Dynamics of Partial Differential Equations

Volume 15 (2018)

Number 3

An exact solution for geophysical trapped waves in the presence of an underlying current

Pages: 201 – 214

DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n3.a3


Lili Fan (College of Mathematics and Information Science, Henan Normal University, Xinxiang, China)

Hongjun Gao (School of Mathematical Sciences, Nanjing Normal University, Nanjing, China; Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing Normal University, Nanjing, China)

Qingkun Xiao (College of Sciences, Nanjing Agricultural University, Nanjing, China)


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