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

  • Adrián Rodríguez-SanjurjoEmail author


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.


Geophysical flows Exact solutions Short-wavelength stability method 

Mathematics Subject Classification

76B15 76E20 37H15 



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

Compliance with ethical standards

Conflict of interest

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


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity College CorkCorkIreland

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