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A shell-model approach to fractal-induced turbulence |
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| Authors: | B Mazzi F Okkels JC Vassilicos |
| Affiliation: | DAMTP, University of Cambridge, Cambridge CB3 9 EW, UK, GB OFD, Ris? National Laboratory and CATS, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark, DK Dept. of Aeronautics, Imperial College London, London, UK, GB |
| Abstract: | We present a shell-model of fractal induced turbulence which predicts that structure function scaling exponents decrease in absolute value as the fractal dimension of the turbulence-inducing fractal object increases. This qualitative prediction is in agreement with laboratory measurements. Finer details of the fractal induced turbulence statistics and dynamics depend on the fractal force's phases, i.e. on the detailed construction of the fractal stirrer. In a case of deterministic forcing phases, a critical fractal dimension exists below which the average rate of inter-scale energy transfer <T n> is a decreasing function of the wavenumber kn and the structure function scaling exponents take close to Kolmogorov values. Above this critical fractal dimension, <T n> is an increasing function of kn and the structure function scaling exponents deviate significantly from Kolmogorov values. Received 25 June 2001 / Received in final form 5 April 2002 Published online 19 July 2002 |
| Keywords: | PACS 47 27 Ak Fundamentals – 47 27 Gs Isotropic turbulence homogeneous turbulence |
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