This book, originally published in Moscow in 1965, is of interest to a wide scientific and technical audience, including geophysicists, meteorologists, aerodynamicists, chemical, mechanical, and civil engineers—in short, all interested in the fundamental problems of flow, mass, and heat transfer. The authors deal with the theory of hydrodynamic instability and the development of turbulence, the application of dimensional analysis, and the theory of similarity to turbulent flow in pipes, ducts, and boundary layers, as well as free turbulence. They discuss semiempirical theories of turbulence, develop the similarity theory for turbulence in nonhomogeneous media, and present Lagrangian characteristics of turbulence and the theory of turbulent diffusion. Every effort has been made to present a wealth of experimental material; a large number of examples are drawn from physics of the atmosphere, permitting a generalization of results beyond that which can be obtained in the laboratory. Considerable attention has been given to Kolmogorov's theory of the local structure of developed turbulence and to the theory of turbulence in stratified media. Contents: I. Laminar and Turbulent Motion: Equations of dynamics of a fluid and their most important consequences; Hydrodynamic instability and development of turbulence. II. Mathematical Methods for Describing Turbulence, Mean Values and Correlation Functions: Methods for taking mean; The fields of hydrodynamic characteristics regarded as stochastic fields; The moments of hydrodynamic fields. III. The Reynolds Equation and Semiempirical Theories of Turbulence: Turbulent flow in pipes and in the boundary layer; Turbulent energy balance and results derived from it. IV. Turbulence in a Medium Stratified with Respect to Temperature: Generalization of the theory of the logarithmic boundary layer to the case of a medium stratified with respect to temperature; Comparison of the theory with experimental data on the atmospheric layer near the ground. V. Motion of Particles (or Elements) in a Turbulent Stream: Lagrangian description of Turbulence; Turbulent diffusion.

Statistical Fluid Mechanics: Mechanics of Turbulence

Science & Math

A. M. Yaglom

A. S. Monin

Mathematics

Mit Pr

Designed for advanced high school students, undergraduates, graduate students, mathematics teachers, and any lover of mathematical challenges, this two-volume set offers a broad spectrum of challenging problems — ranging from relatively simple to extremely difficult. Indeed, some rank among the finest achievements of outstanding mathematicians. Translated from a well-known Russian work entitled Non-Elementary Problems in an Elementary Exposition, the chief aim of the book is to acquaint the readers with a variety of new mathematical facts, ideas, and methods. And while the majority of the problems represent questions in higher ("non-elementary") mathematics, most can be solved with elementary mathematics. In fact, for the most part, no knowledge of mathematics beyond a good high school course is required. Volume One contains 100 problems, with detailed solutions, all dealing with probability theory and combinatorial analysis. Topics include the representation of integers as sums and products, combinatorial problems on the chessboard, geometric problems on combinatorial analysis, problems on the binomial coefficients, problems on computing probabilities, experiments with infinitely many possible outcomes, and experiments with a continuum of possible outcomes. Volume Two contains 74 problems from various branches of mathematics, dealing with such topics as points and lines, lattices of points in the plane, topology, convex polygons, distribution of objects, nondecimal counting, theory of primes, and more. In both volumes the statements of the problems are given first, followed by a section giving complete solutions. Answers and hints are given at the end of the book. Ideal as a text, for self-study, or as a working resource for a mathematics club, this wide-ranging compilation offers 174 carefully chosen problems that will test the mathematical acuity and problem-solving skills of almost any student, teacher, or mathematician.

Challenging Mathematical Problems With Elementary Solutions, Vol. 1

I.M. Yaglom

Dover Publications

Challenging Mathematical Problems With Elementary Solutions (Volume 2)

Challenging Mathematical Problems with Elementary Solutions, Vol. 1: Combinatorial Analysis and Probability Theory.

Holden-Day

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Books by A. M. Yaglom