Field correlations and the ultimate regime of turbulent convection

TL;DR

This study uses direct numerical simulations to explore how correlations in turbulent convection scale with Rayleigh number, providing insights into the ultimate regime and experimental observations.

Contribution

It demonstrates the scaling behavior of correlation functions and dissipation rates in turbulent convection, linking numerical results to experimental Nusselt number scaling.

Findings

Correlation functions scale as Ra^{-0.22} for large Ra

Normalized correlation functions are constant under periodic boundary conditions

Results explain the observed Nu exponent of around 0.3 in experiments

Abstract

Using direct numerical simulations of Rayleigh-B\'{e}nard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ for moderately large Rayleigh number $Ra$. This scaling accounts for the Nusselt number ($Nu$) exponent to be around 0.3 observed in experiments. Numerical simulations also reveal that the above normalized correlation functions are constants for the convection simulation under periodic boundary conditions.