Next Article in Journal
Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory
Next Article in Special Issue
Entropy “2”-Soft Classification of Objects
Previous Article in Journal
A Combined Entropy/Phase-Field Approach to Gravity
Previous Article in Special Issue
Impact Location and Quantification on an Aluminum Sandwich Panel Using Principal Component Analysis and Linear Approximation with Maximum Entropy
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(4), 154; doi:10.3390/e19040154

Is Turbulence a State of Maximum Energy Dissipation?

1
SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
2
LSCE-IPSL, CEA Saclay l’Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
*
Author to whom correspondence should be addressed.
Received: 2 February 2017 / Revised: 23 March 2017 / Accepted: 28 March 2017 / Published: 31 March 2017
(This article belongs to the Special Issue Maximum Entropy and Its Application II)
View Full-Text   |   Download PDF [993 KB, uploaded 5 April 2017]   |  

Abstract

Turbulent flows are known to enhance turbulent transport. It has then even been suggested that turbulence is a state of maximum energy dissipation. In this paper, we re-examine critically this suggestion in light of several recent works around the Maximum Entropy Production principle (MEP) that has been used in several out-of-equilibrium systems. We provide a set of four different optimization principles, based on maximization of energy dissipation, entropy production, Kolmogorov–Sinai entropy and minimization of mixing time, and study the connection between these principles using simple out-of-equilibrium models describing mixing of a scalar quantity. We find that there is a chained-relationship between most probable stationary states of the system, and their ability to obey one of the four principles. This provides an empirical justification of the Maximum Entropy Production principle in this class of systems, including some turbulent flows, for special boundary conditions. Otherwise, we claim that the minimization of the mixing time would be a more appropriate principle. We stress that this principle might actually be limited to flows where symmetry or dynamics impose pure mixing of a quantity (like angular momentum, momentum or temperature). The claim that turbulence is a state of maximum energy dissipation, a quantity intimately related to entropy production, is therefore limited to special situations that nevertheless include classical systems such as shear flows, Rayleigh–Bénard convection and von Kármán flows, forced with constant velocity or temperature conditions. View Full-Text
Keywords: maximum entropy production; turbulence; Kolmogorov–Sinai entropy maximum entropy production; turbulence; Kolmogorov–Sinai entropy
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Mihelich, M.; Faranda, D.; Paillard, D.; Dubrulle, B. Is Turbulence a State of Maximum Energy Dissipation? Entropy 2017, 19, 154.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top