A modified equatorial β-plane approximation modelling nonlinear wave-current interactions
A modification of the standard geophysical equatorial β-plane model equations, incorporating a gravitational-correction term in the tangent plane approximation, is derived. We present an exact solution satisfying the modified equations, whose form is explicit in the Lagrangian framework, and which represents three-dimensional, nonlinear oceanic wave-current interactions. It is rigorously established, by way of analytical and degree-theoretical considerations, that the solution is dynamically possible, in the sense that the mapping it prescribes from Lagrangian to Eulerian coordinates is a global diffeomorphism.
Exact solution , Global diffeomorphism , Lagrangian variables , Wave-current interactions , β-Plane
Henry, D. (2017) 'A modified equatorial β-plane approximation modelling nonlinear wave-current interactions', Journal of Differential Equations, 263 (5), pp. 2554-2566. doi: 10.1016/j.jde.2017.04.007