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

In turbulent rotating Rayleigh-Benard 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 Gamma equivalent to 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/Ro(c), with 1/Ro(c) proportional to 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. Here it is used to estimate the suppression of the heat-transport enhancement by the sidewall.