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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Longitudinal Dimensions of Polygon-shaped Planetary Waves

Journal of Applied Nonlinear Dynamics 4(2) (2015) 153--167 | DOI:10.5890/JAND.2015.06.005

Ranis N. Ibragimov; Guang Lin

$^{1}$ GE Global Research 1 Research Circle, Niskayuna, NY 12309, USA

$^{2}$ Department ofMathematics, and School of Mechanical Engineering, Purdue University,West Lafayette, IN 47907, USA

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Polygon-shaped longitudinal large-scale waves are described by means of higher-order shallow water approximation corresponding to the Cauchy–Poisson free boundary problem on the stationary motion of a perfect incompressible fluid circulating around a circle. It is shown that there are four basic physical parameters, which exert an influence on a wave number (or wave length), which is one of the basic values used to characterize the planetary flow pattern in mid-troposphere. Some analogy with the jet-stream following hexagon-shaped path at Saturn’s north pole is observed.


This research was supported in part by an appointment to the U.S. Department of Energy’s Visiting Faculty Program.


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