The renormalization group (RG) theory of fully developed hydrodynamical turbulence is a new and developing field of research. This book gives a detailed and comprehensive review of the results obtained using this theory over the past 20 years. The authors have systematically adopted the highly successful field theoretic RG technique, which has a reliable base in the form of quantum- field renormalization theory, involves powerful and convenient methods of calculation such as analytic regularization and minimal subtractions, and allows one to obtain results which are difficult to achieve using other methods.
In the first chapter the basic theory and technique are presented, while the next chapter deals with more advanced aspects of the theory, including the critical dimensions of various composite operators, infrared asymptotic behavior of scaling functions, the equation of spectral energy balance, and calculating the amplitudes in scaling laws. The third chapter presents a series of examples, such as turbulent convection of passive scalar admixture, the influence of anisotropy and gyrotropy, magnetohydrodynamical turbulence, and Langmuir turbulence of plasma.
In contrast to more established disciplines, such as the theory of critical phenomena, in the RG theory of turbulence there is as yet no unique and generally accepted calculation technique. For this reason the authors also present the necessary information on the renormalization theory of the RG technique, making the subject accessible to a wide range of readers. The book will therefore be a useful source of reference for students and researchers in turbulence, statistical mechanics, and related fields, including those with no prior experience of using quantum-field techniques.
1. The Renormalization Group Method in the Stochastic Model of Isotropic Turbulence 2. Composite Operators, Operator Expansions, and the First Kolmogorov Hypothesis 3. Multicharge Problems in the Stochastic Theory of Turbulence