Pozo Soler, J.M., Geeers, A.J., Villa-Uriol, M.C. et al. (1 more author) (2017) Flow complexity in open systems: interlacing complexity index based on mutual information. Journal of Fluid Mechanics, 825. pp. 704-742. ISSN 0022-1120
Abstract
Flow complexity is related to a number of phenomena in science and engineering and has been approached from the perspective of chaotic dynamical systems, ergodic processes or mixing of fluids, just to name a few. To the best of our knowledge, all existing methods to quantify flow complexity are only valid for infinite time evolution, for closed systems or for mixing of two substances. We introduce an index of flow complexity coined interlacing complexity index (ICI), valid for a single-phase flow in an open system with inlet and outlet regions, involving finite times. ICI is based on Shannon’s mutual information (MI), and inspired by an analogy between inlet–outlet open flow systems and communication systems in communication theory. The roles of transmitter, receiver and communication channel are played, respectively, by the inlet, the outlet and the flow transport between them. A perfectly laminar flow in a straight tube can be compared to an ideal communication channel where the transmitted and received messages are identical and hence the MI between input and output is maximal. For more complex flows, generated by more intricate conditions or geometries, the ability to discriminate the outlet position by knowing the inlet position is decreased, reducing the corresponding MI. The behaviour of the ICI has been tested with numerical experiments on diverse flows cases. The results indicate that the ICI provides a sensitive complexity measure with intuitive interpretation in a diversity of conditions and in agreement with other observations, such as Dean vortices and subjective visual assessments. As a crucial component of the ICI formulation, we also introduce the natural distribution of streamlines and the natural distribution of world-lines, with invariance properties with respect to the cross-section used to parameterize them, valid for any type of mass-preserving flow.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2017 Cambridge University Press. This is an author produced version of a paper subsequently published in Journal of Fluid Mechanics. Article available under the terms of the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | blood flow; chaotic advection; mixing |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Electronic and Electrical Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 02 Jun 2017 13:11 |
Last Modified: | 14 May 2020 12:38 |
Published Version: | https://doi.org/10.1017/jfm.2017.392 |
Status: | Published |
Publisher: | Cambridge University Press |
Refereed: | Yes |
Identification Number: | 10.1017/jfm.2017.392 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:117070 |