Statistics of defect motion in spatiotemporal chaos in inclined layer convection

We report experiments on defect-tracking in the state of undulation chaos observed in thermal convection of an inclined fluid layer. We characterize the ensemble of defect trajectories according to their velocities, relative positions, diffusion, and gain and loss rates. In particular, the defects exhibit incidents of rapid transverse motion which result in power law distributions for a number of quantitative measures. We examine connections between this behavior and L\'evy flights and anomalous diffusion. In addition, we describe time-reversal and system size invariance for defect creation and annihilation rates.Comment: (21 pages, 17 figures

Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition

We present measurements of the orientation $\theta_0$ and temperature amplitude $\delta$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Benard convection (RBC) with aspect ratio $\Gamma \equiv D/L = 1.00$ ($D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr \simeq 0.8$. Results for $\theta_0$ revealed a preferred orientation with upflow in the West, consistent with a broken azimuthal invariance due to Earth's Coriolis force [see \cite{BA06b}]. They yielded the azimuthal diffusivity $D_\theta$ and a corresponding Reynolds number $Re_{\theta}$ for Rayleigh numbers over the range $2\times 10^{12} < Ra < 1.5\times 10^{14}$. In the classical state ($Ra < 2\times 10^{13}$) the results were consistent with the measurements by \cite{BA06a} for $Ra < 10^{11}$ and $Pr = 4.38$ which gave $Re_{\theta} \propto Ra^{0.28}$, and with the Prandtl-number dependence $Re_{\theta} \propto Pr^{-1.2}$ as found previously also for the velocity-fluctuation Reynolds number $Re_V$ \cite[]{HGBA15b}. At larger $Ra$ the data for $Re_{\theta}(Ra)$ revealed a transition to a new state, known as the "ultimate" state, which was first seen in the Nusselt number $Nu(Ra)$ and in $Re_V(Ra)$ at $Ra^*_1 \simeq 2\times 10^{13}$ and $Ra^*_2 \simeq 8\times 10^{13}$. In the ultimate state we found $Re_{\theta} \propto Ra^{0.40\pm 0.03}$. Recently \cite{SU15} 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 G\"ottingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as "ultimate".Comment: 12 pages, 4 figures, to be pub. in JFM

Lagrangian view of time irreversibility of fluid turbulence

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity (the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for single-particle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the "arrow of time." Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.Comment: accepted for publication in Science China - Physics, Mechanics & Astronom

Logarithmic temperature profiles of turbulent Rayleigh-B\'enard convection in the classical and ultimate state for a Prandtl number of 0.8

We report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical sample with aspect ratio (diameter over height) of 0.50, both in the classical and in the ultimate state. The Prandtl number was close to 0.8. We find a "logarithmic layer" in which the temperature varies as A*ln(z/L) + B with the distance z from the bottom plate of the sample. The amplitude A varies with radial position r. In the classical state these results are in good agreement with direct numerical simulations (DNS); in the ultimate state there are as yet no DNS. A close analogy between the temperature field in the classical state and the "Law of the Wall" for the time-averaged down-stream velocity in shear flow is discussed.Comment: 27 pages, 15 figure

Dissipative Effects on Inertial-Range Statistics at High Reynolds numbers

Using the unique capabilities of the Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization, G\"{o}ttingen, we report experimental result on classical grid turbulence that uncover fine, yet important details of the structure functions in the inertial range. This was made possible by measuring extremely long time series of up to $10^{10}$ samples of the turbulent fluctuating velocity, which corresponds to $\mathcal{O}\left(10^5\right)$ large eddy turnover times. These classical grid measurements were conducted in a well-controlled environment at a wide range of high Reynolds numbers from $R_\lambda=110$ up to $R_\lambda=1600$, using both traditional hot-wire probes as well as NSTAP probes developed at Princeton University. We found that deviations from ideal scaling are anchored to the small scales and that dissipation influences the inertial-range statistics at scales larger than the near-dissipation range.Comment: 6 pages, 5 figure

Evolution of geometric structures in intense turbulence

We report measurements of the evolution of lines, planes, and volumes in an intensely turbulent laboratory flow using high-speed particle tracking. We find that the classical characteristic time scale of an eddy at the initial scale of the object considered is the natural time scale for the subsequent evolution. The initial separation may only be neglected if this time scale is much smaller than the largest turbulence time scale, implying extremely high turbulence levels.Comment: 10 pages, 6 figures, added more detail

Defect turbulence and generalized statistical mechanics

We present experimental evidence that the motion of point defects in thermal convection patterns in an inclined fluid layer is well-described by Tsallis statistics with an entropic index $q \approx 1.5$. The dynamical properties of the defects (anomalous diffusion, shape of velocity distributions, power law decay of correlations) are in good agreement with typical predictions of nonextensive models, over a range of driving parameters