Lagrangian Irreversibility and Energy Exchanges in Rotating-Stratified Turbulent Flows.

Turbulence in stratified and rotating turbulent flows is characterized by an interplay between waves and eddies, resulting in continuous exchanges between potential and kinetic energy. Here, we study how these processes affect the turbulent energy cascade from large to small scales, which manifests itself by an irreversible evolution of the relative kinetic energy between two tracer particles. We find that when r_{0}, the separation between particles, is below a characteristic length ℓ_{t}, potential energy is on average transferred to kinetic energy, reducing time irreversibility, and conversely when r_{0}>ℓ_{t}. Our Letter reveals that the scale ℓ_{t} coincides with the buoyancy length scale L_{B} over a broad range of configurations until a transition to a wave-dominated regime is reached.

Inertia Induces Strong Orientation Fluctuations of Nonspherical Atmospheric Particles.

The orientation of nonspherical particles in the atmosphere, such as volcanic ash and ice crystals, influences their residence times and the radiative properties of the atmosphere. Here, we demonstrate experimentally that the orientation of heavy submillimeter spheroids settling in still air exhibits decaying oscillations, whereas it relaxes monotonically in liquids. Theoretical analysis shows that these oscillations are due to particle inertia, caused by the large particle-fluid mass-density ratio. This effect must be accounted for to model solid particles in the atmosphere.

Lagrangian Supersaturation Fluctuations at the Cloud Edge.

Evaporation of cloud droplets accelerates when turbulence mixes dry air into the cloud, affecting droplet-size distributions in atmospheric clouds, combustion sprays, and jets of exhaled droplets. The challenge is to model local correlations between droplet numbers, sizes, and supersaturation, which determine supersaturation fluctuations along droplet paths (Lagrangian fluctuations). We derived a statistical model that accounts for these correlations. Its predictions are in quantitative agreement with results of direct numerical simulations, and explain the key mechanisms at play.

Stochastic Interpolation of Sparsely Sampled Time Series via Multipoint Fractional Brownian Bridges.

We propose and test a method to interpolate sparsely sampled signals by a stochastic process with a broad range of spatial and/or temporal scales. To this end, we extend the notion of a fractional Brownian bridge, defined as fractional Brownian motion with a given scaling (Hurst) exponent H and with prescribed start and end points, to a bridge process with an arbitrary number of intermediate and nonequidistant points. Determining the optimal value of the Hurst exponent H_{opt}, appropriate to interpolate the sparse signal, is a very important step of our method. We demonstrate the validity of our method on a signal from fluid turbulence in a high Reynolds number flow and discuss the implications of the non-self-similar character of the signal. The method introduced here could be instrumental in several physical problems, including astrophysics, particle tracking, and specific tailoring of surrogate data, as well as in domains of natural and social sciences.

Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence.

The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.

Energy flux fluctuations in a finite volume of turbulent flow.

The flux of turbulent kinetic energy from large to small spatial scales is measured in a small domain of varying size . The probability distribution function of the flux is obtained using a time-local version of Kolmogorov four-fifths law. The measurements, made at a moderate Reynolds number, show frequent events where the flux is backscattered from small to large scales, their frequency increasing as is decreased. The observations are corroborated by a numerical simulation based on the motion of many particles and on an explicit form of the eddy damping.

Control of rotating waves in cardiac muscle: analysis of the effect of an electric field.

The effect of an electric field on rotating waves in cardiac muscle is considered from a theoretical point of view. A model of excitation propagation taking into account the cellular structure of the heart is presented and studied. The application of a direct current electric field along the cardiac tissue is known to induce changes in membrane potential which decay exponentially with distance. Investigation of the model shows that the electric field induces a gradient of potential inside a cell which does not decay with distance, and results in modification of excitation propagation which extends a considerable distance from the electrodes. In two dimensions, it induces a drift of rotating waves. The effect of the electric field on propagation velocity and on rotating waves cannot be obtained in any arbitrary models of cardiac muscle. For an electric field of about 1 V cm-1 and junctional resistances of about 20 M omega, the change in velocity of propagation can be up to several percent, resulting in a drift velocity of rotating waves of the order of 1 cm s-1. To test these predictions, experiments with cardiac preparations are proposed.

Statistics of Fourier modes in a turbulent flow.

Fourier series are often used to discuss the properties of a homogeneous turbulent field. We investigate the statistics of Fourier modes of the turbulent velocity field and of a passive scalar. The statistics of individual Fourier modes is known to be Gaussian when the size of the system L is much larger that the integral (correlation) size l(0). The case where the integral size is of the order of the system size L approximately l(0), is studied by direct numerical simulations in the range 20 < or approximately = Rlambda < or approximately = 80. At a given Rlambda, we find that the probabilities of large fluctuations become larger when the wave number increases, in qualitative agreement with the notion of intermittency. As the Reynolds number increases, however, the probability density functions become closer to Gaussian, in sharp contrast with the behavior of velocity increments. We also show that in a simple model of cascade, the Fourier series decomposition is not appropriate to capture intermittency effects. Last, we discuss other issues related to our results.

