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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 4, Pages 46–61 (Mi vuu348)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Model of three dimensional double-diffusive convection with cells of an arbitrary shape

S. B. Kozitskii

Pacific Oceanological Institute, Vladivostok, Russia

Abstract: Three-dimensional double-diffusive convection in a horizontally infinite layer of an uncompressible liquid interacting with horizontal vorticity field is considered in the neighborhood of Hopf bifurcation points. A family of amplitude equations for variations of convective cells amplitude is derived by multiple-scaled method. Shape of the cells is given as a superposition of a finite number of convective rolls with different wave vectors.
For numerical simulation of the obtained systems of amplitude equations a few numerical schemes based on modern ETD (exponential time differencing) pseudospectral methods have been developed. The software packages have been written for simulation of roll-type convection and convection with square and hexagonal type cells. Numerical simulation has showed that the convection takes the form of elongated “clouds” or “filaments”. It has been noted that in the system quite rapidly a state of diffusive chaos is developed, where the initial symmetric state is destroyed and the convection becomes irregular both in space and time. At the same time in some areas there are bursts of vorticity.

Keywords: double-diffusive convection, amplitude equation, multiple-scale method.

Full text: PDF file (1265 kB)
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UDC: 517.955.8+532.529.2
MSC: 34E13, 76E06, 76R99
Received: 16.05.2012

Citation: S. B. Kozitskii, “Model of three dimensional double-diffusive convection with cells of an arbitrary shape”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 4, 46–61

Citation in format AMSBIB
\Bibitem{Koz12}
\by S.~B.~Kozitskii
\paper Model of three dimensional double-diffusive convection with cells of an arbitrary shape
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 4
\pages 46--61
\mathnet{http://mi.mathnet.ru/vuu348}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kazarnikov, S. V. Revina, “Bifurkatsii v sisteme Releya s diffuziei”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 499–514  mathnet  crossref  elib
    2. Kozitskiy S., “Numerical Simulation of Nonstationary Dissipative Structures in 3D Double-Diffusive Convection At Large Rayleigh Numbers”, Ocean Dyn., 68:6 (2018), 713–722  crossref  isi  scopus
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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