Journal of Nonlinear Mathematical Physics

Volume 26, Issue 4, July 2019, Pages 579 - 603

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

Authors
Dong Su
Institute of Mathematics, Nanjing Normal University Nanjing 210023, P.R. China dongsu@163.com.
Hongjun Gao
Institute of Mathematics, Nanjing Normal University Nanjing 210023, P.R. China gaohj@hotmail.com.
Received 10 September 2018, Accepted 23 May 2019, Available Online 9 July 2019.
DOI
https://doi.org/10.1080/14029251.2019.1640468How to use a DOI?
Keywords
Geophysical internal waves, modified β-plane, exact solution, mean velocity, mass flow, Lagrangian variables
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.

Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
26 - 4
Pages
579 - 603
Publication Date
2019/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2019.1640468How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Dong Su
AU  - Hongjun Gao
PY  - 2019
DA  - 2019/07
TI  - An exact solution for geophysical internal waves with underlying current in modified equatorial β-plane approximation*
JO  - Journal of Nonlinear Mathematical Physics
SP  - 579
EP  - 603
VL  - 26
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1640468
DO  - https://doi.org/10.1080/14029251.2019.1640468
ID  - Su2019
ER  -