Convective heat transport in slender cells is close to that in wider cells at high Rayleigh and Prandtl numbers^(a)

¹ Center for Space Science, New York University Abu Dhabi - Abu Dhabi 129188, United Arab Emirates
² Department of Physics, Courant Institute of Mathematical Sciences, Tandon School of Engineering, New York University - New York, NY 11201, USA

^(b) ambrish.pandey@nyu.edu (corresponding author)

Received: 14 June 2021
Accepted: 9 August 2021

Abstract

Direct numerical simulations of turbulent convection at high Rayleigh numbers in large aspect ratio cells are challenging because of the prohibitive computational resources required. One can achieve high Rayleigh numbers at affordable costs for low aspect ratios, but the effect of small aspect ratio remains to be understood fully. In this work, we explore integral quantities in convection in a cell with the small aspect ratio of 0.1 by varying both the Rayleigh and Prandtl numbers systematically. We find that the heat transport in this flow is within 10% of that in cells with large aspect ratios for high enough Rayleigh numbers and for Prandtl numbers larger than unity. For low Prandtl numbers, the increase of the heat transport is steeper for low aspect ratios, approaching that in large aspect ratios as the Prandtl number increases. Further, the global momentum transport, quantified by the Reynolds number, is reduced for all Prandtl numbers, presumably because of the larger volume of flow affected by the friction from sidewalls, compared to that in cells of larger aspect ratio.