Phase-Mean Drift Equation for Convection Patterns in Large Aspect Ratio Containers
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.
KeywordsPrandtl Number Rayleigh Number Phase Equation Convection Pattern Circular Patch
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- Busse, F. H., “On the stability of two-dimensional convection in a layer heated from below,” J. Math. Phys., 46, 149–150 (1967).Google Scholar
- Eckhaus, A. W., Studies in Nonlinear Stability Theory, (New York: Springer-Verlag) (1965).Google Scholar
- Steinberg, V., Ahlers, G., Cannell, D. S., “Pattern formation and wavenumber selection by Rayleigh-Bénard convection in a cylindrical container,” Physica Scripta, T13, 135 (1985).Google Scholar