Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems pp 197-209 | Cite as

# Phase-Mean Drift Equation for Convection Patterns in Large Aspect Ratio Containers

## Abstract

We present the phase diffusion and mean drift equation which describe the convection pattern in large aspect ratio containers for arbitrary large Rayleigh numbers. An exact agreement is found with the borders of the Busse balloon, concerning the long wavelength instabilities. We propose a calculation of the selected wavenumber which agrees closely with experiments and we predict a new instability which appears to be important in initiating time dependence. We predict also the Rayleigh numbers at which loss of spatial correlation due to global defect nucleation will occur.

## Keywords

Prandtl Number Rayleigh Number Phase Equation Convection Pattern Circular Patch## Preview

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