Article
Ufa Mathematical Journal
Volume 4, Number 4, pp. 78-89
Symmetries and exact solutions of the model of dynamic convection of the sea.
Golovin S.V., Kazakova M.Yu.
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Equations of the mathematical model of dynamic convection of the sea are considered. The model describes incompressible flows of shallow water with variable density under the action of the Coriolis force. This approximation is widely used for modeling mit-latitude oceanic and atmospheric flows. This model is exceptional from the group-theoretical point of view to its infinite-dimensional group of transformations that involves five arbitrary functions of time. The goal of the paper is to demonstrate the physical meaning of the symmetry transformations, to construct the optimal system of small dimensional subalgebras, and to represent new exact solutions, constructed on the base of the symmetry analysis.