On temperature reconstruction from velocity fields in turbulent Rayleigh-Benard convection

Abstract

Here we propose a method to reconstruct the temperature field from spatially and temporally well resolved velocity fields in thermal convection. Here, in the first place, we consider a Rayleigh-B\'enard system with a quadratic cross section and a rather large aspect ratio. To reconstruct the temperature distribution at any horizontal cross-section and any time, using the proposed method, one needs to solve the Poisson equation with a right-hand-side function that depends exclusively on the temporal and spatial distribution of the velocity field. In this paper, we first present the theoretical method, then validate the method using direct numerical simulation data of thermal convection in a box of aspect ratio $\Gamma=8$ and finally we apply this method to experimental velocity measurements of the flow in a rectangular RBC cell of $\Gamma=16$ filled with water.