Abstract
This paper focuses on the evolution of material filaments in chaotic flows. This evolution is numerically calculated for three cases of the sine flow corresponding to a mainly regular, a mainly chaotic, and a globally chaotic case without discernible islands. In all cases, the stretched filament has an extremely non-uniform spatial distribution, with densities spanning several orders of magnitude and being the largest in the neighborhood of hyperbolic periodic points. Such spatial non-uniformity is a permanent property of time-periodic flows. As expected, the length of the filament increases exponentially in time, but due to the spatial non-uniformities in filament density, its growth is much faster than predicted by the Lyapunov exponent. The stretched filaments are self-similar in time, as revealed by their spatial structure and by the frequency distribution of the logarithm of the striation thickness, which is described by a family of curves that have an invariant shape and that can be collapsed onto a single curve by means of a simple scaling.
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© 1997 Springer-Verlag London Limited
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Alvarez, M.M., Muzzio, F.J., Cerbelli, S., Adrover, A. (1997). Self-Similar Spatio-Temporal Structure of Material Filaments in Chaotic Flows. In: Lévy Véhel, J., Lutton, E., Tricot, C. (eds) Fractals in Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0995-2_24
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DOI: https://doi.org/10.1007/978-1-4471-0995-2_24
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