Is Turbulence a State of Maximum Energy Dissipation?

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 reexamine 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.

Entropy-Based Method to Evaluate Contact-Pressure Distribution for Assembly-Accuracy Stability Prediction

“…The maximum entropy principle is extensively applied in many disciplines [ 28 , 29 , 30 , 31 , 32 ]. In information theory, if there is a discrete random variable, X , with possible values of { x1, x2, …, xn }, and probability mass function, P(X ), the entropy, H, of X is defined as follows: where E is the expectation operator, r is the logarithmic base, which generally takes a value of two [ 33 , 34 , 35 ] (in this study, r = 2).…”

Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

“…For example, we already know that, in the presence of a strong shear, dissipation is much more efficient, in particular through the formation of localized fronts and filaments [61]. In fact, one commanding question regarding turbulent flows is whether they are best described through a state of maximal energy dissipation, or of maximum entropy production (see, e.g., [62] and references therein). Rotating stratified flows in general develop sharp gradients with localized dissipative events.…”

Maximum entropy production as a necessary admissibility condition for the fluid Navier–Stokes and Euler equations

“…The maximum entropy production principle (MEPP), as a principle of physics, has a long history, of which we cite [12,13,28,29]. This principle has been used in two key ways: (i) to derive an evolution system of equations; (ii) to select the physically relevant solution of a given evolution system.…”