Near isotropic behaviour of turbulent thermal convection

TL;DR

This study uses direct numerical simulations to analyze anisotropy in turbulent thermal convection, finding near isotropic behavior at Prandtl number 1 and revealing energy transfer mechanisms similar to hydrodynamic turbulence.

Contribution

It provides detailed quantitative analysis of anisotropy and energy transfer in turbulent convection across different Prandtl numbers, highlighting near isotropic behavior at Pr=1.

Findings

Flow is nearly isotropic at Pr=1

Anisotropy increases with Prandtl number

Energy transfer is local and forward, akin to hydrodynamic turbulence

Abstract

We investigate the anisotropy in turbulent convection in a 3D box using direct numerical simulation. We compute the anisotropic parameter $A = u_\perp^{2}/(2u_{\parallel}^{2})$, where $u_{\perp}$ and $u_{\parallel}$ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number $\mathrm{Pr} \approx 1$, but the anisotropy increases with the Prandtl number. For $\mathrm{Pr}=\infty$, $A \approx 0.3$, thus anisotropy is not very significant even in extreme cases. We also observe that $u_{\parallel}$ feeds energy to $u_{\perp}$ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al.~[Phys. Rev. E {\bf 90}, 023016 (2014)] for turbulent convection.