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.KeywordsPrandtl NumberRayleigh NumberPhase EquationConvection PatternCircular PatchThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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