Mean Flows and the Onset of Time-Dependence in Convection
We report recent progress in the understanding of the transition to time-dependence in convective patterns. These works refer to the fundamental role played by mean flows in convection and especially to their non-local character. In the following, two different situations are addressed. In the first one, the mean flow effects are forced; in the second one, they develop freely. In the latter case, we construct an analytical solution which succeeds in simultaneously handling global nonlocal modes and local unstable ones. This solution provides an understanding of the overinstability of distorted patterns in convection and of the influence of the Prandtl number on the route to turbulence.
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