New Special Issue "Statistical Mechanics of Nonequilibrium Fluid Flows"
Dear Colleagues,
In turbulence research, in the last few decades, some of the remaining burning questions have been answered, leading to deeper insights into the nature of turbulence. This started, on the one hand, when nonlinear dynamic concepts, e.g., in-sta-bi-li-ties, bifurcation scenarios, self-similartity, fractal geometry, were intro-duced to describe turbulent processes. It became evi-dent that fractal Lévy flight distributions describe intermittency and spatial clustering, both re-lating to a two-phase picture of turbulence with laminar streaks and turbulent patches characterizing the two phases of a possibly dynamical phase transition. On the other hand, equilibrium Boltz-mann–Gibbs thermo-dy-na-mics was generalized to nonequilibrium thermodynamics, today better known by the scientific term nonextensive thermo-dynamics. At present, this domain finds its mathematics in fractional calculus. In 2019, Egolf and Hutter proved that some of the descriptions of fractional derivatives and recently proposed nonlocal descriptions of the Reynolds shear stresses coincide. For a long time, it has been known that turbulence is not only a nonlinear phenomenon, but also one showing nonlocality. Fractional Langevin and Fokker–Planck equations support the deve-lop-ment of such new promising concepts of turbulence. Finally, Alemany and Zanette proved that for the low-wave number regime of turbulent eddies, the probability distribution of Lévy flights directly copes with the nonextensive ther-mo-dy-namics of Tsallis. Through this all the above described theories and models:
- Nonlinear and nonlocal modeling;
- Fractal geometry;
- Fractional calculus;
- Lévy flight statistics;
- Nonextensive thermodynamics;
have been proven to be tightly linked. Therefore, it is, for example, impossible to deny the fractal nature or the applicability of Lévy flight statistics to model turbulence without denying the nonlocality and fractionality of turbulence and vice versa. Lévy flight statistics leads to turbulent energy intensity spectra of power law nature describing intermittency, including as a special case the Kolmogorov–Oboukov spectrum.
The present Special Issue of Entropy, “Statistical Mechanics of Nonequilibrium Fluid Flows”, con-tains articles contributing to the modern aspects of turbulence described above. This also contains con-tributions to turbulent flow stability, anomalous diffusion, information theory and turbulence, ge-neralized entropies, e.g., Shan-non entropy, Kolmogorov entropy, Tsallis entropy, non-equi-li-brium and nonextensive thermo-dynamics, phase change models of turbulence, etc.
Prof. Dr. Peter W. Egolf
Prof. Dr. Kolumban Hutter
Guest Editors
https://www.mdpi.com/journal/entropy/special_issues/nonequilibrium_fluid_flows