The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: for cellular flows we observe V f ∼ U 1/4 for fast advection, and V f ∼ U 3/4 for slow advection.

Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we provide an analytical approximation for the front speed, v f , as a function of the stirring intensity, U , in good agreement with the numerical results and, for large U , the behavior v f ∼ U/ log(U ) is predicted. The large scale of the velocity field mainly rules the front speed behavior even in the presence of smaller scales. In the unsteady (time-periodic) case, the front speed displays a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is chaotic, chaos in front dynamics only survives for a transient. Asymptotically the front evolves periodically and chaos manifests only in the spatially wrinkled structure of the front.

The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the enhancement of front speed with respect to the non-stirred case. By means of numerical simulations and theoretical arguments we describe the behavior of front speed as a function of the stirring intensity, $U$. For slow reaction, the front propagates with a speed proportional to $U^{1/4}$, conversely for fast reaction the front speed is proportional to $U^{3/4}$. In the geometrical optics limit, the front speed asymptotically behaves as $U/\ln U$.Comment: 10 RevTeX pages, 10 included eps figure

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We study a reaction diffusion system where we consider a non-gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with tails approaching to zero faster than a power law, the usual qualitative behaviours of the standard reaction diffusion system, i.e., exponential tails for the reacting field and a constant front speed, are recovered. On the contrary if the process has power law tails, also the reacting field shows power law tail and the front speed increases exponentially with time. The comparison with other reaction-transport systems which exhibit anomalous diffusion shows that, not only the presence of anomalous diffusion, but also the detailed mechanism, is relevant for the front propagation.Pacs: 47.70.Fw

The exit-time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (inverse structure functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out that the inverse structure functions show a much more extended intermediate dissipative range than the structure functions, leading to the first clear evidence of the existence of such a range of scales.

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to the evolution of the single (or microscopic) elements of the system. The usual Lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon. Using the recently introduced notion of finite size Lyapunov exponent, we characterize, in a consistent way, these macroscopic behaviours. Basically, at small values of the perturbation we recover the usual (microscopic) Lyapunov exponent, while at larger values a sort of macroscopic Lyapunov exponent emerges, which can be much smaller than the former. A quantitative characterization of the chaotic motion at hydrodynamical level is then possible, even in the absence of the explicit equations for the time evolution of the macroscopic observables.Comment: 24 pages revtex, 9 figures included. Improved version also with 1 figure and some references adde

We present a numerical study of mixing and reaction efficiency in closed domains. In particular we focus our attention on laminar flows. In the case of inert transport the mixing properties of the flows strongly depend on the details of the Lagrangian transport. We also study the reaction efficiency. Starting with a little spot of product we compute the time needed to complete the reaction in the container. We found that the reaction efficiency is not strictly related to the mixing properties of the flow. In particular, reaction acts as a "dynamical regulator".