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Exact Solution and Instability for Geophysical Waves with Centripetal Forces and at Arbitrary Latitude

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Abstract

The aim of this paper is to provide, in a \(\beta \)-plane approximation with centripetal forces, an explicit three-dimensional nonlinear solution for geophysical waves propagating at an arbitrary latitude, in the presence of a constant underlying background current. This solution is linearly unstable when the steepness of the wave exceeds a specific threshold.

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Acknowledgements

We would like to show our thanks to the anonymous referees for their valuable suggestions and comments.

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Authors and Affiliations

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

    Jifeng Chu

  2. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit No. 6, P.O. Box 1-764, 014700, Bucharest, Romania

    Delia Ionescu-Kruse

  3. Department of Mathematics, Hohai University, Nanjing, 210098, China

    Yanjuan Yang

Authors
  1. Jifeng Chu
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  2. Delia Ionescu-Kruse
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  3. Yanjuan Yang
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Corresponding author

Correspondence to Delia Ionescu-Kruse.

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Communicated by A. Constantin

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Jifeng Chu was supported by the National Natural Science Foundation of China (Grant No. 11671118 and No. 11871273). Yanjuan Yang was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2017B715X14).

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Chu, J., Ionescu-Kruse, D. & Yang, Y. Exact Solution and Instability for Geophysical Waves with Centripetal Forces and at Arbitrary Latitude. J. Math. Fluid Mech. 21, 19 (2019). https://doi.org/10.1007/s00021-019-0423-8

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