Pair dispersion in inhomogeneous turbulent thermal convection

Abstract

Due to large scale flow inhomogeneities and the effects of temperature, turbulence small-scale structure in thermal convection is still an active field of investigation, especially considering sophis- ticated Lagrangian statistics. Here we experimentally study Lagrangian pair dispersion (one of the canonical problems of Lagrangian turbulence) in a Rayleigh-B enard convection cell. A sufficiently high temperature difference is imposed on a horizontal layer of fluid to observe a turbulent flow. We perform Lagrangian tracking of sub-millimetric particles on a large measurement volume in- cluding part of the Large Scale Circulation (LSC) revealing some large inhomogeneities. Our study brings to light several new insights regarding our understanding of turbulent thermal convection: (i) by decomposing particle Lagrangian dynamics into the LSC contribution and the turbulent fluc- tuations, we highlight the relative impact of both contributions on pair dispersion; (ii) using the same decomposition, we estimate the Eulerian second-order velocity structure functions from pair statistics and show that after removing the LSC contribution, the remaining statistics recover usual homogeneous and isotropic behaviours which are governed by a local energy dissipation rate to be distinguished from the global dissipation rate classically used to characterise turbulence in thermal convection; and (iii) we revisit the super-diffusive Richardson-Obukhov regime of particle dispersion and propose a refined estimate of the Richardson constant.