Temperature Statistics in Turbulent Rayleigh-B\'enard Convection

TL;DR

This paper develops a statistical framework for analyzing temperature and velocity distributions in turbulent Rayleigh-Bénard convection, linking flow dynamics with temperature statistics and heat transfer.

Contribution

It derives exact evolution equations for temperature and velocity PDFs from first principles and estimates unclosed terms using numerical simulations.

Findings

Provides a theoretical interpretation of temperature statistics in turbulent convection

Links flow features to temperature distribution and heat transfer

Offers insights into the dynamics-statistics connection in turbulence

Abstract

Rayleigh-B\'enard convection in the turbulent regime is studied using statistical methods. Exact evolution equations for the probability density function of temperature and velocity are derived from first principles within the framework of the Lundgren-Monin-Novikov hierarchy known from homogeneous isotropic turbulence. The unclosed terms arising in the form of conditional averages are estimated from direct numerical simulations. Focusing on the statistics of temperature, the theoretical framework allows to interpret the statistical results in an illustrative manner, giving deeper insight into the connection between dynamics and statistics of Rayleigh-B\'enard convection. The results are discussed in terms of typical flow features and the relation to the heat transfer.