Plane-layer Rayleigh-B\'enard convection up to $Ra=10^{11}$: Near-wall fluctuations and role of initial conditions

TL;DR

This study uses direct numerical simulations to analyze turbulent Rayleigh-Bénard convection at high Rayleigh numbers, focusing on near-wall fluctuations, initial condition effects, and the impact of added shear flows on heat transfer and boundary layer properties.

Contribution

It provides new insights into the role of initial conditions and shear flows on turbulent convection, especially regarding near-wall dynamics and boundary layer behavior at very high Rayleigh numbers.

Findings

Weak logarithmic near-wall layers form with sinusoidal forcing.

Full turbulent boundary layers re-establish only with constant pressure gradient.

No significant enhancement in heat transfer from sinusoidal forcing was observed.

Abstract

We study turbulent Rayleigh-B\'enard convection through direct numerical simulations in a three-dimensional plane layer of aspect ratio 4 for Rayleigh numbers $10^5 \leq Ra \leq 10^{11}$ and Prandtl number $Pr=0.7$. We summarize the height-dependent statistics of velocity and temperature fluctuations and corresponding scalings with the Rayleigh number. We include an analysis on the role of coherent and incoherent flow regions near the wall for global heat transfer. Furthermore, we investigate the dependence of turbulent transport on a finite-amplitude sinusoidal shear flow added at time $t=0$, which either freely decays in a long transient or remains existent when a steady sinusoidal volume forcing is added. In the latter case, weak logarithmic near-wall layers are formed, however, with von K\'arm\'an and offset constants that differ from standard values. The typical magnitude of both coefficients, and thus a full turbulent boundary layer of velocity and temperature, is re-established only for a switch from sinusoidal to constant pressure gradient driving of the flow. In all cases, except for the constant pressure gradient-driven flow, no enhancement of global turbulent heat and momentum transfer within error bars is detected, even though the sinusoidal amplitude is of the order of the characteristic free-fall velocity.