Prandtl number dependence of the small-scale properties in turbulent Rayleigh-B\'enard convection

TL;DR

This study investigates how the Prandtl number influences small-scale turbulence properties in Rayleigh-Bénard convection, revealing that lower Prandtl numbers lead to stronger nonlinearity and increased energy fluxes, while heat flux fluctuations grow with Pr.

Contribution

It provides a detailed numerical analysis of Prandtl number effects on energy spectra, fluxes, and heat flux fluctuations in turbulent convection, highlighting new dependencies.

Findings

Kinetic energy flux and spectra increase as Pr decreases.

Flow exhibits more nonlinearity at lower Prandtl numbers.

Heat flux fluctuations grow with increasing Prandtl number.

Abstract

We analyze the Prandtl number (Pr) dependence of spectra and fluxes of kinetic energy, as well as the energy injection rates and dissipation rates, of turbulent thermal convection using numerical data. As expected, for a flow with $ \mathrm{Pr} \lessapprox 1 $, the inertial-range kinetic energy flux is constant, and the kinetic energy spectrum is Kolmogorov-like ($ k^{-5/3} $). More importantly, we show that the amplitudes of the kinetic energy fluxes and spectra and those of structure functions increase with the decrease of Pr, thus exhibiting stronger nonlinearity for flows with small Prandtl numbers. Consistent with these observations, the kinetic energy injection rates and the dissipation rates too increase with the decrease of Pr. Our results are in agreement with earlier studies that report the Reynolds number to be a decreasing function of Prandtl number in turbulent convection. On the other hand, the tail of the probability distributions of the local heat flux grows with the increase of Pr, indicating increased fluctuations in the local heat flux with Pr.