Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1999-09-15
Nonlinear Sciences
Chaotic Dynamics
27 pages, 19 figures
Scientific paper
We consider a convection process in a thin loop. At $Ra=Ra^{\prime}_{cr}$ 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 $\bar{v} \propto \dot{m} \propto Ra^{0.45}$ and $Nu\propto Ra^{0.9}$, 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.
Tomboulides Ananias G.
Yakhot Victor
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