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Turbulence in fluids. 3rd rev. and enlarg. ed. (English) Zbl 0876.76002
Fluid Mechanics and its Applications. 40. Dordrecht: Kluwer Academic Publishers. xvi, 515 p. (1997).
This monograph is devoted to the study of the modern point of view on turbulence in fluids and its numerous applications. The author considers the book as “an attempt to reconcile the statistical point of view and the basic concepts of fluid mechanics which determine the evolution of flows arising in the various fields”.
The first chapter prensents the general discussion of turbulence and chaos and the definition of basic terms used in the turbulence study. The second chapter includes the basic definitions and equations of fluid dynamics. The third chapter contains the Reynolds number, the calculation of normal modes, the transition to turbulence in flows which can be shear or wall-bounded, and the thermal convection. The shear flow turbulence is discussed in the fourth chapter. In the fifth chapter, the methods of Fourier analysis are applied to the nonanisotropic tubulence, together with the Fourier transform of Navier-Stokes equations and the Boussinesq approximation, the Craya decomposition, etc. The axisymmetric turbulence is considered as a special case of homogeneous anisotropic turlulence, and certain results on scalar-velocity correlation function are obtained. In the sixth chapter, the isotropic turbulence is investigated. The numerical results on the transfer function and kinematic energy spectrum are given. The results on viscous flows are presented, and the pressure spectrum is obtained by numerical calculation.
The seventh chapter is logically divided into two parts. In the first part, the quasi-normal and the eddy-damped quasi-normal Markovian (E.D.Q.N.M.) approximations are presented, whereas in the second part the results which are obtained using these approximations – analytical and numerical – are summarized. In the eighth chapter the author discusses the turbulence in two dimensions. The ninth chapter is devoted to the discussion of turbulence on a rotating sphere, which is quite valuable for studying the dynamics of large-scale rotating planetary flows. The tenth chapter contains the discussion of turbulence within a box in two and three dimensions. In the eleventh chapter the predictability of the system is studied, and the E.D.Q.N.M. predictability equations are formulated. The predictability is also studied in both two and three dimensions. The twelfth chapter contains the discussion of the numerical simulations of turbulence using only the large scales of motion (large eddy simulation, LES). The last, thirteenth, chapter explains how the theory works in the real world where the turbulence is no more isotropic. The effects of stratification, rotation, separation, and compressibility are studied used experiments, direct numerical simulation and LES.
The book contains the concise description of methods of studying the turbulence. Strict account and fullness of the bibliography must be also noted.

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76Fxx Turbulence