ALBERT

Description: Experimental and theoretical investigations of undulation patterns in high-pressure inclined layer gas convection at a Prandtl number near unity are reported. Particular focus is given to the competition between the spatiotemporal chaotic state of undulation chaos and stationary patterns of ordered undulations. In experiments, a competition and bistability between the two states is observed, with ordered undulations most prevalent at higher Rayleigh number. The spectral pattern entropy, spatial correlation lengths and defect statistics are used to characterize the competing states. The experiments are complemented by a theoretical analysis of the Oberbeck-Boussinesq equations. The stability region of the ordered undulations as a function of their wave vectors and the Rayleigh number is obtained with Galerkin techniques. In addition, direct numerical simulations are used to investigate the spatiotemporal dynamics. In the simulations, both ordered undulations and undulation chaos were observed dependent on initial conditions. Experiment and theory are found to agree well. © 2008 Cambridge University Press.

Description: For the Rayleigh-number range 107 ≲ Ra ≲ 10 11 we report measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for cylindrical samples of helium gas (Prandtl number Pr = 0.674) that have aspect ratio γ ≡ D/L = 0.50 (D and L are the diameter and the height respectively) and are heated from below. The results for Nu are consistent with recent direct numerical simulations. We measured the amplitude σ of the azimuthal temperature variation induced by the LSC at the sidewall, and the LSC circulation-plane orientation θ0, at three vertical positions. For the entire Ra range the LSC involves a convection roll that is coherent over the height of the system. However, this structure frequently collapses completely at irregular time intervals and then reorganizes from the incoherent flow. At σ small the probability distribution p(σ) increases linearly from zero; for θ= 1 and Pr = 4.38 this increase is exponential. No evidence of a two-roll structure, with one above the other, was observed. This differs from recent direct numerical simulations for θ= 0.5 and Pr = 0.7, where a one-roll LSC was found to exist only for Ra ≲ 109 to 1010, and from measurements for θ = 0.5 and Pr ̃ 5, where one-and two-roll structures were observed with transitions between them at random time intervals. © 2009 Cambridge University Press.

Description: We use silicon strip detectors (originally developed for the CLEO III high-energy particle physics experiment) to measure fluid particle trajectories in turbulence with temporal resolution of up to 70 000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 ≥ Rλ ≥ 970. Particle trajectories exhibiting accelerations up to 16 000 m s-2 (40 times the r.m.s. value) are routinely observed. The probability density function of the acceleration is found to have Reynolds-number-dependent stretched exponential tails. The moments of the acceleration distribution are calculated. The scaling of the acceleration component variance with the energy dissipation is found to be consistent with the results for low-Reynolds-number direct numerical simulations, and with the K41-based Heisenberg-Yaglom prediction for Rλ ≥ 500. The acceleration flatness is found to increase with Reynolds number, and to exceed 60 at Rλ = 970. The coupling of the acceleration to the large-scale anisotropy is found to be large at low Reynolds number and to decrease as the Reynolds number increases, but to persist at all Reynolds numbers measured. The dependence of the acceleration variance on the size and density of the tracer particles is measured. The autocorrelation function of an acceleration component is measured, and is found to scale with the Kolmogorov time τη.

Description: This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle and the Rayleigh number . The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck-Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy driven and shear-flow driven pattern forming mechanisms. The former are expressed as longitudinal convection rolls with their axes oriented parallel to the incline, the latter as perpendicular transverse rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3-D convection patterns above onset of convection in the plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies. © 2016 Cambridge University Press.

Description: We present measurements of the orientation and temperature amplitude of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Bénard convection (RBC) with aspect ratio ( and are the diameter and height respectively) and for the Prandtl number . The results for revealed a preferred orientation with up-flow in the west, consistent with a broken azimuthal invariance due to the Earth's Coriolis force (see Brown & Ahlers (Phys. Fluids, vol. 18, 2006, 125108)). They yielded the azimuthal diffusivity and a corresponding Reynolds number for Rayleigh numbers over the range . In the classical state the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351-386) for and , which gave , and with the Prandtl-number dependence as found previously also for the velocity-fluctuation Reynolds number (He et al., New J. Phys., vol. 17, 2015, 063028). At larger the data for revealed a transition to a new state, known as the 'ultimate' state, which was first seen in the Nusselt number and in at and . In the ultimate state we found . Recently, Skrbek and Urban (J. Fluid Mech., vol. 785, 2015, pp. 270-282) claimed that non-Oberbeck-Boussinesq effects on the Nusselt and Reynolds numbers of turbulent RBC may have been interpreted erroneously as a transition to a new state. We demonstrate that their reasoning is incorrect and that the transition observed in the Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as 'ultimate'. © 2016 Cambridge University Press.

