A Lagrangian analysis of advection-diffusion equation for a three dimensional chaotic flow

Journal Article · Tue Jun 01 04:00:00 EDT 1999 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.870006· OSTI ID:338677

Tang, X Z ^[1]; Boozer, A H ^[2]

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1. Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
2. Department of Applied Physics, Columbia University, New York, New York 10027 (United States)

The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial differential equations. If the flow has chaotic streamlines, the diffusion will dominate the solution at a critical time, which scales logarithmically with the diffusivity. The subsequent rapid diffusive relaxation is completed on the order of a few Lyapunov times, and it becomes more anisotropic the smaller the diffusivity. The local Lyapunov time of the flow is the inverse of the finite time Lyapunov exponent. A finite time Lyapunov exponent can be expressed in terms of two convergence functions which are responsible for the spatio-temporal complexity of both the advective and diffusive transports. This complexity gives a new class of diffusion barrier in the chaotic region and a fractal-like behavior in both space and time. In an integrable flow with shear, there also exist fast and slow diffusion. But unlike that in a chaotic flow, a large gradient of the scalar field across the KAM surfaces can be maintained since the fast diffusion in an integrable flow is strictly confined within the KAM surfaces. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 338677
• Journal Information: Physics of Fluids (1994), Journal Name: Physics of Fluids (1994) Journal Issue: 6 Vol. 11; ISSN PHFLE6; ISSN 1070-6631
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ADVECTION
DIFFUSION
FLUID FLOW
FLUID MECHANICS
FRACTALS
LYAPUNOV METHOD
PARTIAL DIFFERENTIAL EQUATIONS
THREE-DIMENSIONAL CALCULATIONS