Pattern Formation and Transients in the Convection Instability
In this contribution and the following one by Friedrich and Haken we want to show how methods of synergetics, in particular the slaving principle and the order parameter concept, allow us to calculate patterns, including transients, in fluids. The slaving principle enables us to reduce the full equations of fluid dynamics to “generalized Ginzburg Landau equations” for order parameters. These equations can be solved by a mediate size computer in a reasonable time. While in this paper we shall be concerned with regular patterns, the following one will also include chaotic motion.
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