Anomalous Diffusion and Mixing in an Oscillating Rayleigh-Benard Flow : General and Mathematical Physics

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The diffusion and mixing of tracer particles by chaotic advection in two-dimensional oscillating Rayleigh-Benard convection are shown to be anomalous due to the existence of two kinds of islands of tori. The dependence of the diffusion constant D on the amplitude B of the roll oscillation is calculated, which leads to the √<B> dependence with several fine-grained peaks. It is found that accelerator-mode islands appear around the oscillating roll boundaries in a peak range of B, and the intermittent sticking of tracer particles to these islands leads to an anomalous diffusion with D=∞. The diffusion and the formation of the islands are elucidated in terms of the lobe dynamics. The spectrum ψ(Λ) and the probability density P(Λ; n) of the coarse-grained expansion rates Λ_n of nearby particle orbits with length n in fluid space are also discussed to characterize the mixing. We have ψ(Λ)=0 for 0< Λ < Λ^∞, where Λ^∞ is the Liapunov exponent. This is caused by the intermittent sticking of tracer particles to the coexisting normal islands. The distribution function f(n) of sticking times n obeys power-law decay f(n)∝n^<-1-β>, (1<β<2). Then Ρ(Λ;n) for Λ>0 obeys an anomalous scaling law Ρ(Λ; n)=n^δp(n^δΛ^^^) with δ=(β-1)/β<1/2,Λ^^^ ≡Λ-Λ^∞, where p(x)∝∣x∣^<-(1+β)> for -x≫1 and exp[-ax^<1/δ>], (a >0) for x≫1. These remarkable features of the mixing are numerically justified for the oscillating Rayleigh-Benard flow.
理論物理学刊行会の論文
1992-09-25

Anomalous Diffusion and Mixing in an Oscillating Rayleigh-Benard Flow : General and Mathematical Physics

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