The distribution of “time of flight” in three dimensional stationary chaotic advection

Physics of Fluids - Tập 27 Số 4 - 2015
Florence Raynal1, Philippe Carrière1
1LMFA, UMR CNRS–Université de Lyon, École Centrale de Lyon–Université Lyon 1–INSA Lyon , École Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Écully cédex, France

Tóm tắt

The distributions of “time of flight” (time spent by a single fluid particle between two crossings of the Poincaré section) are investigated for five different three dimensional stationary chaotic mixers. Above all, we study the large tails of those distributions and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically different, with a very large tail following a power law with an exponent close to −3.

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See supplemental material at http://dx.doi.org/10.1063/1.4918750 for the trajectory of a single particle in the case of global chaos U1 = 0.25: The trajectory is regularly trapped in the vicinity of the manifolds associated to fixed points of type (3) and (4), see Figure 12(a)and for advection of spot containing a large number of particles in the case of global chaosU1 = 0.25: spreading is limited in the vicinity of the manifolds associated to fixed points of type (3) and (4), see Figure 12(a).

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Physics of Fluids

Tập 27 Số 4

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