竖直热对流中的速度与温度分布~

Li Min, et al. J. Fluid Mech. (2023), 977, A51

In this study, mean velocity and temperature profiles for turbulent vertical convection
(VC) confined in an infinite channel are investigated theoretically. The analysis starts from
the governing equations of the thermal flow, with Reynolds shear stress and turbulent
heat flux closed by the mixing length theory. Employing a three-sublayer description
of the mean fields, the mean velocity and temperature profiles are found to be linear
laws near the channel wall (viscosity-dominated sublayer), and they follow power laws
close to the channel centre (turbulence-dominated sublayer). The characteristic scales of
velocity, temperature and length in the present profiles arise naturally from the system
normalisation, rather than from scaling analyses, thus ensuring a sound mathematical
description. The derived profiles are verified fully via various literature data available
in the classical regime; further, they are compared with the reported profiles, and the
results indicate that the present profiles are the only ones with the ability to interpret
data accurately from different sources, demonstrating much better versatility. Meanwhile,
we provide analytical arguments showing that in the ultimate regime, the mean profiles
in VC may remain in power laws, rather than the log laws inferred by analogy with
Rayleigh–Bénard convection (RBC) systems. The power profiles recognised in this study
are induced by the effect of buoyancy, which is in parallel with the mean flow in VC and
contributes to the streamwise momentum transport, whereas in RBC systems, buoyancy
is perpendicular to the mean flow, and does not influence the streamwise momentum
transport, resulting in log profiles, being similar to the case of wall shear flows.