Phase Turbulence and Mean Flow Effects in Rayleigh-Bénard Convection
Hydrodynamical experiments have been widely used to study the transition to turbulence, especially when they could provide closed flows, well controlled and without external disturbances. Two famous examples of such situations are provided by the Rayleigh-Bénard and the Couette Taylor flow instabilities, but we will focus on the first one here. This instability arises when a fluid is heated from below and cooled from above, beyond a temperature difference threshold. Convective motions then set in and organize themselves in patches of counterrotating rolls. The convective features are governed by the Rayleigh number Ra, proportional to this difference, and by the Prandtl number Pr of the fluid (at threshold the Rayleigh number is written Rac). When the roll pattern is so confined by the sidewalls that only two or three rolls are present, the transition to turbulence recovers the various scenarios inherent to the systems of a few degrees of freedom /1/. However, we will concentrate here on the opposite case of extended systems, containing a large number of rolls.
KeywordsGauge Theory Prandtl Number Rayleigh Number Gauge Field Phase Equation
Unable to display preview. Download preview PDF.