Eur. Phys. J. B 28, 243-251 (2002)
https://doi.org/10.1140/epjb/e2002-00226-6

A shell-model approach to fractal-induced turbulence

¹ DAMTP, University of Cambridge, Cambridge CB3 9 EW, UK
² OFD, Risø National Laboratory and CATS, Niels Bohr Institute, University of Copenhagen, Copenhagen, Danemark
³ Dept. of Aeronautics, Imperial College London, London, UK

Corresponding authors: ^a b.mazzi@damtp.cam.ac.uk - ^b j.c.vassilicos@ic.ac.uk

Received: 25 June 2001
Revised: 5 April 2002
Published online: 19 July 2002

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 is a decreasing function of the wavenumber k_n and the structure function scaling exponents take close to Kolmogorov values. Above this critical fractal dimension, is an increasing function of k_n and the structure function scaling exponents deviate significantly from Kolmogorov values.