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Instability of equatorial edge waves in the background flow


Authors: Lili Fan and Hongjun Gao
Journal: Proc. Amer. Math. Soc. 145 (2017), 765-778
MSC (2010): Primary 35Q86, 76E20, 34E20, 76B70
DOI: https://doi.org/10.1090/proc/13308
Published electronically: October 20, 2016
MathSciNet review: 3577876
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Abstract: In this paper, we first present an explicit exact solution to the edge wave problem in stratified geophysical flows with an underlying longshore current. Then we analyze the short-wavelength perturbation approach for barotropic incompressible fluids. Finally, we prove, by applying this method to geophysical equatorial edge waves in the background flow, that these waves are unstable when their steepness exceeds a specific threshold.


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Additional Information

Lili Fan
Affiliation: School of Mathematical Sciences, Institute of Mathematics, Nanjing Normal University, Nanjing 210023, People’s Republic of China; College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, People’s Republic of China
Email: fanlily89@126.com

Hongjun Gao
Affiliation: School of Mathematical Sciences, Institute of Mathematics and Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing Normal University, Nanjing 210023, People’s Republic of China—and—Institute of Mathematics, Jilin University, Changchun 130012, People’s Republic of China, corresponding author
Email: gaohj@njnu.edu.cn

DOI: https://doi.org/10.1090/proc/13308
Keywords: Short-wavelength method, localized instability analysis, edge waves, Coriolis effects, stratification, exact solutions, current
Received by editor(s): April 18, 2016
Published electronically: October 20, 2016
Communicated by: Catherine Sulem
Article copyright: © Copyright 2016 American Mathematical Society