Evolution of triangles in a two-dimensional turbulent flow.

As a turbulent flow advects a swarm of Lagrangian markers, the mutual separation between particles grows, and the shape of the swarm gets distorted. By following three points in an experimental turbulent two-dimensional flow with a k(-5/3) spectrum, we investigate the geometry of triangles, in a statistical sense. Two well-characterized shape distributions are identified. At long times when the average size of the triangles is larger than the integral scale, the distribution of shapes is Gaussian. When the size of the triangle is in the inertial range and grows as t(3/2) (Richardson's law), a plausibly self-similar, non-Gaussian probability distribution is observed, where very elongated triangles have a much larger probability than in the Gaussian regime. These results are discussed, and, in the latter case, compared with the predictions of a stochastic model recently introduced [A. Pumir et al., Phys. Rev. Lett. 85, 5324 (2000)].

Kinematic simulation of turbulent dispersion of triangles.

As three particles are advected by a turbulent flow, they separate from each other and develop nontrivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of three Lagrangian particles advected, in two dimensions, by kinematic simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no use of any delta correlation in time at any level. With this approach, situations with a very large range of inertial scales and varying persistence of spatial flow structure can be studied. We first demonstrate that the model flow reproduces recent experimental results at low Reynolds numbers. The statistical properties of the shape distribution at a much higher Reynolds number is then considered. The numerical results support the existence of nontrivial shape statistics, with a high probability of having elongated triangles. Even at the highest available inertial range of scales, corresponding to a ratio between large and small scale L/eta=17,000, a perfect self-similar regime is not found. The effects of the parameters of the synthetic flow, such as the exponent of the spectrum and the effect of the sweeping affect our results, are also discussed. Special attention is given to the effects of persistence of spatial flow structure.

Models of defibrillation of cardiac tissue.

Heterogeneities, such as gap junctions, defects in periodical cellular lattices, intercellular clefts and fiber curvature allow one to understand the effect of an electric field in cardiac tissue. They induce membrane potential variations even in the bulk of the myocardium, with a characteristic sawtooth shape. The sawtooth potential, induced by heterogeneities at large scales (tissue strands) can be more easily observed, and lead to stronger effects than the one induced at the cellular level. In the generic model of propagation in cardiac tissue (FitzHugh), 4 mechanisms of defibrillation were found, two mechanisms based on excitation (E(A),E(M)), and two-on de-excitation (D(A),D(M)). The lowest electric field is required by an E(M) mechanism. In the Beeler-Reuter ionic model, mechanism D(M) is impossible. We critically review the experimental basis of the theory and propose new experiments. (c) 1998 American Institute of Physics.

Wave emission from heterogeneities opens a way to controlling chaos in the heart.

The effectiveness of chaos control in large systems increases with the number of control sites. We find that electric field induced wave emission from heterogeneities (WEH) in the heart gives a unique opportunity to have as many control sites as needed. The number of pacing sites grows with the amplitude of the electric field. We demonstrate that WEH has important advantages over methods used in clinics, and opens a new way to manipulate vortices in experiments, and potentially to radically improve the clinical methods of chaos control in the heart.

Unpinning of a rotating wave in cardiac muscle by an electric field.

The possibility of terminating cardiac arrhythmias with electric fields of moderate intensity is a challenging problem from a fundamental point of view and an important issue for clinical applications. In an effort to understand how anatomical re-entries are affected by electric fields, we found that a weak shock, with an amplitude of an order of magnitude less than the defibrillating shock, may unpin the vortices rotating around the defects (obstacles). The unpinning results from a depolarization of the tissue near the obstacle, induced by an external electric field within a distance of order lambda approximately 1 mm. Unpinning was observed both in the FitzHugh model of excitable tissue, and in a specific Beeler-Reuter model of cardiac tissue. This theoretical observation suggests that anatomical re-entries can be transformed into functional re-entries, an effect that can be tested in experiments with cardiac muscle.

Two biophysical mechanisms of defibrillation of cardiac tissue.

We have studied the mechanisms whereby a strong electric shock terminates chaotic wave propagation in cardiac tissue (defibrillation). In a generic model of cellular excitable tissue with two variables, we have found two mechanisms: one based on excitation (E), and another based on de-excitation (D) of cells by the small scale periodic component of transmembrane potential induced by the shock. Symmetry properties of the current-voltage characteristics describing the dynamics of the fast ionic currents, along with the strength of the electric field determine which of these mechanisms operates. A prediction of this work to be tested experimentally is that upon increasing the electric field one mechanism may switch to another, resulting in the following unusual sequence of events: defibrillation is first possible by mechanism E at moderate fields, then impossible, and finally possible by mechanism D, at higher fields.