A numerical Eulerian approach to mixing by chaotic advection

Abstract : Results of numerical simulation of the advection-diffusion equation at large P&let number are reported, describing the mixing of a scalar field under the action of diffusion and of a class of steady, bounded, three-dimensional flows, which can have chaotic streamlines. The time evolution of the variance of scalar field is calculated for different flow parameters and shown to undergo modulated exponential decay, with a decay rate which is a maximum for certain values of the flow parameters, corresponding to cases in which the streamlines are chaotic everywhere. If such global chaos is present, the decay rate tends to oscillate, whereas the presence of regular regions produces a more constant decay rate. Significantly different decay rates are obtained depending on the detailed properties of the chaotic streamlines. The relationship between the decay rate and the characteristic Lyapunov exponents of the flow is also investigated.
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Valérie Toussaint, Philippe Carrière, Florence Raynal. A numerical Eulerian approach to mixing by chaotic advection. Physics of Fluids, American Institute of Physics, 1995, 7 (11), pp.2587-2600. ⟨10.1063/1.868707⟩. ⟨hal-01348398⟩

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