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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


An Approach to the Modeling of Nonlinear Structures in Systems with a Multi-component Convection

Discontinuity, Nonlinearity, and Complexity 4(3) (2016) 323--331 | DOI:10.5890/DNC.2016.09.008

Sergey Kozitskiy

Department of Oceanic and Atmospheric Physics, Il’ichev Pacific Oceanological Institute, 43 Baltiyskay str.Vladivostok, 690041, Russia

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We consider 3D multi-component convection in a horizontally infinite layer of an uncompressible fluid slowly rotating around a vertical axis. A family of CGLE type amplitude equations is derived by multiple-scaled method in the neighborhood of Hopf bifurcation points. We numerically simulate a case of the three-mode convection at large Rayleigh numbers. It was shown that the convection typically takes a form of hexagonal structures for a localized initial conditions. The rotation of the system prevents the spread of the convective structures on the entire area. The approach to the modeling of the Saturn’s polar hexagon on the basis of amplitude equations is discussed.


This work is supported by RFBR grant 14-05-00017.


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