Eberhard Bodenschatz

Fluid Particle Accelerations in Fully Developed Turbulence

The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport, processes in stirred chemical reactors and combustion systems, and in the industrial production of nanoparticles. The concept of particle trajectories has been used successfully to describe mixing and transport in turbulence, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg–Yaglom prediction of fluid particle accelerations, based on the 1941 scaling theory of Kolmogorov. Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that, within experimental errors, Kolmogorov scaling of the acceleration variance is attained at high Reynolds numbers. Our data indicate that the acceleration is an extremely intermittent variable—particles are observed with accelerations of up to 1,500 times the acceleration of gravity (equivalent to 40 times the root mean square acceleration). We find that the acceleration data reflect the anisotropy of the large-scale flow at all Reynolds numbers studied.

Measurement of particle accelerations in fully developed turbulence

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 70000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 [ges ] R λ [ges ] 970. Particle trajectories exhibiting accelerations up to 16000 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 R λ [ges ] 500. The acceleration flatness is found to increase with Reynolds number, and to exceed 60 at R λ = 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 τ η .

Low-energy control of electrical turbulence in the heart

Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves in a heterogeneous anatomical substrate. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation. Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ Eα. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.

Experimental Lagrangian acceleration probability density function measurement

Abstract We report experimental results on the acceleration component probability distribution function at Rλ=690 to probabilities of less than 10−7. This is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55. We compare our probability distribution to those predicted by several models inspired by non-extensive statistical mechanics. We also look at acceleration component probability distributions conditioned on a velocity component for conditioning velocities as high as three times the standard deviation and find them to be highly non-Gaussian.

Lagrangian acceleration measurements at large Reynolds numbers

We report experimental measurements of Lagrangian accelerations in a turbulent water flow between counter-rotating disks for Taylor–Reynolds numbers 900<Rλ<2000. Particle tracks were recorded by imaging tracer particles onto a position sensitive photodiode, and Lagrangian information was obtained from fits to the position versus time data. Several challenges associated with extracting Lagrangian statistical quantities from particle tracks are addressed. The acceleration variance is obtained as a function of Reynolds number and shows good agreement with Kolmogorov (1941) scaling. The Kolmogorov constant for the acceleration variance is found to be a0=7±3.

Termination of Atrial Fibrillation Using Pulsed Low-Energy Far-Field Stimulation

Background— Electrically based therapies for terminating atrial fibrillation (AF) currently fall into 2 categories: antitachycardia pacing and cardioversion. Antitachycardia pacing uses low-intensity pacing stimuli delivered via a single electrode and is effective for terminating slower tachycardias but is less effective for treating AF. In contrast, cardioversion uses a single high-voltage shock to terminate AF reliably, but the voltages required produce undesirable side effects, including tissue damage and pain. We propose a new method to terminate AF called far-field antifibrillation pacing, which delivers a short train of low-intensity electric pulses at the frequency of antitachycardia pacing but from field electrodes. Prior theoretical work has suggested that this approach can create a large number of activation sites (“virtual” electrodes) that emit propagating waves within the tissue without implanting physical electrodes and thereby may be more effective than point-source stimulation. Methods and Results— Using optical mapping in isolated perfused canine atrial preparations, we show that a series of pulses at low field strength (0.9 to 1.4 V/cm) is sufficient to entrain and subsequently extinguish AF with a success rate of 93% (69 of 74 trials in 8 preparations). We further demonstrate that the mechanism behind far-field antifibrillation pacing success is the generation of wave emission sites within the tissue by the applied electric field, which entrains the tissue as the field is pulsed. Conclusions— AF in our model can be terminated by far-field antifibrillation pacing with only 13% of the energy required for cardioversion. Further studies are needed to determine whether this marked reduction in energy can increase the effectiveness and safety of terminating atrial tachyarrhythmias clinically.

Can We Understand Clouds Without Turbulence

Advances at the interface between atmospheric and turbulence research are helping to elucidate fundamental properties of clouds. Just over 50 years ago, Henry Houghton published an essay in Science entitled “Cloud physics: Not all questions about nucleation, growth, and precipitation of water particles are yet answered” (1). Since then, understanding of cloud processes has advanced enormously, yet we still face some of the basic questions Houghton drew attention to. The interest in finding the answers, however, has steadily increased, largely because clouds are a primary source of uncertainty in projections of future climate (2). Why is our understanding of cloud processes still so inadequate, and what are the prospects for the future?

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 ≈ 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.

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Apparatus for the study of Rayleigh–Bénard convection in gases under pressure

We review the history of experimental work on Rayleigh–Benard convection in gases, and then describe a modern apparatus that has been used in our experiments on gas convection. This system allows for the study of patterns in a cell with an aspect ratio (cell radius/fluid layer depth) as large as 100, with the cell thickness uniform to a fraction of a μm, and with the pressure controlled at the level of one part in 105. This level of control can yield a stability of the critical temperature difference for the convective onset of better than one part in 104. The convection patterns are visualized and the temperature field can be inferred using the shadowgraph technique. We describe the flow visualization and image processing necessary for this. Some interesting results obtained with the system are briefly summarized.