Effect of tilting on turbulent convection: cylindrical samples with aspect ratio

Abstract

AbstractWe report measurements of the properties of turbulent thermal convection of a fluid with a Prandtl number $\mathit{Pr}= 4. 38$ 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 properties of the large-scale circulation (LSC) obtained from temperature measurements along the sidewall, are presented. In contradistinction to similar experiments using containers of aspect ratio $\Gamma = 1. 00$ (Ahlers et al., J. Fluid Mech., vol. 557, 2006b, pp. 347–367) and $\Gamma = 0. 50$ (Chillà et al., Eur. Phys. J. B, vol. 40, 2004, pp. 223–227; Sun, Xi & Xia, Phys. Rev. Lett., vol. 95, 2005, p. 074502; Roche et al., New J. Phys., vol. 12, 2010, p. 085014), 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 destabilization of the double-roll state (DRS) (it is known from previous work that the SRS has a slightly larger heat transport than the DRS). Quantitative measurements of the strength and the orientation of the LSC show that its azimuthal diffusion is suppressed with increasing tilt whereas the torsional oscillation becomes more pronounced and its frequency increases.