J. J. Niemela

Turbulent convection at very high Rayleigh numbers

Turbulent convection occurs when the Rayleigh number (Ra)—which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion—becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu ∝ Raβ with β = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (106 ≤ Ra ≤ 10 17), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent β close to 0.31. In particular, we find no evidence for a transition to the Ra1/2 regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

The wind in confined thermal convection

A large-scale circulation velocity, often called the ‘wind’, has been observed in turbulent convection in the Rayleigh–Benard apparatus, which is a closed box with a heated bottom wall. The wind survives even when the dynamical parameter, namely the Rayleigh number, is very large. Over a wide range of time scales greater than its characteristic turnover time, the wind velocity exhibits occasional and irregular reversals without a change in magnitude. We study this feature experimentally in an apparatus of aspect ratio unity, in which the highest attainable Rayleigh number is about 10 16 . A possible physical explanation is attempted.

Confined turbulent convection

New measurements of the Nusselt number have been made in turbulent thermal convection confined in a cylindrical container of aspect ratio unity. The apparatus is essentially the same as that used by Niemela et al. (2000), except that the height was halved. The measurement techniques were also identical but the mean temperature of the flow was held fixed for all Rayleigh numbers. The highest Rayleigh number was

Turbulent convection at high Rayleigh numbers and aspect ratio 4

2 \times 10^{15}

The Use of Particle Image Velocimetry in the Study of Turbulence in Liquid Helium

. Together with existing data, the new measurements are analysed with the purpose of understanding the relation between the Nusselt number and the Rayleigh number, when the latter is large. In particular, the roles played by Prandtl number, aspect ratio, mean wind, boundary layers, sidewalls, and non-Boussinesq effects are discussed. Nusselt numbers, measured at the highest Rayleigh numbers for which Boussinesq conditions hold and sidewall forcing is negligible, are shown to vary approximately as a 1/3-power of the Rayleigh number. Much of the complexity in interpreting experimental data appears to arise from aspects of the mean flow, including complex coupling of its dynamics to sidewall boundary conditions of the container. Despite the obvious practical difficulties, we conclude that the next generation of experiments will be considerably more useful if they focus on large aspect ratios.

Turbulent rotating convection at high Rayleigh and Taylor numbers

We report measurements of the Nusselt number,

Turbulent flows at cryogenic temperatures: a new frontier

\hbox{\it Nu}

Critical fluctuation of wind reversals in convective turbulence.

, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was

Ultra-high Rayleigh number convection in cryogenic helium gas

\hbox{\it Ra} \,{=}\, 2 \,{\times}\, 10^{13}

Thermal turbulence in cryogenic helium gas

. Except for the last half a decade or so of