Abstract
We present an exact solution to the nonlinear governing equations in the \begin{document}$ \beta $\end{document} -plane approximation for geophysical waves propagating at arbitrary latitude on a zonal current. Such an exact solution is explicit in the Lagrangian framework and represents three-dimensional, nonlinear oceanic wave-current interactions. Based on the short-wavelength instability approach, we prove criteria for the hydrodynamical instability of such waves.
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