A. Mazzino

On strong anomalous diffusion

Superdiffusive behavior, i.e., 〈x2(t)〉∼t2ν, with ν>1/2, is in general not completely characterized by a unique exponent. We study some systems exhibiting strong anomalous diffusion, i.e., 〈∣x(t)∣q〉∼tqν(q) where ν(2)>1/2 and qν(q) is not a linear function of q. This feature is different from the weak superdiffusive regime, i.e., ν(q)=const>1/2, occurring in random shear flows. Strong anomalous diffusion can be generated by nontrivial chaotic dynamics, e.g., Lagrangian motion in 2D time-dependent incompressible velocity fields, 2D symplectic maps and 1D intermittent maps. Typically the function qν(q) is piecewise linear. This is due to two mechanisms: a weak anomalous diffusion for the typical events and a ballistic transport for the rare excursions. In order to have strong anomalous diffusion one needs a violation of the hypothesis of the central limit theorem, this happens only in a very narrow region of the control parameters space. In the presence of strong anomalous diffusion one does not have a unique exponent and therefore one has the failure of the usual scaling P(x,t)=t−νF(x/tν) of the probability density. This implies that the effective equation at large scale and long time for P(x,t), obeys neither the usual Fick equation nor other linear equations involving temporal and/or spatial fractional derivatives.

Fronts in passive scalar turbulence

The evolution of scalar fields transported by turbulent flow is characterized by the presence of fronts, which rule the small-scale statistics of scalar fluctuations. With the aid of numerical simulations, it is shown that: Isotropy is not recovered, in the classical sense, at small scales; scaling exponents are universal with respect to the scalar injection mechanisms; high-order exponents saturate to a constant value; nonmature fronts dominate the statistics of intense fluctuations. Results on the statistics inside the “plateaux,” where fluctuations are weak, are also presented. Finally, we analyze the statistics of scalar dissipation and scalar fluxes.

Universality and Saturation of Intermittency in Passive Scalar Turbulence

The statistical properties of a scalar field advected by the nonintermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are probed by comparing the results obtained with two types of injection mechanisms. Scaling properties are shown to be universal, even though anisotropies injected at large scales persist down to the smallest scales and local isotropy is not fully restored. Scalar statistics is strongly intermittent and scaling exponents saturate to a constant for sufficiently high orders. This is observed also for the advection by a velocity field rapidly changing in time, pointing to the genericity of the phenomenon.

Twenty-five years of multifractals in fully developed turbulence: A tribute to Giovanni Paladin

A power factor correction system includes a sensing device in communication with a power supply to measure the line voltage on conventional service lines and detect any voltage fluxuations. A temperature controller receives power from the service lines and supplies an output voltage, based on the line voltage input, to one or more resistive loads, such as heater members. The heater members in turn are used to keep material in a molding device in a molten condition and within a certain temperature range. Fluctuations in the line voltage are detected by the sensing device which prevents corresponding changes in the voltage supplied to the resistive loads from the temperature controller.

Active and passive fields face to face

The statistical properties of active and passive scalar fields transported by the same turbulent flow are investigated. Four examples of active scalar have been considered: temperature in thermal convection, magnetic potential in two-dimensional (2D) magnetohydrodynamics (MHD), vorticity in 2D Ekman turbulence and potential temperature in surface flows. In the cases of temperature and vorticity, it is found that the active scalar behaviour is akin to that of its co- evolving passive counterpart. The two other cases indicate that this similarity is in fact not generic and differences between passive and active fields can be striking: in 2D MHD, the magnetic potential performs an inverse cascade, whereas the passive scalar cascades towards the small scales; in surface flows, although both perform a direct cascade, the potential temperature and the passive scalar have different scaling laws already at the level of low-order statistical objects. These significant differences are rooted in the correlations between the active scalar input and the particle trajectories. The role of such correlations in the issue of universality in active scalar transport and the behaviour of dissipative anomalies is addressed.

Lagrangian Method for Multiple Correlations in Passive Scalar Advection

A Lagrangian method is introduced for calculating simultaneous n-point correlations of a passive scalar advected by a random velocity field, with random forcing and finite molecular diffusivity κ. The method, which is here presented in detail, is particularly well suited for studying the κ→0 limit when the velocity field is not smooth. Efficient Monte Carlo simulations based on this method are applied to the Kraichnan model of passive scalar and lead to accurate determinations of the anomalous intermittency corrections in the fourth-order structure function as a function of the scaling exponent ξ of the velocity field in two and three dimensions. Anomalous corrections are found to vanish in the limits ξ→0 and ξ→2, as predicted by perturbation theory.

Phase-field model for the Rayleigh–Taylor instability of immiscible fluids

The Rayleigh–Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase field) whose variation is continuous across the interfacial layers and is uniform in the bulk region. The phase field model obeys a Cahn–Hilliard equation and is two-way coupled to the standard Navier–Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity-capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both in the case of negligible viscosity and in the case of nonzero viscosity. In the latter situation only upper and lower bounds for the perturbation growth-rate are known. Finally, we have also investigated the weaklynonlinear stage of the perturbation evolution and identified a regime characterized by a constant terminal velocity of bubbles/spikes. The measured value of the terminal velocity is in perfect agreement with available theoretical prediction. The phase-field approach thus appears to be a valuable tecnhique for the dynamical description of the stages where hydrodynamic turbulence and wave-turbulence enter into play.

Simple stochastic models showing strong anomalous diffusion

Abstract:We show that strong anomalous diffusion, i.e. where is a nonlinear function of q, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible to compute analytically where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density function cannot hold, a part (sometimes) in the limit of very small , now . Moreover the comparison with previous numerical results shows that the shape of is not universal, i.e., one can have systems with the same but different F.

Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian, delta-correlated in time, and scales with a positive exponent xi. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to O(xi) using the renormalization group. The exponents exhibit a hierarchy related to the degree of anisotropy; the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in the odd correlation functions: the skewness factor is slowly decreasing going down to small scales and higher odd dimensionless ratios (hyperskewness, etc.) dramatically increase, thus diverging in the r-->0 limit.

Elastically bounded flapping wing for energy harvesting

In this Letter, we present and discuss an energy harvesting device, based on a wing elastically bounded to a fixed support. Large amplitude and periodic oscillations can be induced when this system is subject to wind, if a few parameters are carefully set. A linear stability analysis as well as two-dimensional numerical simulations confirms the existence of instability regions in the parameter space. In order to harvest energy by using this system, different methods are considered. Preliminary results obtained by an electromagnetic coupling are presented.