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

Entropy

Massimo Materassi³  Giuseppe Consolini²  Nathan Smith¹ 

[1] Department of Electronic and Electrical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, UK; E-Mail:;INAF-Istituto di Astrofisica e Planetologia Spaziali Area di Ricerca Roma Tor Vergata, Via del Fosso del Cavaliere, 100, 00133 Roma, Italy; E-Mails:;Istituto dei Sistemi Complessi ISC-CNR, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy

关键词: transfer entropy;    dynamical systems;    turbulence;    cascades;    shell models;   

DOI  :  10.3390/e16031272

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland