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Produktbild: Nonlinear, Nonlocal and Fractional Turbulence

Nonlinear, Nonlocal and Fractional Turbulence Alternative Recipes for the Modeling of Turbulence

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

03.04.2020

Abbildungen

XXXVII, 119 illus., 26 illus. in color., farbige Illustrationen, schwarz-weiss Illustrationen

Verlag

Springer

Seitenzahl

445

Maße (L/B/H)

24,1/16/3,1 cm

Gewicht

842 g

Auflage

1st ed. 2020

Sprache

Englisch

ISBN

978-3-030-26032-3

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

03.04.2020

Abbildungen

XXXVII, 119 illus., 26 illus. in color., farbige Illustrationen, schwarz-weiss Illustrationen

Verlag

Springer

Seitenzahl

445

Maße (L/B/H)

24,1/16/3,1 cm

Gewicht

842 g

Auflage

1st ed. 2020

Sprache

Englisch

ISBN

978-3-030-26032-3

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: [email protected]

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  • Produktbild: Nonlinear, Nonlocal and Fractional Turbulence
  • I. Introduction A. Aims and scopes of this book  B. A brief tour d’horizon through today’s turbulence field and modeling 
    II. Reynolds Averaging of the Navier-Stokes Equations (RANS) 
    III. The closure problem IV. Boussinesq’s ‘constitutive law’ 
    V. First turbulence models for shear flows A. Shear flows and the works of Prandtl, Taylor and contemporaires B. Momentum and vorticity transfer models 1. Prandtl’s mixing length model 2. von Kármán’s local model 3. Reichardt’s inductive model 4. Prandtl’s mean gradient model 5. Prandtl’s shear layer model 6. Taylor’s vorticity transfer model C. Overview of deficiencies of local models D. More general deficiencies and fallacies
    E. Questioning the logarithmic law F. Logarithmic versus (deficit) power law
    VI. Review of nonlinear and nonlocal models A. Nonlocality in phase space B. Atomic and continuum theories C. Stress as an objective polynomial function of the mean rate of strain tensor  D. Modified diffusivity models  E. Truly history-dependent and nonlocal models
    VII. The Difference-Quotient Turbulence Model (DQTM) A. The discovery and Prandtl’s models
    B. Momentum transfer approach 1. Molecular transport 2. Transport by eddies 3. Comparison of laminar and turbu-lent flows 4. Lévy-flight turbulence model and K41 4.1 Introduction 4.2 Lévy walks on a one-dimensional lattice 4.3 Lévy walks, Lévy flights , Lévy pairs and eddies in turbulence
    4.4 Eddy class statistics 4.5 The life time of eddies 4.6 The eddy diameters 4.7 The fractal eddy cascade model  4.8 The occupation number 4.9 The occupation probability 4.10 The momenta of eddies 4.11 The number of eddy classes 4.12 Lévy flight statistics, beta-fractal model and the DQTM
    C. New nonlocal turbulence models 1. Introduction 2. Liouville fractional derivative 3. Overview of the derivation of im- portant nonlocal turbulence models 4. Liouville-Prandtl Mixing-Length Model 5. The Heaviside-Liouville –Prandtl Shear-Layer Model 6. The Liouville-Heaviside Turbu- lence Model 7. The Difference Quotient Turbu-lence Model 8. Summary

    VIII. Self-similar RANS
    IX. Elementary turbulent shear flow solutions A. Plane wake flow B. Axi-symmetric jets 1. Jet in a quiescent surrounding 2. Jet in a parallel co-flow  C. Plane Couette flows  D. Plane Poiseuille flows  E. “Wall-turbulent” flows 
    X. Thermodynamics of turbulence  A. Introduction  1. Micro- and macroscopic theories 2. Langevin and Fokker-Planck equations 3. Reduction of degree of freedom by scaling 4. Different thermodynamic concepts B. A brief review of some essentials of Boltzmann-Gibbs thermodynamics C. Kraichnan’s BG-equilibrium thermody-namics of 2-d and 3-d turbulent fields D. An introduction to extensive thermo-dynamics of Tsallis E. Relation between Lévy statistics and Tsallis extensive thermodynamics F. Escort probability distribution and ex-pectation values G. Generalized thermodynamic potentials H. Fractional calculus: A promising future-oriented method to describe turbulence I. Jackson’s fractional derivative and the DQTM J. Beck-Tsallis thermodynamics of turbulence
    K. Fractional generalization of Kraichnan’s spectra and their validation by numerical experiments L. Velocity structure functions M. Justification of the quadratic form of the energy as a function of space coordinates N. A generalized temperature of turbulence O. Final discussion on the extensive thermodynamics of turbulence 
    XI. Turbulence – a cooperative phenomenon A. Introduction B. Cooperative phenomena 1. What is a critical or cooperative phenomenon? 2. Stress and order parameter 3. Symmetry breaking  4. Response functions and critical exponents 5. Pair correlation function and correlation length 6. Universality: yes, or no? 7. Turbulent phase transition with its two phases C. Mean field theory of a paramagnetic to ferromagnetic phase transition D. Mean field theory of turbulence E. First experiments for a qualitative comparision F. Discussion of results

    XII. Conclusions and outlook Appendices A. Normalization of probability distribution B. The variance of a Lévy flight process C. The structure and the Weierstrass function D. Circular mean velocity profile of plane Turbulent Poiseuille flows E. Fourier transformation for q-generalized energy spectrum of turbulent flows F Extremum principles for Boltzmann-Gibbs entropy G. Laplace multipliers, Tsallis factor and generalized temperature of turbulence
    References