The multi-scale nature of Wall shear stress fluctuations in turbulent Rayleigh-Benard convection

Measurements of wall shear-stress fluctuations on very long timescales ($\ge$ 1900 free-fall time units) are reported for turbulent Rayleigh-Benard (RB) convection in air at the heated bottom plate of a RB cell, 2.5 m in diameter and 2.5 m in height. The novel sensor simultaneously captures the fluctuations of the magnitude and the direction of the wall shear stress vector $\boldsymbol{\tau}(t)$ with high resolution in the slow air currents. The results show the persistence of a tumble-type structure, which is in a bi-stable state as it oscillates regularly about a mean orientation at a timescale that compares with the typical eddy turnover time. The mean orientation can persist almost hundreds of eddy turnovers, until a re-orientation of this structure in form of a slow precession sets in, while a critical weakening of the mean wall shear stress magnitude - respectively the mean wind - is observed. The amplitudes of turbulent fluctuations in the streamwise wall shear-stress $\tau_x$ along mean wind direction reveal a highly skewed Weibull distribution, while the fluctuations happening on larger time scales follow a symmetric Gaussian distribution. Extreme events such as local flow reversals with negative $\tau_x$ are recovered as rare events and correlate with a rapid angular twist of the wall shear-stress vector. Those events - linked to critical points in the skin friction field - correlate with the coincidence of signals at the tails in both probability distributions

Fluctuations of the wall shear stress vector in a large-scale natural convection cell

We report first experimental data of the wall shear stress in turbulent air flow in a large-scale Rayleigh-Bénard experiment. Using a novel, nature-inspired measurement concept (Bruecker and Mikulich 2017, PLoS ONE 12, e0179253), we measured the mean and fluctuating part of the two components of the wall shear stress vector at the heated bottom plate at a Rayleigh number Ra=1.58e10 and a Prandtl number Pr=0.7. The total sampling period of 1,5 hours allowed to capture the dynamics of the magnitude and the orientation of the vector over several orders of characteristic time-scales of the large-scale circulation. We found the amplitude of short-term (turbulent) fluctuations to be following a highly skewed Weibull distribution, while the long-term fluctuations are dominated by the modulation effect of a quasi-regular angular precession of the outer flow around a constant mean, the time-scale of which is coupled to the characteristic eddy turn-over time of the global recirculation roll. Events of instantaneous negative streamwise wall shear occur when rapid twisting of the local flow happens. A mechanical model is used to explain the precession by tilting the spin moment of the large circulation roll and conservation of angular momentum. A slow angular drift of the mean orientation is observed in a phase of considerable weakening of mean wind magnitude

Barrel of Ilmenau: a large-scale convection experiment to study dust devil-like flow structures

We present an experimental facility for the validation of numerical simulations on atmospheric dust devils in a controlled laboratory experiment. Dust devils are atmospheric air vortices with a vertical axis, and are formed by intense solar radiation and the resulting vertical temperature gradient. The structure of a typical dust devil is dominated by a radial inflow near the surface and a vertical upward flow within the vortex. These vortices have been studied in recent years using field observations, in situ measurements, and large-eddy simulation (LES). Field tests suffer from the limited area and their unpredictable behavior, while the LES approach cannot resolve the dust devils well enough. Dust devil-like structures may also occur in direct numerical simulation (DNS) with a Rayleigh number of at least Ra = 10^7 in Rayleigh-Bénard convection, with the advantage that the structures can be resolved more precisely. In order to validate the DNS approach and provide measurement data, the airflow is measured inside of a large-scale Rayleigh-Bénard cell of similar geometry (i.e. inside the Barrel of Ilmenau) to the DNS set-up for Rayleigh numbers from Ra = 10^6 to Ra = 10^12. For the measurement of the flow in a large volume, an optical measurement method is used to obtain the trajectories of single particles. Since there are no commercial systems that are suitable for such a large measurement volume, we developed our own system

Viscous boundary layers in turbulent Rayleigh-Bénard convection

Highly resolved local velocity profiles inside the boundary layers in turbulent Rayleigh-Bénard convection in air are presented and discussed. The present work makes progress to our work in the past (see du Puits & Resagk, 2007) that our actual set-up permits the measurement of the wall-normal velocity component w up to a distance of 200 mm away from the wall. All component profiles were performed in a cylindrical box with an aspect ratio Γ = 1, a Prandtl number Pr = 0.7 and Rayleigh numbers Ra = 3 × 10 9 , Ra = 3 × 10 10 . We compare the experimental results with numerics at Ra = 3 × 10 10 directly. We found that the profiles of mean velocity from both experiments and numerics collapse very well with each other and both of the mean horizontal velocity profiles differ from the laminar Blasius prediction at the boundary layer. The wall-normal mean velocity at the central window tends to zero in both experiment and numerics

The cause of oscillations of the large-scale circulation of turbulent Rayleigh-B{\'e}nard convection

In agreement with a recent experimental discovery by Xia et. al. (2009), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling and Ahlers (2004). We show that both modes can be described by an extension of a model developed previously [Brown and Ahlers (2008)] which consists of permitting a lateral displacement of the LSC circulation plane away from the vertical center line of the sample as well as a variation in displacements with height (such displacements had been excluded in the original model). Pressure gradients produced by the side wall of the container on average center the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model predicts the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude, and probability distributions of the displacements.Comment: 16 pages, 6 figures, submitted to Journal of Fluid Mechanic