Dynamics of Partial Differential Equations
Volume 15 (2018)
An exact solution for geophysical trapped waves in the presence of an underlying current
Pages: 201 – 214
In this paper we propose an exact and explicit nonlinear solution to the governing equations which retains all the Coriolis terms. In the presence of an underlying current, we seek the trapped waves induced by these solutions in Northern and Southern hemisphere respectively, showing that the retention of the Coriolis force in the governing equations affects significantly the range of the admissible following and adverse currents.
exact solution, Lagrangian variables, Coriolis force, wave-current interactions
2010 Mathematics Subject Classification
37N10, 74G05, 76B15
The work of Fan is supported by a NSFC Grant No. 11701155, NSF of Henan Normal University, Grant No. 2016QK03, and the Startup Foundation for Introducing Talent of Henan Normal University, Grant No. qd16150. The work of Gao is partially supported by the NSFC grant No. 11171158, National Basic Research Program of China (973 Program) No. 2013CB834100, and PAPD of Jiangsu Higher Education Institutions. The work of Xiao is partially supported by the Fundamental Research Funds for the Central Universities (Grant No. KYZ201748).
Received 19 December 2017
Published 29 May 2018