Geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences, this introductory text covers kinematics, momentum principle, Newtonian fluid, compressibility, and other subjects. 1971 edition.

These notes are based on a one-quarter (i. e. very short) course in fluid mechanics taught in the Department of Mathematics of the University of California, Berkeley during the Spring of 1978. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approxima tion procedures. The goals were: (i) to present some of the basic ideas of fluid mechanics in a mathematically attractive manner (which does not mean "fully rigorous"); (ii) to present the physical back ground and motivation for some constructions which have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems; (iil. ) 'to interest some of the students in this beautiful and difficult subject. The notes are divided into three chapters. The first chapter contains an elementary derivation of the equations; the concept of vorticity is introduced at an early stage. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers. A construction of boundary layers using vortex sheets and random walks is presented; it is hoped that it helps to clarify the ideas. The third chapter contains an analysis of one-dimensional gas iv flow, from a mildly modern point of view. Weak solutions, Riemann problems, Glimm's scheme, and combustion waves are discussed. The style is informal and no attempt was made to hide the authors' biases and interests.

Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.

To classify a book as 'experimental' rather than 'theoretical' or as 'pure' rather than 'applied' is liable to imply umeal distinctions. Nevertheless, some Classification is necessary to teIl the potential reader whether the book is for him. In this spirit, this book may be said to treat fluid dynamies as a branch of physics, rather than as a branch of applied mathematics or of engineering. I have often heard expressions of the need for such a book, and certainly I have feIt it in my own teaching. I have written it primariIy for students of physics and of physics-based applied science, aIthough I hope others may find it useful. The book differs from existing 'fundamental' books in placing much greater emphasis on what we know through laboratory experiments and their physical interpretation and less on the mathe matieal formalism. It differs from existing 'applied' books in that the choice of topics has been made for the insight they give into the behaviour of fluids in motion rather than for their practical importance. There are differences also from many existing books on fluid dynamics in the branches treated, reflecting to some extent shifts of interest in reeent years. In particular, geophysical and astrophysical applications have prompted important fundamental developments in topics such as conveetion, stratified flow, and the dynamics of rotating fluids. These developments have hitherto been reflected in the contents of textbooks only to a limited extent.

This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

"Why Study Fluid Mechanics? 1.1 Getting Motivated Flows are beautiful and complex. A swollen creek tumbles over rocks and through crevasses, swirling and foaming. A child plays with sticky tafy, stretching and reshaping the candy as she pulls it and twist it in various ways. Both the water and the tafy are fluids, and their motions are governed by the laws of nature. Our goal is to introduce the reader to the analysis of flows using the laws of physics and the language of mathematics. On mastering this material, the reader becomes able to harness flow to practical ends or to create beauty through fluid design. In this text we delve deeply into the mathematical analysis of flows, but before beginning, it is reasonable to ask if it is necessary to make this significant mathematical effort. After all, we can appreciate a flowing stream without understanding why it behaves as it does. We can also operate machines that rely on fluid behavior - drive a car for exam- 15 behavior? mathematical analysis. ple - without understanding the fluid dynamics of the engine, and we can even repair and maintain engines, piping networks, and other complex systems without having studied the mathematics of flow What is the purpose, then, of learning to mathematically describe fluid The answer to this question is quite practical: knowing the patterns fluids form and why they are formed, and knowing the stresses fluids generate and why they are generated is essential to designing and optimizing modern systems and devices. While the ancients designed wells and irrigation systems without calculations, we can avoid the wastefulness and tediousness of the trial-and-error process by using mathematical models"--

In this translation of the German edition, the authors provide insight into the numerical simulation of fluid flow. Using a simple numerical method as an expository example, the individual steps of scientific computing are presented: the derivation of the mathematical model; the discretization of the model equations; the development of algorithms; parallelization; and visualization of the computed data. In addition to the treatment of the basic equations for modeling laminar, transient flow of viscous, incompressible fluids - the Navier-Stokes equations - the authors look at the simulation of free surface flows; energy and chemical transport; and turbulence. Readers are enabled to write their own flow simulation program from scratch. The variety of applications is shown in several simulation results, including 92 black-and-white and 18 color illustrations. After reading this book, readers should be able to understand more enhanced algorithms of computational fluid dynamics and apply their new knowledge to other scientific fields.

This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.

It is over three hundred and fifty years since Torricelli discovered the law obeyed by fountains, yet fluid dynamics remains an active and important branch of physics. This book provides an accessible and comprehensive account of the subject, emphasising throughout the fundamental physical principles, and stressing the connections with other branches of physics. Beginning with a gentle introduction, the book goes on to cover Bernouilli's theorem, compressible flow, potential flow, surface waves, viscosity, vorticity dynamics, thermal convection and instabilities, turbulence, non-Newtonian fluids and the propagation and attenuation of sound in gases. Undergraduate or graduate students in physics or engineering who are taking courses in fluid dynamics will find this book invaluable, but it will also be of great interest to anyone who wants to find out more about this fascinating subject.