For turbulent flows at relatively low speeds there exists an excellent mathematical model in the incompressible Navier–Stokes equations. Why then is the 'problem of turbulence' so difficult? One reason is that these nonlinear partial differential equations appear to be insoluble, except through numerical simulations, which offer useful approximations but little direct understanding. Three recent developments offer new hope. First, the discovery by experimentalists of coherent structures in certain turbulent flows. Secondly, the suggestion that strange attractors and other ideas from finite-dimensional dynamical systems theory might play a role in the analysis of the governing equations. And, finally, the introduction of the Karhunen-Loève or proper orthogonal decomposition. This book introduces these developments and describes how they may be combined to create low-dimensional models of turbulence, resolving only the coherent structures. This book will interest engineers, especially in the aerospace, chemical, civil, environmental and geophysical areas, as well as physicists and applied mathematicians concerned with turbulence.

‘This book is an important contribution from a stable with a distinguished reputation and an impressive publications record … The text is lucid in style, and there is a useful section on notation and mathematical jargon that will be welcome to many readers. The book is highly recommended to anyone working in or embarking on research in this field.’

R. H. Barnard Source: The Aeronautical Journal

‘… exceptionally clearly laid out … in an exemplary writing style that belies the great difficulty of the task being attempted.’

Robert Matthews Source: New Scientist

‘… a worthwhile introduction to an important direction for understanding turbulence.’

Howell Peregrine Source: Mathematics Today

‘For those who are willing to take time to study this work be they an expert or just an interested bystander, the effort into this book makes for stimulating reading.’

N. C. Freeman - University of Newcastle

‘… a worthwhile introduction to an important direction for understanding turbulence.’

Howell Peregrine Source: Mathematics Today

‘The book is highly recommended to anyone working in or embarking on research in this field.’

R. H. Barnard Source: The Aeronautical Journal

‘Despite its formidable mathematical content, this book is written in a rather appealing ‘racy’ style. I believe that it will stimulate research and lead to a deeper understanding in a number of fields.’

Michael J. Rycroft Source: Journal of Atmospheric and Solar - Terrestrial Physics

‘I can certainly recommend the book to anyone interested in modern turbulence research, especially those concerned with new ideas about the control and modification of turbulence near walls.’

Source: Journal of Fluid Mechanics

‘ … will certainly interest engineers and applied mathematicians concerned with fluid and gas dynamics and can also be useful for a more general audience of postgraduate students and scientists working in nonlinear dynamics. The price of the paperback edition is affordable enough to recommend this book for personal collections.’

Source: Contemporary Physics