Bifurcations in turbulent rotating Rayleigh-Bénard convection: A finite-size effect

In turbulent rotating Rayleigh-Bénard convection Ekman vortices extract hot or cold fluid from thermal boundary layers near the bottom or top plate and enhance the Nusselt number. It is known from experiments and direct numerical simulation on cylindrical samples with aspect ratio Γ ≡ D/L (D is the diameter and L the height) that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number 1/Roc, with 1/Roc ∝ 1/Γ. We present a Ginzburg-Landau like model that explains the existence of a bifurcation at finite 1/Roc as a finite-size effect. The model yields the proportionality between 1/Roc and 1/Γ and is consistent with several other measured or computed system properties. Here it is used to estimate the suppression of the heat-transport enhancement by the sidewall.