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 proportional to Ra(beta) with beta = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (10(6) < or = Ra < or = 10(7)), 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 beta close to 0.31. In particular, we find no evidence for a transition to the Ra(1/2) regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

A large-scale circulation velocity, often called the ‘wind’, has been observed in turbulent convection in the Rayleigh–Bénard 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 1016. A possible physical explanation is attempted.

Properties of the mean wind in thermal convection, especially the abrupt reversal of its direction at high Rayleigh numbers, are studied. Measurements made in a closed cylindrical container of aspect ratio 1 are analyzed, and both the long-term and short-term behaviors of the direction reversals are discussed. A first look at the data suggests a Brownian-type process in action, but a closer look suggests the existence of hierarchical features with time scales extending roughly over a decade and a half. A physical model consistent with experimental observations is presented, and the origin of the cutoff scales is discussed. It appears that the generation of the wind as well as the reversal of its direction can be understood in terms of the imbalance between buoyancy effects and friction.

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 $2 \times 10^{15}$. 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.

We report experimental measurements of heat transport in rotating Rayleigh-Bénard convection in a cylindrical convection cell with aspect ratio Γ = 1/2. The fluid was helium gas with Prandtl number Pr = 0.7. The range of control parameters was Rayleigh number 4 × 10 9 < Ra < 4 × 10 11 and Ekman number 2 × 10 −7 < Ek < 3 × 10 −5 (corresponding to Taylor number 4 × 10 9 < Ta < 1 × 10 14 and convective Rossby number 0.07 < Ro < 5). We determine the crossover from weakly rotating turbulent convection to rotation dominated geostrophic convection through experimental measurements of the normalized heat transport Nu. The heat transport for the rotating state in the geostrophic regime, normalized by the zero-rotation heat transport, is consistent with scaling of (RaEk −7/4 ) β with β ≈ 1. A phase diagram is presented that encapsulates measurements on the potential geostrophic turbulence regime of rotating thermal convection. PACS numbers: 47.20.Bp, 47.54.+r Thermal convection in the presence of rotation occurs in many geophysical contexts, including the Earth's mantle [1], oceans [2], planetary atmospheres such as Jupiter [3], and solar interiors [4]. It also remains a fundamental problem in fluid dynamics, balancing rotation and buoyancy in a simple system that can be studied theoretically [5], experimentally [6][7][8][9][10][11] and numerically [12,13] with high precision. Thus, the problem of rotating thermal convection is of interest across a wide spectrum of scientific disciplines.The parameters of rotating convection are Ra = gα∆Td 3 /νκ which measures the buoyant forcing of the flow, Ek = ν/(2d 2 Ω) which represents an inverse dimensionless rotation rate, and Pr = ν/κ, where g is acceleration of gravity, ∆ T is the temperature difference between top and bottom plates separated by distance d, ν and κ are the fluid kinematic viscosity and thermal diffusivity, respectively, and Ω = 2πf is the angular rotation about an axis parallel to gravity for rotation frequency f . Rotation can also be represented by the Taylor number Ta = 1/Ek 2 or by the convective Rossby number Ro = Ek Ra/Pr which reflects the ratio of rotational time to buoyancy time. Here we use the representation of Ek or Ro such that high dimensionless rotation rates correspond to small values of the rotational control parameter in the spirit of the asymptotic equation approach of expanding in a small variable [14]. The measured response of the system in this space of buoyant and rotational forcing is the Nusselt number, Nu =Q/(λ∆T) whereQ is the applied heater power through the fluid and λ is the thermal conductance of the fluid.Much of the experimental work on rotating convection at high dimensionless rotation rates has focused on either the transition to convection where rotation-induced wall modes play an important role [7,15] or the turbulent state far from onset where thermal boundary layers control heat transport [6,[8][9][10][11]. Recently, the numerical simulation [16,17] of the appropriate equations of motion [14] in the asymptotic limit of h...