SPATIOTEMPORAL PATTERNS IN THE THERMOCONVECTION OF A PLANAR NEMATIC LAYER - I - WEAKLY NONLINEAR MODELS

We study theoretically the formation of convection patterns in a later ally extended planar nematic layer heated from below, in the linear an d weakly nonlinear regimes. By reformulating the viscous coupling term s of the basic nematohydrodynamic equations, a simple interpretation o f the flow effects on the director dynamics can be proposed. A detaile d linear analysis of the problem is presented. A systematic method to investigate nonlinear mechanisms is developed, and exemplified by the study of the nonlinear saturation in roils. The extension of the roll amplitude equation with the envelope formalism is used to characterize the dynamics of the roll modulations near threshold. Coupled envelope equations are shown to describe the structure of the point defects in zig-tags observed experimentally. Finally the bifurcation to the bimo dal varicose is studied. The secondary wavevector in the bimodal appea rs to be selected by a rotation of the director in the horizontal plan e. Quantitative predictions concerning the amplitude of this rotation are given.