Fronts in cellular flows

The material is organized as follows. In Section II we discuss particles motion in (both regular and chaotic) laminar flows. In Section III after a brief discussion on some general results that do not depend on the specific properties of the velocity field, we shall analyze front propagation in cellular flows. 

In cellular flows, the front border is wrinkled by the velocity field during propagation and its length increases until pockets of fresh material develop [37,38] (see Fig. 6). After this, the front propagates periodically in space and time with an enhanced speed Vf > vo-... 

M. Abel, M. Cencini, D. Vergni, and A. Vulpiani. Front speed enhancement in cellular flows. Chaos, 12 481, 2002. 

The front velocity v/ is the result of the interplay among the flow characteristics (i.e., intensity U and length scale L), the diffusivity D, and the production time scale x. In this chapter we shall study the problem of front propagation in the case of cellular flows. In particular, introducing the Damkohler number Da = L/(Ux) (the ratio of advective to reactive time scales) and the Pec let number Pe = UL/D (the ratio of diffusive to advective time scales), we shall discuss how the front speed can be expressed as a nondimensional function such as Vf/vo = < >(Da,Pe). A crucial role in determining i >(Da. Pe) is played by the renormalization of the diffusion coefficient and chemical time scale [13] induced by the advection. 

Figure 7.8 Propagation of BZ reaction fronts in an oscillating cellular flow. Images are shown every flow oscillation period. Left Phase-locked front in which the concentration pattern at the front edge repeats every oscillation period. Right example of an unlocked front. From Paoletti and Solomon (2005b).

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