and its distortion and derive an infinite regularity about the interface.

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Acknowledgements

The work of Fan is partially supported by a NSF of Henan Province of China Grant No. 222300420478 and the NSF of Henan Normal University Grant No. 2021PL04.

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  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Lili Fan & Shuge Shen

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  1. Lili Fan
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  2. Shuge Shen
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Correspondence to Lili Fan.

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Communicated by Adrian Constantin.

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Fan, L., Shen, S. A cylindrical coordinates approach concerning azimuthal geophysical flows. Monatsh Math 202, 791–806 (2023). https://doi.org/10.1007/s00605-023-01876-5

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