Nonlinear, Nonlocal and Fractional Turbulence : Alternative Recipes for the Modeling of Turbulence / by Peter William Egolf, Kolumban Hutter.

Format:

Book

Author/Creator:

Egolf, Peter William, author.

Hutter, Kolumban, author.

Contributor:

SpringerLink (Online service)

Series:

Physics and Astronomy (Springer-11651)

Language:

English

Subjects (All):

Fluids.

Statistical physics.

Fluid mechanics.

Differential equations, Partial.

Thermodynamics.

Hydrogeology.

Fluid- and Aerodynamics.

Applications of Nonlinear Dynamics and Chaos Theory.

Engineering Fluid Dynamics.

Partial Differential Equations.

Local Subjects:

Fluid- and Aerodynamics.

Applications of Nonlinear Dynamics and Chaos Theory.

Engineering Fluid Dynamics.

Partial Differential Equations.

Thermodynamics.

Hydrogeology.

Physical Description:

1 online resource (XXXVII, 445 pages) : 119 illustrations, 26 illustrations in color

Edition:

First edition 2020.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2020.

System Details:

text file PDF

Summary:

Experts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Lévy flights), fractal geometry (fractal-β, bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new 'law of the wall' and a generalization of Kraichnan's energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, et cetera; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures. This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.

Contents:

Introduction

Reynolds Averaging of the Navier-Stokes Equations (RANS)

The closure problem

Boussinesq's 'constitutive law'

First turbulence models for shear flows

Review of nonlinear and nonlocal models

The Difference-Quotient Turbulence Model (DQTM)

Self-similar RANS

Elementary turbulent shear flow solutions

Thermodynamics of turbulence

Turbulence - a cooperative phenomenon

Conclusions and outlook.

Other Format:

Printed edition:

ISBN:

978-3-030-26033-0

9783030260330

Access Restriction:

Restricted for use by site license.