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

The aim of this paper is to provide, in a β -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.