Geodesic
Model of three dimensional double-diffusive convection with cells of an arbitrary shape
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2012), pp. 46-61

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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.
Mots-clés : double-diffusive convection, amplitude equation
Keywords: multiple-scale method. 
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     author = {S. B. Kozitskii},
     title = {Model of three dimensional double-diffusive convection with cells of an arbitrary shape},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {46--61},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2012_4_a3/}
}
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S. B. Kozitskii. Model of three dimensional double-diffusive convection with cells of an arbitrary shape. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2012), pp. 46-61. http://geodesic.mathdoc.fr/item/VUU_2012_4_a3/