Types of discrete symmetries of convection in a plane fluid layer

Abstract

The Rayleigh–Benard convection in a plane fluidlayer is actively studied both theoretically and experi-mentally. Diverse types of structures observed undernatural and laboratory conditions [1, 2] should be clas-sified, and the conditions of their existence should bedetermined. In this paper, in order to determine permis-sible types of convection structures in a fluid layerheated uniformly from below, the method of calculat-ing discrete symmetries is first applied. It unites themethods of continuous-group theory, the formalism ofdifferential forms, and the method of imbedding inhigher dimension space [3, 4].We consider the steady motion of a single fluidwhose density depends only on temperature as ρ = ρ