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Research Problems on Chaotic Advection in Three Dimensions and at Higher Reynolds Number.
Final rept. 1 May 93-30 Jun 94,
COLUMBIA UNIV NEW YORK LOWELL MEMORIAL LIBRARY
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Over the past ten years the study of chaotic advection, namely the chaotic motion of particles in deterministic dynamical systems derived from velocity fields associated with simple fluid flows, has come to the fore as a model and means of obtaining efficient mixing. The main question addressed in the research supported by this grant has been to determine how useful the ideas and tools of dynamical system theory, successful in analyzing chaotic advection models, are for studying mixing in high Reynolds number, i.e. turbulent flows. The link between dynamical systems ideas and turbulence is provided by the Lagrangian picture of the fluid, namely the fluid particle description. Accordingly our work has centered on developing Lagrangian descriptions of the stretching and alignment, the processes by which mixing is achieved, for passive and non-passive scalars and vectors. This has led to some new insights into the mechanisms of fine scale vorticity dynamics and identified the subtle and critical role of pressure fluctuations. In the case of the non-passive vector dynamics of magnetic field lines, a Lagrangian formulation of 3-dimensional magneto-hydrodynamics equations has identified the possibility of a finite time singularity around magnetic null points.
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