Characterization Of Intermittency Research Articles

Reexamining the framework for intermittency in Lagrangian stochastic models for turbulent flows: A way to an original and versatile numerical approach

The characterization of intermittency in turbulence has its roots in the refined similarity hypotheses of Kolmogorov, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in an attempt to reproduce it. The first contribution of this work is to propose a requirement list to be satisfied by models designed within the Lagrangian framework. Multifractal stochastic processes are a natural choice to retrieve multifractal properties of the dissipation. Among them, we investigate the Gaussian multiplicative chaos formalism, which requires the construction of a log-correlated stochastic process X_{t}. The fractional Gaussian noise of Hurst parameter H=0 is of great interest because it leads to a log correlation for the logarithm of the process. Inspired by the approximation of fractional Brownian motion by an infinite weighted sum of correlated Ornstein-Uhlenbeck processes, our second contribution is to propose a stochastic model: X_{t}=∫_{0}^{∞}Y_{t}^{x}k(x)dx, where Y_{t}^{x} is an Ornstein-Uhlenbeck process with speed of mean reversion x and k is a kernel. A regularization of k(x) is required to ensure stationarity, finite variance, and logarithmic autocorrelation. A variety of regularizations are conceivable, and we show that they lead to the aforementioned multifractal models. To simulate the process, we eventually design a new approach relying on a limited number of modes for approximating the integral through a quadrature X_{t}^{N}=∑_{i=1}^{N}ω_{i}Y_{t}^{x_{i}}, using a conventional quadrature method. This method can retrieve the expected behavior with only one mode per decade, making this strategy versatile and computationally attractive for simulating such processes, while remaining within the proposed framework for a proper description of intermittency.

Characterization of intermittency at the onset of turbulence in the forced and damped nonlinear Schrödinger equation

In this paper we characterized intermittent transitions from temporal chaos to turbulence in the forced and damped nonlinear Schrödinger equation. We demonstrate using finite time Lyapunov exponents that during the transition a fraction of unstable periodic orbits embedded in a low dimensional chaotic attractor loses transversal stability, in a way that nearby trajectories are expelled away from its vicinity (a mechanism referred to as intermittency induced by Unstable Dimension Variability). During the transition, an appropriate decomposition of the Fourier phase space into transversal and longitudinal modes is performed. The analysis of modes dynamics sheds new light in the understanding of intermittency in spatially extended dynamical systems. Subsequently a perturbation is applied to the system in order to control the intermittent extreme events and reduce their occurrence.

Characterization of intermittency in zooplankton behaviour in turbulence.

We consider Lagrangian velocity differences of zooplankters swimming in still water and in turbulence. Using cumulants, we quantify the intermittency properties of their motion recorded using three-dimensional particle tracking velocimetry. Copepods swimming in still water display an intermittent behaviour characterized by a high probability of small velocity increments, and by stretched exponential tails. Low values arise from their steady cruising behaviour while heavy tails result from frequent relocation jumps. In turbulence, we show that at short time scales, the intermittency signature of active copepods clearly differs from that of the underlying flow, and reflects the frequent relocation jumps displayed by these small animals. Despite these differences, we show that copepods swimming in still and turbulent flow belong to the same intermittency class that can be modelled by a log-stable model with non-analytical cumulant generating function. Intermittency in swimming behaviour and relocation jumps may enable copepods to display oriented, collective motion under strong hydrodynamic conditions and thus, may contribute to the formation of zooplankton patches in energetic environments.

Characterization of Intermittency in Hierarchy of Chaotic Maps with Invariant Measure

We introduce a type-I intermittent behavior happening in one-dimensional nonlinear chaotic maps with the interesting property of being ergodic or having stable period-one fixed point. These maps bi...

Characterization of Intermittency in Plasma Edge Turbulence

AbstractThe intermittency in the edge turbulence of the magnetic confinement devices, caused by large‐scale events with high radial velocity, has been the object of several recent studies. It is well known that bursty behavior in the scrape‐off layer of magnetically confined plasmas, and the departure from random diffusion models is caused by intermittent large‐scale plasma structures radially convected at high speed. Recently performed statistical analysis of plasma density fluctuations have demonstrated universal features of intermittent phenomena in plasma turbulence in the sense that they originate and have the same properties in many devices with distinct configurations. We extend the universal features of turbulence to Laplace distributions of derivatives of plasma density flucutations and show the properties of distributions for various confinement regimes. We further demonstrate that universal features are not complete by performing multifractal analysis which reveals unique features for each device and for each confinement regime. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Statistical methods in nonlinear dynamics

Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.

Symbolic dynamics analysis of nonstationary data from a model of a magnetic system with solitons.

The probability distribution of a complexity measure is used to characterize chaotic states: an estimator of the algorithmic complexity of a time series of symbolic words is calculated within a fixed length time window, which sweeps through the time series analyzed. The words are derived through a symbolic dynamics scheme applied in an m-dimensional delay coordinate space. Time intervals instead of the variables of the system are used. The chaotic states of a model of a magnetic domain wall are characterized better by the methods presented than with the use of fractal dimensions and new intermittent states of the system were easily identified. Using an artificial nonstationary signal composed of different chaotic states of the Bloch wall as a test for chaos-chaos intermittency we demonstrate that the method developed is suitable for the detection and characterization of intermittency. It is also shown that nonstationarity in the form of a slow monotonic drift in the control parameter may extend the stability range of periodic states of the spatially extended system studied-a trackinglike phenomenon.