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Entropy 2014, 16(3), 1272-1286; doi:10.3390/e16031272

Information Theory Analysis of Cascading Process in a Synthetic Model of Fluid Turbulence

1,* , 2
1 Istituto dei Sistemi Complessi ISC-CNR, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy 2 INAF-Istituto di Astrofisica e Planetologia Spaziali Area di Ricerca Roma Tor Vergata, Via del Fossodel Cavaliere, 100, 00133 Roma, Italy 3 Department of Electronic and Electrical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, UK
* Author to whom correspondence should be addressed.
Received: 29 September 2013 / Revised: 12 February 2014 / Accepted: 19 February 2014 / Published: 27 February 2014
(This article belongs to the Special Issue Transfer Entropy)
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The use of transfer entropy has proven to be helpful in detecting which is the verse of dynamical driving in the interaction of two processes, X and Y . In this paper, we present a different normalization for the transfer entropy, which is capable of better detecting the information transfer direction. This new normalized transfer entropy is applied to the detection of the verse of energy flux transfer in a synthetic model of fluid turbulence, namely the Gledzer–Ohkitana–Yamada shell model. Indeed, this is a fully well-known model able to model the fully developed turbulence in the Fourier space, which is characterized by an energy cascade towards the small scales (large wavenumbers k), so that the application of the information-theory analysis to its outcome tests the reliability of the analysis tool rather than exploring the model physics. As a result, the presence of a direct cascade along the scales in the shell model and the locality of the interactions in the space of wavenumbers come out as expected, indicating the validity of this data analysis tool. In this context, the use of a normalized version of transfer entropy, able to account for the difference of the intrinsic randomness of the interacting processes, appears to perform better, being able to discriminate the wrong conclusions to which the “traditional” transfer entropy would drive.
Keywords: transfer entropy; dynamical systems; turbulence; cascades; shell models transfer entropy; dynamical systems; turbulence; cascades; shell models
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Materassi, M.; Consolini, G.; Smith, N.; De Marco, R. Information Theory Analysis of Cascading Process in a Synthetic Model of Fluid Turbulence. Entropy 2014, 16, 1272-1286.

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