Symmetry breaking, anomalous scaling, and large-scale flow generation in aconvection cell - art. no. 035304

We consider a convection process in thin loops of different goeomrtries. At Ra= Ra'(cr) a first transition leading to the generation of corner vortice s is observed. At higher Ra (Ra> Ra-cr) a coherent large-scale flow, which persists for a very long time, sets up. The mean velocity <(<nu>)over bar>, mass flux m, and the Nusselt number Nu in this flow scale with Ra as <(<nu >)over bar>proportional tom proportional to Ra-0.45 and Nu proportional to Ra-0.9, respectively, in a wide range of r=(Ra-Ra-cr)/Ra-cr variation. The "normal'' scaling <(<nu>)over bar>proportional to root Ra is detected as r- ->0 and its range shrinks with decrease of the aspect ratio. The time evolu tion of the coherent flow is well described by the Landau amplitude equatio n with the appropriate selection of the Ra-dependent Landau constants. Anal ysis of the aspect ratio influence on the range of validity of anomalous sc aling, observed in this paper, indicates the important role played by both thermal boundary conditions and geometry of the system.