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Russia Vladivostok
Year
2012
Issue
4
Pages
46-61
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Section Mathematics
Title Model of three dimensional double-diffusive convection with cells of an arbitrary shape
Author(-s) Kozitskii S.B.a
Affiliations Pacific Oceanological Institute, Far Eastern Branch of the Russian Academy of Sciencesa
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
UDC 517.955.8, 532.529.2
MSC 34E13, 76E06, 76R99
DOI 10.20537/vm120404
Received 16 May 2012
Language Russian
Citation Kozitskii S.B. Model of three dimensional double-diffusive convection with cells of an arbitrary shape, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 4, pp. 46-61.
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