The Lagrangian description of turbulence is characterized by a unique conceptual simplicity and by an immediate connection with the physics of dispersion and mixing. In this article, we report some motivations behind the Lagrangian description of turbulence and focus on the statistical properties of particles when advected by fully developed turbulent flows. By means of a detailed comparison between experimental and numerical results, we review the physics of particle acceleration, Lagrangian velocity structure functions, and pairs and shapes evolution. Recent results for nonideal particles are discussed, providing an outlook on future directions.

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.

Cardiac defibrillation is usually achieved using a single high-energy electric shock of up to 4,000 volts, which can be damaging to the heart tissue. Eberhard Bodenschatz and colleagues show how the disordered electrical dynamics that underlie cardiac fibrillation can be controlled using low-energy electrical pulses. They show, in tests on dogs, that intrinsic homogeneities in the cardiac tissue (such as the vasculature) serve as nucleation sites for the generation of waves of electrical activity that can target the instabilities and bring the tissue dynamics back into synchrony. The new technique, called low-energy antifibrillation pacing or LEAP, delivers five sequential low-energy electrical field pulses to the fibrillating heart — an average energy reduction of 84% compared to standard defibrillation. 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 substrate1,2,3,4. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation5,6,7. 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.

Going with the flow: The interstitial spaces of the brain are filled with cerebrospinal fluid (CSF). Faubel et al. studied fluid transport in the third ventricle of the brain of mice, rats, and pigs. Sophisticated, state-of-the-art fluid dynamic studies revealed a complex pattern of cilia beating that leads to an intricate network of “highways” of CSF flow. This flow rapidly and efficiently transports and partitions CSF. Science , this issue p. 176