Spectra and probability distributions of thermal flux in turbulent Rayleigh-B\'{e}nard convection

TL;DR

This paper investigates the spectral behavior and probability distributions of turbulent heat flux in Rayleigh-Bénard convection, revealing a consistent $k^{-2}$ scaling and non-Gaussian flux distributions with exponential tails.

Contribution

It provides new insights into the spectral scaling laws and probability distributions of heat flux in turbulent convection, including effects of rotation and parameter dependencies.

Findings

Heat flux spectrum scales as $k^{-2}$.

Scaling exponent is nearly independent of rotation and Prandtl number at high Rayleigh numbers.

Local heat fluxes follow non-Gaussian distributions with exponential tails.

Abstract

The spectra of turbulent heat flux $\mathrm{H}(k)$ in Rayleigh-B\'{e}nard convection with and without uniform rotation are presented. The spectrum $\mathrm{H}(k)$ scales with wave number $k$ as $\sim k^{-2}$. The scaling exponent is almost independent of the Taylor number $\mathrm{Ta}$ and Prandtl number $\mathrm{Pr}$ for higher values of the reduced Rayleigh number $r$ ($ > 10^3$). The exponent, however, depends on $\mathrm{Ta}$ and $\mathrm{Pr}$ for smaller values of $r$ ($<10^3$). The probability distribution functions of the local heat fluxes are non-Gaussian and have exponential tails.