Properties of Quasi One-Dimensional Rayleigh Benard Convection
Rayleigh Bénard convection1 is a well known phenomenon which develops striking spatial periodic structures in a fluid layer submitted to a destabilizing temperature gradient. In a rectangular container of horizontal extensions L x and L y large compared to the depth d, nice straight parallel rolls can be observed under some particular conditions2 near the critical Rayleigh number Ra c . When the convection is achieved with a high Prandtl number fluid, an increase of Ra beyond a well defined value RaII (about 10 Ra c ) generates a new set of rolls superimposed on the critical roll pattern. The axes of the two sets are mutually perpendicular. In both cases, the convection is stationary. The velocity field associated with the simple critical rolls (below RaII) is two-dimensional while, in the case of the two perpendicular sets of rolls a three-dimensional velocity field is excited. As far as the horizontal planeform is concerned (meaning that we disregard the vertical dependence of the velocity) the spatial properties only depend on one coordinate, say X, in the case of the rolls below Ra II; in this context we speak of one-dimensional convection, while above Ra II, where the two sets of rolls coexist, we speak of two-dimensional convection.
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