Communications in Mathematical Physics

, Volume 247, Issue 3, pp 553–599 | Cite as

Averaging Versus Chaos in Turbulent Transport?

  • Houman OwhadiEmail author


In this paper we analyze the transport of passive tracers by deterministic stationary incompressible flows which can be decomposed over an infinite number of spatial scales without separation between them. It appears that a low order dynamical system related to local Peclet numbers can be extracted from these flows and it controls their transport properties. Its analysis shows that these flows are strongly self-averaging and super-diffusive: the delay τ (r) for any finite number of passive tracers initially close to separate till a distance r is almost surely anomalously fast (τ (r)∼ r 2–ν , with ν > 0). This strong self-averaging property is such that the dissipative power of the flow compensates its convective power at every scale. However as the circulation increases in the eddies the transport behavior of the flow may (discontinuously) bifurcate and become ruled by deterministic chaos: the self-averaging property collapses and advection dominates dissipation. When the flow is anisotropic a new formula describing turbulent conductivity is identified.


Spatial Scale Advection Transport Property Infinite Number Dissipative Power 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.LATP, UMR CNRS 6632CMI, Université de ProvenceMarseille Cedex 1France

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