Topology, finite time Lyapunov exponents, and barriers for diffusive transport in advection-diffusion problems

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:489499

Tang, Xianzhu ^[1]; Boozer, A H ^[2]

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1. College of William and Mary, Williamsburg, VA (United States)
2. Columbia Univ., New York, NY (United States)

A wide range of transport problems are of advection-diffusion type. Typical fluid problems of this type are the relaxation of temperature differences in a room or the spread of a contaminant in a river. Important examples in plasma include the relaxation of electrons in a region of stochastic magnetic field lines and the evolution of the magnetic field embedded in a conducting fluid. The archetypal model equation is the advection-diffusion equation. The quantity being transported is {phi}. The flow velocity of the medium, v(x, t), is assumed given and independent of {phi}. The diffusive flux is {Tau}{sub d} = -D{del}{phi}. If the flow is chaotic, the properties of the transport are determined by the spatial and time dependence of the finite time Lyapunov exponent {lambda}({xi}, t). The rapid diffusive transport occurs only along the field line (s line) of the vector s, which defines the stable direction in which neighboring points asymptotically converge. The topology of the s lines affects the diffusive transport through the finite time Lyapunov exponent. We discover that the spatial variation of the finite time Lyapunov exponent along the s lines is smooth and determined by the topology of the s lines. For example, the finite time Lyapunov exponent reaches local minima if the s line makes a sharp bend. These topological bends hinder the diffusive transport and act as a barrier for diffusive relaxation. Such barriers for diffusion reside inside the chaotic region and they persist even the flow is highly chaotic. In the case of the electron relaxation in a region of stochastic field lines, there is a rapid diffusive relaxation of the spatial inhomogeneity in the electron distribution function which is typical of the chaotic transport of a passive scalar. But the diffusive relaxation of the pitch angle distribution is much slower.

• OSTI ID: 489499
• Report Number(s): CONF-960354--
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ADVECTION
DIFFUSION
LYAPUNOV METHOD
PLASMA FLUID EQUATIONS
TOPOLOGY
TRANSPORT THEORY