Non-perturbative Methods in Statistical Descriptions of Turbulence

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 NavierStokes 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 NavierStokes 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 wantto get acquainted with the prevalent concepts and methods in this research area.

Provides an overview of recent concepts for a possible statistical description of turbulence Focuses on non-perturbative methods for the closure problem of turbulence Explains why common perturbative methods such as the renormalization group of critical phenomena have not been successful Discusses the roots of each method in its original field of application Reflects the status quo of turbulence theory and provides an outlook on a possible solution of the closure problem

Inhalt
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.