Effect of tilting on turbulent convection: Cylindrical samples with aspect ratio $\Gamma=0.50$

Abstract

We report measurements of properties of turbulent thermal convection of a fluid with a Prandtl number $\Pra=4.38$ in a cylindrical cell with an aspect ratio $\Gamma=0.50$. The rotational symmetry was broken by a small tilt of the sample axis relative to gravity. Measurements of the heat transport (as expressed by the Nusselt number \Nu), as well as of large-scale-circulation (LSC) properties by means of temperature measurements along the sidewall, are presented. In contradistinction to similar experiments using containers of aspect ratio $\Gamma=1.00$ \cite[]{ABN06} and $\Gamma=0.50$ \cite[]{CRCC04,SXX05,RGKS10}, we see a very small increase of the heat transport for tilt angles up to about 0.1 rad. Based on measurements of properties of the LSC we explain this increase by a stabilization of the single-roll state (SRS) of the LSC and a de-stabilization of the double-roll state (DRS) (it is known from previous work that the SRS has a slightly larger heat transport than the DRS). Further, we present quantitative measurements of the strength of the LSC, its orientation, and its torsional oscillation as a function of the tilt angle.