Dynamics and length scales in vertical convection of liquid metals

Abstract

Using complementary experiments and direct numerical simulations, we study turbulent thermal convection of a liquid metal (Prandtl number $\textit {Pr}\approx 0.03$ ) in a box-shaped container, where two opposite square sidewalls are heated/cooled. The global response characteristics like the Nusselt number ${\textit {Nu}}$ and the Reynolds number $\textit {Re}$ collapse if the side height $L$ is used as the length scale rather than the distance $H$ between heated and cooled vertical plates. These results are obtained for various Rayleigh numbers $5\times 10^3\leq {\textit {Ra}}_H\leq 10^8$ (based on $H$ ) and the aspect ratios $L/H=1, 2, 3$ and $5$ . Furthermore, we present a novel method to extract the wind-based Reynolds number, which works particularly well with the experimental Doppler-velocimetry measurements along vertical lines, regardless of their horizontal positions. The extraction method is based on the two-dimensional autocorrelation of the time–space data of the vertical velocity.