Persistent patterns in uniform medium

The transition between the two regimes takes place when the characteristic timescale of chaotic mixing (e.g. the inverse Lyapunov exponent) is comparable to the characteristic decorrelation time of the of the local oscillations, that was found to be significantly larger than the oscillation period of the reaction. 

Non-decaying patterns in a similar stirred oscillatory system were also found numerically by Perez-Munuzuri (2006) in the weakly chaotic flow regime of the blinking vortex flow, i.e. for small /x. When the distance between the vortices is large, the flow has little effect on the spatial structure and a pattern of spiral waves forms as in the 

Another set of experiments, by Paoletti et al. (2006), investigated the synchronization of stirred oscillatory BZ reaction over distances larger than the characteristic lengthscale of the flow. In this experiment the flow was composed of an annular ring of counter-rotating vortices with a superimposed additional oscillatory azimuthal flow. A simplified model of the corresponding velocity field can be written as 

Typically, large scale transport in flows with a finite correlation length of the velocity field is diffusive with an effective diffusion coefficient Deff (Sect. 2.2.2). Therefore the coarse grained structure of the oscillatory reaction in this flow should be similar to a onedimensional oscillatory reaction-diffusion system, i.e. propagating waves and no synchronization of the local oscillations on large scales. 

This wavelike behavior is indeed observed in the experiments when the drift velocity is smaller than the velocity of the oscillatory part of the flow, Vd Vo However, when Vd vq the oscillations synchronize over the whole system consisting of about 20 vortices. Two types of coherent oscillatory modes are observed depending on the flow parameters corotating synchronization when even and odd cells synchronize independently with arbitrary phases, and global synchronization when the BZ reaction oscillates in synchrony in every cell (Fig. 8.3). 

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