Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-B\'enard convection

TL;DR

This paper demonstrates that finite-size effects cause supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection, with a critical inverse Rossby number proportional to the aspect ratio, supported by experiments, simulations, and a Ginzburg-Landau model.

Contribution

It introduces a Ginzburg-Landau like model explaining finite-size induced bifurcations and their dependence on aspect ratio in turbulent convection.

Findings

Bifurcation at a critical inverse Rossby number proportional to inverse aspect ratio.

Enhanced heat transfer occurs only above the bifurcation point.

Model aligns with experimental and numerical data.

Abstract

In turbulent thermal convection in cylindrical samples of aspect ratio \Gamma = D/L (D is the diameter and L the height) the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis, because of the formation of Ekman vortices that extract additional fluid out of thermal boundary layers at the top and bottom. We show from experiments and direct numerical simulations that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number $1/\Ro_c$, with $1/\Ro_c \propto 1/\Gamma$. We present a Ginzburg-Landau like model that explains the existence of a bifurcation at finite $1/\Ro_c$ as a finite-size effect. The model yields the proportionality between $1/\Ro_c$ and $1/\Gamma$ and is consistent with several other measured or computed system properties.