TITLE:
Visualization of Exact Invariant Solutions Associated with Atmospheric Waves in a Thin Circular Layer
AUTHORS:
Ranis N. Ibragimov, Lauren D. Mongrain, Benjamin Stimmel, Olga Trozkaya, Guang Lin, Sheng Zhang, Vesselin Vatchev, Daniel Stankiewicz
KEYWORDS:
Atmospheric Waves, Shallow Water Theory, Exact Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.5,
May
19,
2021
ABSTRACT: The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing the nonstationary motion of an incompressible perfect fluid propagating around a solid circle. We consider water waves for which the ratio of the depth of fluid above the circular bottom to the radius of the circle is small (shallow water).