Structure of thermal boundary layers in turbulent Rayleigh–Bénard convection

Abstract

We report high-resolution local-temperature measurements in the upper boundary layer of turbulent Rayleigh–Bénard (RB) convection with variable Rayleigh number Ra and aspect ratio Γ. The primary purpose of the work is to create a comprehensive data set of temperature profiles against which various phenomenological theories and numerical simulations can be tested. We performed two series of measurements for air (Pr = 0.7) in a cylindrical container, which cover a range from Ra≈109 to Ra≈1012 and from Γ≈1 to Γ≈10. In the first series Γ was varied while the temperature difference was kept constant, whereas in the second series the aspect ratio was set to its lowest possible value, Γ=1.13, and Ra was varied by changing the temperature difference. We present the profiles of the mean temperature, root-mean-square (r.m.s.) temperature fluctuation, skewness and kurtosis as functions of the vertical distance z from the cooling plate. Outside the (very short) linear part of the thermal boundary layer the non-dimensional mean temperature Θ is found to scale as Θ(z)∼zα, the exponent α≈0.5 depending only weakly on Ra and Γ. This result supports neither Prandtl's one-third law nor a logarithmic scaling law for the mean temperature. The r.m.s. temperature fluctuation σ is found to decay with increasing distance from the cooling plate according to σ(z)∼zβ, where the value of β is in the range -0.30>β>-0.42 and depends on both Ra and Γ. Priestley's β=−1/3 law is consistent with this finding but cannot explain the variation in the scaling exponent. In addition to profiles we also present and discuss boundary-layer thicknesses, Nusselt numbers and their scaling with Ra and Γ.

New perspectives in turbulent Rayleigh-Bénard convection

“…Several gases have been used at ambient temperatures: argon Ar [56,57], nitrogen N 2 [56][57][58], helium He [56,59], ethane C 2 H 6 [60], sulfur hexafluoride SF 6 [56,58,61,62], and air [63]. Globally, the range 60 < Ra < 10 15 of Rayleigh numbers has been spanned with gases.…”

“…An extreme case in terms of system size is occupied by the actually largest thermal convection laboratory experiment in the world, known as the "Barrel of Ilmenau (BOI)" with a height and diameter of up to seven meters [63]. The working fluid is air at ambient temperature and pressure.…”

“…Velocity boundary layers over a certain range of Rayleigh numbers have been measured first by Xin et al [120] and Adrian [121]. Measurements of boundary layer profiles beyond Ra ∼ 10 10 require large experimental devices such as the BOI for the convection in air [63] or high-resolution particle image velocimetry for convection in water [53].…”

Fine-scale statistics of temperature and its derivatives in convective turbulence

“…However, most experiments can provide pointwise measurements of time series of the turbulent fields only (see e.g. du Puits et al 2007 and references therein). Only recently, two-dimensional cuts through the flow field have been analysed by combining particle image velocimetry and shadowgraph techniques (Xi, Lam & Xia 2004).…”

Highly turbulent Taylor-Couette turbulence

“…In the past twenty years, the investigation on RB flow has been extended to the high-Rayleigh-number regime, which is well beyond onset of turbulence. To vary the controlled parameters experimentally, RB apparatuses with different aspect ratios and sizes have been built in many research groups in the past twenty years [24,[31][32][33][34][35][36][37][38]. Direct numerical simulation (DNS) of three-dimensional RB flow allows for quantitative comparison with experimental data up to Ra = 10 11 [39], which is well beyond the onset of turbulence [31].…”