Description: Abstract We ask whether the scaling exponents or the Kolmogorov constants depend on the anisotropy of the velocity fluctuations in a turbulent flow with no shear. According to our experiment, the answer is no for the Eulerian second-order transverse velocity structure function. The experiment consisted of 32 loudspeaker-driven jets pointed toward the centre of a spherical chamber. We generated anisotropy by controlling the strengths of the jets. We found that the form of the anisotropy of the velocity fluctuations was the same as that in the strength of the jets. We then varied the anisotropy, as measured by the ratio of axial to radial root-mean-square (r.m.s.) velocity fluctuations, between 0.6 and 2.3. The Reynolds number was approximately constant at around R λ = 481. In a central volume with a radius of 50μmm, the turbulence was approximately homogeneous, axisymmetric, and had no shear and no mean flow. We observed that the scaling exponent of the structure function was 0. 70 ± 0. 03, independent of the anisotropy and regardless of the direction in which we measured it. The Kolmogorov constant, C 2, was also independent of direction and anisotropy to within the experimental error of 4 %. © 2012 Cambridge University Press.

Description: We critically analyse the different ways to evaluate the dependence of the Nusselt number on the Rayleigh number in measurements of the heat transport in turbulent Rayleigh-Bénard convection under general non-Oberbeck-Boussinesq conditions and show the sensitivity of this dependence to the choice of the reference temperature at which the fluid properties are evaluated. For the case when the fluid properties depend significantly on the temperature and any pressure dependence is insignificant we propose a method to estimate the centre temperature. The theoretical predictions show very good agreement with the Göttingen measurements by He et al. (New J. Phys., vol. 14, 2012, 063030). We further show too the values of the normalized heat transport are independent of whether they are evaluated in the whole convection cell or in the lower or upper part of the cell if the correct reference temperatures are used. © 2018 Cambridge University Press.

Description: We report experimental results on the dynamics of heavy particles of the size of the Kolmogorov scale in a fully developed turbulent flow. The mixed Eulerian structure function of two-particle velocity and acceleration difference vectors delta rv· δ ra p was observed to increase significantly with particle inertia for identical flow conditions. We show that this increase is related to a preferential alignment between these dynamical quantities. With increasing particle density the probability for those two vectors to be collinear was observed to grow. We show that these results are consistent with the preferential sampling of strain-dominated regions by inertial particles. © 2012 Cambridge University Press.

Description: We report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh-Bénard convection for a cylindrical sample with an aspect ratio (diameter D over height L) equal to 0.50, in both the classical and the ultimate state. The measurements are for Rayleigh numbers Ra from 6 × 1011 to 1013 in the classical and 7 × 1014 to 1.1 × 1015 (our maximum accessible Ra) in the ultimate state. The Prandtl number was close to 0.8. Although to lowest order the bulk is often assumed to be isothermal in the time average, we found a 'logarithmic layer' (as reported briefly by Ahlers et al., Phys. Rev. Lett., vol. 109, 2012, 114501) in which the reduced temperature Θ = [〈T(z)〉 - Tm]/ΔT (with Tm the mean temperature, ΔT the applied temperature difference and 〈⋯〉 a time average) varies as A ln(z/L) + B or A′ ln(1 - z/L) + B′ with the distance z from the bottom plate of the sample. In the classical state, the amplitudes -A and A′ are equal within our resolution, while in the ultimate state there is a small difference, with -A/A′ ≃ 0.95. For the classical state, the width of the log layer is approximately 0.1L, the same near the top and the bottom plate as expected for a system with reflection symmetry about its horizontal midplane. For the ultimate state, the log-layer width is larger, extending through most of the sample, and slightly asymmetric about the midplane. Both amplitudes A and A′ vary with radial position r, and this variation can be described well by A = A0[(R - r)/R]-0.65, where R is the radius of the sample. In the classical state, these results are in good agreement with direct numerical simulations (DNS) for Ra = 2 × 1012; in the ultimate state there are as yet no DNS. The amplitudes -A and A′ varied as Ra-n, with n ≃ 0.12 in the classical and n ≃ 0.18 in the ultimate state. A close analogy between the temperature field in the classical state and the 'law of the wall' for the time-averaged downstream velocity in shear flow is discussed. A two-sublayer mean-field model of the temperature profile in the classical state was analysed and yielded a logarithmic z dependence of Θ. The Ra dependence of the amplitude A given by the model corresponds to an exponent nth = 0.106, in good agreement with the experiment. In the ultimate state the experimental result n ≃ 0.18 differs from the prediction nth ≃ 0.043 by Grossmann & Lohse. © Cambridge University Press 2014.