Physics – General Physics
Scientific paper
Apr 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrva..39.3660o&link_type=abstract
Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 39, April 1, 1989, p. 3660-3671. Research supported by DO
Physics
General Physics
61
Chaos, Conducting Fluids, Incompressible Flow, Turbulent Flow, Fractals, Liapunov Functions, Magnetic Effects, Three Dimensional Flow, Two Dimensional Flow
Scientific paper
Considering the astrophysical medium to be a flowing plasma, the kinematic dynamo problem is of basic interest in that it addresses the question of why magnetic fields occur in the universe. Motivated by that problem (in the vector case) and recent experiments (in the scalar case) which demonstrate the possibility of measuring the fractal dimension of the gradient squared of convected passive scalars, the authors consider the convection of vector fields and scalar functions by incompressible, chaotic fluid flows. Measures based on the magnitudes of the vectors and the gradients of scalars are defined and shown to be multifractals. The dimension spectra for these fractal measures are related to the stretching properties of the fluid flows by a partition function formalism, and the utility of this formalism is demonstrated by application to examples.
Antonsen Thomas M. Jr.
Ott Edward
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