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Lyapunov exponent for small particles in smooth one-dimensional flows

Wilkinson, Michael (2011). Lyapunov exponent for small particles in smooth one-dimensional flows. Journal of Physics A: Mathematical and Theoretical, 44(4) 045502.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1088/1751-8113/44/4/045502
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Abstract

This paper discusses the Lyapunov exponent λ for small particles in a spatially and temporally smooth flow in one dimension. The Lyapunov exponent is obtained as a series expansion in the Stokes number, St, which is a dimensionless measure of the importance of inertial effects. The approach described here can be extended to calculations of the Lyapunov exponents and of the correlation dimension for inertial particles in higher dimensions. It is shown that there is a correction to this theory which arises because the particles do not sample the velocity field ergodically. Using this non-ergodic correction, it is found that (contrary to expectations) the first-order term in the expansion of λ does not vanish.

Item Type: Journal Article
Copyright Holders: 2011 IOP Publishing Ltd
Keywords: fluid dynamics; isotropic turbulence; homogeneous turbulence
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30915
Depositing User: Michael Wilkinson
Date Deposited: 06 Jan 2012 15:52
Last Modified: 30 Nov 2012 16:50
URI: http://oro.open.ac.uk/id/eprint/30915
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