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Instability of Nonlinear Wave–Current Interactions in a Modified Equatorial \(\beta \)-Plane Approximation

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Abstract

We present an instability analysis of some exact and explicit solutions to the geophysical equatorial \(\beta \)-plane equations incorporating a gravitational-correction term. A criterion for the instability is given by means of the short-wavelength perturbation method. Thresholds for both, a solution with a zonal current under constant density and a solution admitting stratification, are derived and expressed in terms of the steepness of the waves.

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Acknowledgements

The author acknowledges the support of the Science Foundation Ireland (SFI) research Grant 13/CDA/2117

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  1. School of Mathematical Sciences, University College Cork, Cork, Ireland

    Adrián Rodríguez-Sanjurjo

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  1. Adrián Rodríguez-Sanjurjo
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Correspondence to Adrián Rodríguez-Sanjurjo.

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The author declares that he receives the support of the research Grant 13/CDA/2117 Science Foundation Ireland (SFI).

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Communicated by A. Constantin.

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Rodríguez-Sanjurjo, A. Instability of Nonlinear Wave–Current Interactions in a Modified Equatorial \(\beta \)-Plane Approximation. J. Math. Fluid Mech. 21, 24 (2019). https://doi.org/10.1007/s00021-019-0427-4

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  • DOI: https://doi.org/10.1007/s00021-019-0427-4

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