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Abstract

We investigate the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection
in a large box of aspect ratio Γ = 32 for Rayleigh numbers up to Ra = 109 and at a fixed
Prandtl number Pr = 1. A conditional averaging technique allows us to extract statistics of
the LSC even though the number and the orientation of the structures vary throughout the
domain. We find that various properties of the LSC obtained here, such as the wall-shear
stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not
differ significantly from results in confined domains (Γ ≈ 1). This is remarkable given
that the size of the structures (as measured by the width of a single convection roll) more
than doubles at the highest Ra as the confinement is removed. An extrapolation towards
the critical shear Reynolds number of Recrit
s ≈ 420, at which the boundary layer (BL)
typically becomes turbulent, predicts that the transition to the ultimate regime is expected
at Racrit ≈ O(1015) in unconfined geometries. This result is in line with the Göttingen
experimental observations (He et al., Phys. Rev. Lett., vol. 108, 2012, 024502; New J.
Phys., vol. 17, 2015, 063028). Furthermore, we confirm that the local heat transport close
to the wall is highest in the plume impacting region, where the thermal BL is thinnest,
and lowest in the plume emitting region, where the thermal BL is thickest. This trend,
however, weakens with increasing Ra.