Blinking vortex flow

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... 

Figure 2.15 Instantaneous view of the chaotic saddle (a), stable (b) and unstable (c) manifolds for the advection dynamics in the blinking vortex-sink flow. The vortex-sinks are at (x,y) = ( — 1,0) and (0,1) (from Karolyi and Tel (1997)).

A simple model that illustrates the chaotic scattering process and fractal manifolds in open flows is the blinking vortex-sink flow (Karolyi and Tel, 1997) that consists of two point vortex-sinks, with their centers separated by distance L, in an unbounded two-dimensional domain. Each vortex-sink is opened alternately for a half period T/2 and, while active, it generates a flow given by the streamfunction... 

In the blinking vortex-sink chaotic open flow system we have again two qualitatively different regimes, depending on Da, with a transition at the critical value Dac 2.3. As before, for small Da the initial perturbation decays fast towards C = 0. This is, however, not followed by an homogeneous transition to the C = 1 state from the (7 0 unstable configuration. The perturbation is now completely... 

Figure 7.4 Snapshots of the spatial distribution for the autocatalytic model (7.1) in the open blinking vortex-sink flow at time intervals equal to the flow period for a supercritical Damkohler number, Da = 7.0. Note, that after a transient time a time-periodic asymptotic state is reached where the autocatalytic growth, localized on the fractal unstable manifold, is balanced by the loss of product due to the outflow from the mixing region, in this case through the point sinks.

Figure 7.11 Total concentration (C ) in the stationary state vs Da for the FitzHugh-Nagumo dynamics in the open blinking vortex-sink flow showing two discontinuous transitions.

---