An exact solution for geophysical internal waves with underlying current in modified equatorial β -plane approximation^*

* The work is supported in part by a NSFC Grant No. 11531006, PAPD of Jiangsu Higher Education Institutions, and the Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Applications.

Abstract

In this paper, 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 to meet the modified governing equations, whose form is explicit in the Lagrangian framework and which represents internal oceanic waves in the presence of a constant underlying current. It is rigorously established, that the solution is dynamically possible, by way of analytical and degree-theoretical considerations. In the sense that the mapping it prescribes from Lagrangian to Eulerian coordinates is a global diffeomorphism. In addition, the paper an analysis of the mean flow velocities and related mass transport are presented in this paper, they are induced by certain geophysical internal waves. In particular, we examine an exact solution to the geophysical governing equations in the modified β-plane approximation at the equator which incorporates a constant underlying current.

Keywords:

• Geophysical internal waves
• modified β-plane
• exact solution
• mean velocity
• mass flow
• Lagrangian variables

2000 Mathematics Subject Classification:

• 22E46
• 53C35
• 57S20

Notes

* The work is supported in part by a NSFC Grant No. 11531006, PAPD of Jiangsu Higher Education Institutions, and the Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Applications.