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.

About the Authors

Philip Holmes is Eugene Higgins Professor of Mechanical and Aerospace Engineering and Professor of Applied and Computational Mathematics, Princeton University. He works on nonlinear dynamics and differential equations.

John L. Lumley is Professor Emeritus in the Department of Mechanical and Aerospace Engineering, Cornell University. He has authored or co-authored over two hundred scientific papers and several books.

Gahl Berkooz leads the area of Information Management for Ford Motor Company, covering all aspects of Business Information Standards and Integration.

Clarence W. Rowley is an Associate Professor of Mechanical and Aerospace Engineering at Princeton University. His research interests lie at the intersection of dynamical systems, control theory and fluid mechanics.

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