Abstract
Rayleigh-Benard convection in a plane layer with poorly conducting boundaries is considered. Two-dimensional equations, asymptotically exact for small supercriticalities, are obtained for describing largescale flows whose characteristic dimensions considerably exceed the thickness of the layer. An increase in the dimensions of the layer in plan and higher levels of supercriticality lead to complex turbulent motions of the fluid which are investigated by network methods and by means of an hierarchical model of turbulence. It is shown that the kinetic energy accumulates in the largest eddies, and that the temperature fluctuation spectrum has a maximum at intermediate scales.
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