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Non-perturbative Methods in Statistical Descriptions of Turbulence [electronic resource] / by Jan Friedrich.

By: Friedrich, Jan [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Progress in Turbulence - Fundamentals and Applications: 1Publisher: Cham : Springer International Publishing : Imprint: Springer, 2021Edition: 1st ed. 2021.Description: XI, 164 p. 53 illus., 11 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783030519773.Subject(s): Dynamics | Nonlinear theories | Multibody systems | Vibration | Mechanics, Applied | Nonlinear Optics | Fluid mechanics | Continuum mechanics | Applied Dynamical Systems | Multibody Systems and Mechanical Vibrations | Nonlinear Optics | Engineering Fluid Dynamics | Continuum MechanicsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515.39 Online resources: Click here to access online
Contents:
Introduction -- Basic Properties of Hydrodynamic Turbulence -- Statistical Formulation of the Problem of Turbulence -- Overview of Closure Methods for the Closure Problem of Turbulence -- Non-Perturbative Methods -- Outlook.
In: Springer Nature eBookSummary: This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier–Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier–Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area.
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Introduction -- Basic Properties of Hydrodynamic Turbulence -- Statistical Formulation of the Problem of Turbulence -- Overview of Closure Methods for the Closure Problem of Turbulence -- Non-Perturbative Methods -- Outlook.

This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier–Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier–Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area.

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