An international group of outstanding scientists presents a balanced discussion of various controversies in current turbulence theory. Six topics from the present-day approach to turbulence are each introduced by a survey, followed by three commentaries and a panel discussion. This analysis evaluates future developments of theories presently used for understanding and modelling turbulent flows.

This book contains the proceedings of an IUTAM Symposium on turbulent flows at low Mach number, in which fluctuations in density occur as a result of heat transfer or of mixing of different fluids. Such flows occur in the atmosphere, the ocean, and in chemical engineering. In addition, in combustion large fluctuations in density occur as a result of heat release; the flows that are considered here do not involve heat release, for the most part, but the variable density flows that are considered can serve as a paradigm for many of the problems that arise in combustion as a result of the density fluctuations. Compressible flows - such as supersonic ones - are also considered in order to underline their similarities to and their differences from low-speed variable density flows. The book will be of interest to mechanical, aerospace, civil, and chemical engineers, meteorologists and oceanographers - in fact, anyone who deals with fluids in which fluctuations of density occur. The book will be accessible to professional and graduate students. There are no other works that deal with this interesting area.

The first four symposia in the series on turbulent shear flows have been held alternately in the United States and Europe with the first and third being held at universities in eastern and western States, respectively. Continuing this pattern, the Fifth Symposium on Turbulent Shear Flows was held at Cornell University, Ithaca, New York, in August 1985. The meeting brought together more than 250 participants from around the world to present the results of new research on turbulent shear flows. It also provided a forum for lively discussions on the implications (practical or academic) of some of the papers. Nearly 100 formal papers and about 20 shorter communications in open forums were presented. In all the areas covered, the meeting helped to underline the vitality of current research into turbulent shear flows whether in experimental, theoretical or numerical studies. The present volume contains 25 of the original symposium presentations. All have been further reviewed and edited and several have been considerably extended since their first presentation. The editors believe that the selection provides papers of archival value that, at the same time, give a representative statement of current research in the four areas covered by this book: - Homogeneous and Simple Flows - Free Flows - Wall Flows - Reacting Flows Each of these sections begins with an introductory article by a distinguished worker in the field.

This book is a collection of papers presented at a symposium held in honor of Sidney Leibovich. According all papers deal with mathematical or computational aspects of fluid dynamics applied mostly to atmospheric or oceanographic problems. All contributions are research papers having not only the specialist but also graduate students in mind.

This is the first book specifically designed to offer the student a smooth transitionary course between elementary fluid dynamics (which gives only last-minute attention to turbulence) and the professional literature on turbulent flow, where an advanced viewpoint is assumed. The subject of turbulence, the most forbidding in fluid dynamics, has usually proved treacherous to the beginner, caught in the whirls and eddies of its nonlinearities and statistical imponderables. This is the first book specifically designed to offer the student a smooth transitionary course between elementary fluid dynamics (which gives only last-minute attention to turbulence) and the professional literature on turbulent flow, where an advanced viewpoint is assumed. Moreover, the text has been developed for students, engineers, and scientists with different technical backgrounds and interests. Almost all flows, natural and man-made, are turbulent. Thus the subject is the concern of geophysical and environmental scientists (in dealing with atmospheric jet streams, ocean currents, and the flow of rivers, for example), of astrophysicists (in studying the photospheres of the sun and stars or mapping gaseous nebulae), and of engineers (in calculating pipe flows, jets, or wakes). Many such examples are discussed in the book. The approach taken avoids the difficulties of advanced mathematical development on the one side and the morass of experimental detail and empirical data on the other. As a result of following its midstream course, the text gives the student a physical understanding of the subject and deepens his intuitive insight into those problems that cannot now be rigorously solved. In particular, dimensional analysis is used extensively in dealing with those problems whose exact solution is mathematically elusive. Dimensional reasoning, scale arguments, and similarity rules are introduced at the beginning and are applied throughout. A discussion of Reynolds stress and the kinetic theory of gases provides the contrast needed to put mixing-length theory into proper perspective: the authors present a thorough comparison between the mixing-length models and dimensional analysis of shear flows. This is followed by an extensive treatment of vorticity dynamics, including vortex stretching and vorticity budgets. Two chapters are devoted to boundary-free shear flows and well-bounded turbulent shear flows. The examples presented include wakes, jets, shear layers, thermal plumes, atmospheric boundary layers, pipe and channel flow, and boundary layers in pressure gradients. The spatial structure of turbulent flow has been the subject of analysis in the book up to this point, at which a compact but thorough introduction to statistical methods is given. This prepares the reader to understand the stochastic and spectral structure of turbulence. The remainder of the book consists of applications of the statistical approach to the study of turbulent transport (including diffusion and mixing) and turbulent spectra.

Turbulence pervades our world, from weather patterns to the air entering our lungs. This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures - recurrent patterns - in turbulent flows, it describes mathematical methods that reduce the governing (Navier-Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995. The book is ideal for engineering, physical science and mathematics researchers working in fluid dynamics and other areas in which coherent patterns emerge.

This accessible treatment offers the mathematical tools for describing and solving problems related to stochastic vector fields. Advanced undergraduates and graduate students will find its use of generalized functions a relatively simple method of resolving mathematical questions. It will prove a valuable reference for applied mathematicians and professionals in the fields of aerospace, chemical, civil, and nuclear engineering.
The author, Professor Emeritus of Engineering at Cornell University, starts with a survey of probability distributions and densities and proceeds to examinations of moments, characteristic functions, and the Gaussian distribution; random functions; and random processes in more dimensions. Extensive appendixes--which include information on Fourier transforms, tensors, generalized functions, and invariant theory--contribute toward making this volume mathematically self-contained.

The internal combustion engine that powers the modern automobile has changed very little from its initial design of some eighty years ago. Unlike many high tech advances, engine design still depends on an understanding of basic fluid mechanics and thermodynamics. This text offers a fresh approach to the study of engines, with an emphasis on design and on fluid dynamics. Professor Lumley, a renowned fluid dynamicist, provides a lucid explanation of how air and fuel are mixed, how they get into the engine, what happens to them there, and how they get out again. Particular attention is given to the complex issue of pollution. Every chapter includes numerous illustrations and examples and concludes with homework problems. Examples are taken from the early days of engine design, as well as the latest designs, such as stratified charge gasoline direct injection engines. It is intended that the text be used in conjunction with the Stanford Engine Simulation Program (ESP). This user-friendly, interactive software tool answers a significant need not addressed by other texts on engines. Aimed at undergraduate and first-year graduate students, the book will also appeal to hobbyists and car buffs who will appreciate the wealth of illustrations of classic, racing, and modern engines.

This book provides students and researchers in fluid engineering with an up-to-date overview of turbulent flow research in the areas of simulation and modeling. A key element of the book is the systematic, rational development of turbulence closure models and related aspects of modern turbulent flow theory and prediction. Starting with a review of the spectral dynamics of homogenous and inhomogeneous turbulent flows, succeeding chapters deal with numerical simulation techniques, renormalization group methods and turbulent closure modeling. Each chapter is authored by recognized leaders in their respective fields, and each provides a thorough and cohesive treatment of the subject.