Book Review of Grae Worster’s Understanding Fluid Flow

Note: This review was originally published in the April, 2010, newsletter of the Mathematical Association of America’s Special Interest Group on Business, Industry, and Government (BIG SIGMAA). It is reprinted here with the gracious permission of the MAA and from the then-editor, Dr. Greg Coxson. Edits and corrections are indicated using square brackets. – Christopher Tong, Ph.D. (physics)

Understanding Fluid Flow, by M. Grae Worster (Cambridge University Press, AIMS Library Series, 2009). Reviewed by Christopher Tong.

Wouldn’t it be nice if, before a student embarks on a course on fluid dynamics, he or she has the opportunity to tour the subject and get a flavor of what it will be like to study it? This brief, informal book provides just that, and there is nothing else like it in the fluids literature.

At about 100 pages in length, the book provides neither depth nor breadth in the field. Rather, it offers a whirlwind tour of many of the major concepts and flows in fluid mechanics. Examples include parallel shear flows, boundary layers, vorticity dynamics, potential flow, separation and D’Alembert’s paradox, aerodynamic lift, surface waves, ship wakes, and the Kelvin- Helmholtz instability. There is a strong emphasis on intuition, dimensional analysis, and scaling arguments, and an avoidance of excessive mathematical formalism. The Navier-Stokes equations are presented and motivated, but not given a thorough derivation.

There are 25 exercises included; several are solved within the text itself. The book focuses on theory, but there are also two rather involved “Assignments” included, one experimental and the other computational. Both deal with a viscous gravity current, generated by a spreading pool of syrup, poured onto a horizontal disk.

The author is an applied mathematician and Professor of Fluid Dynamics at Cambridge University. [At the time the book was published, Worster was] also the co-chief editor of the most important journal in the field, the Journal of Fluid Mechanics. This book is one of the first published in the AIMS Library Series, affiliated with the African Institute [for Mathematical Sciences] (Muizenberg, South Africa), and is based on lectures given by the author there. Several movies associated with the book are available on the corresponding website from the publisher.

Some basic facility with vector calculus and partial differential equations is required by the reader. The writing style is very conversational, and readability is high (although the material becomes more difficult towards the end). There is no shortage of diagrams to illustrate the text; only a handful of photographs are included.

Unfortunately, the book does not attempt to bring the reader to the forefront of research. Turbulence earns a single paragraph. Given that the transition to turbulence is considered [one of the most] important unsolved problem[s] in fluid dynamics, the intended reader might have benefited from more discussion. More mathematically inclined students might also appreciate a mention of the Clay Mathematics Prize offered for an existence and smoothness proof for solutions of the 3D Navier-Stokes equations. Finally, the book does very little to develop the thermodynamics of flow, an arguably fundamental aspect. Of course, one could go on and on about other missing topics and concepts, which underlines the richness and diversity of fluid dynamics. This book pushes the door open on only a small sliver of the field. However, the brevity of the book is a major factor in its friendliness and accessibility.

The book is ideal for an upper level undergraduate or beginning graduate student in physics, applied mathematics, the geosciences, or engineering, for whom fluid dynamics is a potential future course of study or research. It will also benefit more mature physicists and applied mathematicians who are new to fluid dynamics, and would like a taste of the field and a start on achieving some literacy in it. I would recommend this book, along with the two chapters on fluids in The Feynman Lectures on Physics, to any beginner.

(This review was originally published in April, 2010, in The BIG Notebook, volume 6, number 1, pp. 4-5.)

Return to main page

Disclaimers

The content on this site was developed solely on my personal time. The views expressed are solely my own, and do not necessarily represent the views, policies, or opinions of my employer or any organization with which I am affiliated.