Temperature reconstruction from velocity fields in turbulent Rayleigh-Benard convection

Abstract

Rayleigh-Benard convection (RBC), where a horizontal fluid layer is driven by a vertical temperature gradient, is not only a model system for thermal convection, but also a canonical flow to study turbulence. Due to recent advances in the development of flow measurement techniques, turbulent velocity fields can nowadays be measured with high temporal and spatial resolution using, for example, high density particle tracking. However, at this point no similar techniques exist for temperature measurements. Here, we propose a method to reconstruct the temperature field from spatially and temporally well resolved velocity fields in thermal convection. In the first place, we consider a Rayleigh-Benard 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 a Poisson equation with a right-hand-side function that depends exclusively on the temporal development and spatial distribution of the velocity field. In this talk, we will first apply this approach to data from direct numerical simulation of thermal convection in a rectangular box of width-to-height aspect ratio $\Gamma = 8$. The Rayleigh number was set to Ra = 10^6, the Prandtl number was Pr= 7.0 and the simulation was done using the Goldfish code.(see e.g., Shishkina et al., Phys. Rev. Fluids, 2, 103502 (2017) and Reiter & Shishkina, J. Fluid Mech, 892, R1 (2020)). These simulations allow a precise comparison between the simulated and the reconstructed temperature fields. We also apply this method to experimental velocity measurements of the flow in a rectangular RBC cell of $\Gamma=16$ filled with water at the same Ra and Pr (fig.~\ref{fig:abstract}). For this, the flow velocity was measured via high density Lagrangian particle tracking and interpolated onto a regular grid. (see e.g., Weiss et al. Exp. Fluids, 64, 82 (2023), Weiss et al., J. Fluid Mech, 999, A90 (2024)) In this talk, we will present and discuss statistical properties of the reconstructed temperature fields as well as the spatially resolved convective heat flux for different vertical positions.