Similarities between 2D and 3D convection for large Prandtl number

TL;DR

This study uses direct numerical simulations to compare 2D and 3D Rayleigh-Bénard convection at large Prandtl numbers, revealing close spectral similarities and quasi-2D behavior in 3D flows.

Contribution

It demonstrates that 3D RBC at large Prandtl numbers behaves similarly to 2D RBC, showing spectral and flow mode similarities, and explains the quasi-2D nature of 3D flows.

Findings

Kinetic energy spectrum follows $k^{-13/3}$ in both 2D and 3D.

Entropy spectrum exhibits a dominant $k^{-2}$ branch.

3D RBC is quasi two-dimensional, explaining spectral similarities.

Abstract

Using direct numerical simulations of Rayleigh-B\'{e}nard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular the kinetic energy spectrum $E_u(k) \sim k^{-13/3}$, and the entropy spectrum exhibits a dual branch with a dominant $k^{-2}$ spectrum. We showed that the dominant Fourier modes in the 2D and 3D flows are very close. Consequently, the 3D RBC is quasi two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large- and infinite Prandtl numbers.