Turbulence in the Atmosphere

Turbulence in the Atmosphere, John C. Wyngaard, Cambridge U. Press, New York, 2010. $75.00 (393 pp.). ISBN 978-0-521-88769-4

Turbulence is a subject of great importance in engineering, aeronautics, and atmospheric and oceanic dynamics. Three-dimensional turbulence is an important part of the variability at the one-meter scale behind airplanes, whereas the kinetic-energy spectrum of winds in the upper troposphere resembles spectra found in 2D turbulent flows. Turbulence is important for energy dissipation at the microscale, but it also contributes to the unpredictability of the weather. The subject fascinates many researchers, both for its chaotic nature and for its lack of a closed analytical description.

There are numerous books on turbulence. George Batchelor’s seminal work, The Theory of Homogeneous Turbulence (Cambridge University Press, 1982), laid the groundwork for the statistical analysis of turbulent flow. Andrei Monin and Akiva Yaglom’s encyclopedic two-volume Statistical Fluid Mechanics (Dover Books, 1971–75) is another standard reference. There are, in addition, texts on the atmospheric boundary layer—the turbulent lowest kilometer of the atmosphere. These include Roland Stull’s widely used An Introduction to Boundary Layer Meteorology (Springer, 1988) and John Lumley and Hans Panofsky’s The Structure of Atmospheric Turbulence (Interscience, 1964).

Add to those canonical works John Wyngaard’s Turbulence in the Atmosphere. A respected atmospheric scientist and former student of Lumley’s, Wyngaard has been lecturing about turbulence for 40 years and participating in groundbreaking research such as the 1968 Kansas experiment, a milestone boundary-layer field experiment that among other things exploited computerized data acquisition. His book draws on his extensive experience of observing the atmospheric boundary layer and numerically modeling turbulence.

The book is divided into three parts. The first, The Grammar of Turbulence, introduces concepts like turbulent fluxes and the Reynolds averaging of the fluid equations. It also considers the spatial filtering of the equations, an important technique in the construction of numerical models that by necessity cannot resolve all scales of motion. The section also considers the advection of temperature and other tracers, and mixing-length ideas. It examines Andrei Kolmogorov’s landmark 1941 theory, which revolutionized the theoretical analysis of turbulence, and discusses some recent modifications to that theory and its application to 2D flows.

Turbulence in the Atmospheric Boundary Layer, the book’s part 2, deals specifically with the atmosphere. The topics—the convective boundary layer, with free convection throughout, and the stable boundary layer, with stable density stratification—have been treated before, for example, in Stull’s book. However, Wyngaard links them with the general concepts developed in the preceding section and cites numerous recent findings. The energetics of the boundary layer are often quite complex, but Wyngaard provides guidance by highlighting consistent aspects in a unified framework.

In part 3, Statistical Representation of Turbulence, Wyngaard discusses the statistical constructs frequently used when modeling turbulence. Those include probability density functions, isotropic tensors, covariances, and spectra. The initial presentation follows that of Batchelor and Lumley and Panofsky, but Wyngaard critically examines some of the assumptions, principally isotropy, in light of more recent measurements.

In general, the exposition in Turbulence in the Atmosphere is systematic, clear, and self-contained. The book is in many ways a follow-up to Lumley and Panofsky’s now out-of-print text, but Wyngaard’s update is extensive and much-needed. The author presents numerous problems, both qualitative and quantitative, at the end of each section, so the book could function well as a text for a course on turbulence or boundary-layer meteorology. Wyngaard’s accessible treatment of difficult topics also makes the book a useful reference. The author clearly enjoys the subject and the book is enjoyable to read. The many quotations from researchers working in the field provide an interesting historical perspective. Such personal touches are welcome in a turbulence text.

The book would probably be most accessible to students of atmospheric science who are familiar with concepts such as static stability and geostrophic balance. It does assume some knowledge of turbulence phenomenology and might be daunting as an introduction. Students would perhaps benefit from first having seen a more basic text, such as Hendrik Tennekes and Lumley’s A First Course in Turbulence (MIT Press, 1972). Among other minor objections, I dislike the notation used for designating mean and turbulent terms (even though Tennekes and Lumley used the same notation); the convention of using primes to denote fluctuations is more common. And although the publisher suggests the book will be useful to oceanographers, the few oceanographic examples given are noted only in passing.

Nevertheless, Turbulence in the Atmosphere is admirable in its exposition and its breadth. It will serve well as a graduate textbook and certainly conveys the author’s affection for the subject.