Connecting flow structures and heat flux in turbulent Rayleigh-B\'enard convection

TL;DR

This study numerically investigates how the aspect ratio influences heat transfer in turbulent Rayleigh-Bénard convection, revealing complex structures and flow organization effects that depend on Prandtl number and initial conditions.

Contribution

It provides new insights into the aspect ratio dependence of heat transfer and links flow organization to observed Nu variations in turbulent convection.

Findings

Nu shows rich structure with jumps and transitions

Flow organization explains aspect ratio effects

Initial conditions can determine turbulent states

Abstract

The aspect ratio (\Gamma) dependence of the heat transfer (Nusselt number Nu in dimensionless form) in turbulent (two-dimensional) Rayleigh-B\'enard convection is numerically studied in the regime $0.4 \le \Gamma \le 1.25$ for Rayleigh numbers $10^7 \le Ra \le Ra^{9}$ and Prandtl numbers Pr =0.7 (gas) and 4.3 (water). Nu (\Gamma) shows a very rich structure with sudden jumps and sharp transitions. We connect these structures to the way the flow organizes itself in the sample and explain why the aspect ratio dependence of Nu is more pronounced for small Pr. Even for fixed \Gamma different turbulent states (with different resulting Nu) can exist, between which the flow can or cannot switch. In the latter case the heat transfer thus depends on the initial conditions.