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 sophisticated Lagrangian statistics. Here we experimentally study Lagrangian pair dispersion (one of the canonical problems of Lagrangian turbulence) in a Rayleigh-Bénard 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 including 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 fluctuations, 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

Non-local dispersion and the reassessment of Richardson's t3-scaling law

“…Recently, Liot et al (2019) have shown that the ballistic approach of Bourgoin (2015) ( § 2.2) can yield a r 0 -dependent intermediate range consistent with observations and the present model. A t 3 scaling was obtained for r 0 /η ≈ 4, while other initial separations approached t 3 scaling from above or below.…”

“…Dou et al 2018;Petersen, Baker & Coletti 2019), which is limiting when looking for a Richardson scaling regime. There is some evidence to suggest that in Rayleigh-Bénard convection, a t 3 -scaling range also appears for r 0 ≈ 4η with other r 0 approaching from above or below (Liot et al 2019). Pair dispersion experiments at much higher Reynolds numbers would be of considerable interest.…”

“…The ballistic approach is general and can be adapted to turbulent shear flow (Polanco et al 2018). Moreover, the actual S 2 (as opposed the inertial range model) may be inserted, which yields deviations from equation (2.4) (Liot et al 2019, see also §4). However, we focus on the case of homogeneous isotropic turbulence with inertial range and local dispersion assumptions, because it yields the classical Richardson scaling, which is of interest here.…”

On local isotropy and scale dependence of pair dispersion in turbulent canopy flows

“…(2018), Liot et al. (2019) and Ni & Xia (2013). The collapse of the data at short times using the longitudinal structure function is important since it confirms that is the appropriate velocity scale for the separation of particles at a distance .…”

“…Recent studies further examined buoyancy-driven flows (Schumacher 2008; Ni & Xia 2013; Liot et al. 2019) and pair dispersion of inertial particles (Pitton et al. 2012) or in other complex flows, such as in the stroke of a swimming jellyfish (Kim & Chamorro 2019).…”