Symmetry Breaking, Anomalous Scaling and Large-Scale Flow Generation in a Convection Cell

Abstract

We consider a convection process in a thin loop. At $Ra=R{a}_{cr}^{\prime }$ a first transition leading to the generation of corner vortices is observed. At higher $Ra$ a coherent large-scale flow, which persists for a very long time, sets up. The mean velocity $\bar{v}$, mass flux $\dm$, and the Nusselt number $Nu$ in this flow scale with $Ra$ as $\bar{v}\propto \dot{m}\propto R{a}^{0.45}$ and $Nu\propto R{a}^{0.9}$, respectively. The time evolution of the coherent flow is well described by the Landau amplitude equation within a wide range of $Ra$-variation. The anomalous scaling of the mean velocity, found in this work, resembles the one experimentally observed in the ``hard turbulence'' regime of Benard convection. A possible relation between the two systems is discussed.

27 pages, 19 figures