Synopses & Reviews
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.
Review
"This book is an elegantly-written, eminently-readable monograph describing modeling, interpretations, and analysis of some turbulent flows that may be significantly influenced by large scale coherent structures." A.C. Buckingham, Applied Mechanics"The book presents three new discoveries that may enable further understanding of turbulent flows." Bulletin of the American Meteorological Society"This volume is valuable, if for no other reason, in that it reminds us that to understand turbulence at a fundamental level, we must understand it as a nonlinear dynamical process." Earl H. Dowell, American Scientist"This book is an up-to-date research monograph combined with a large amount of background material in turbulence theory and phenomenology, Karhunen-Loéve methods, and both deterministic and stochastic dynamical systems. It will be accessible and of interest to a wide audience, ranging from engineering and applied mathematics graduate studies to active researchers in nearly all of the applied sciences impacted by turbulence in fluids....this book benefits not only from the authors' authoritative insights and intuition ...but also from the high level of clarity of their presentation." Charles R. Doering, Mathematical Reviews"...the book is a remarkable success. The exposition is scholarly, and the style lucid and lively. The book represents one of the refreshing developments in the modern era on turbulence research, and should be of value to everyone interested in turbulence. I recommend it wholeheartedly." Journal of Statistical Physics
Synopsis
First-time paperback of successful book on turbulence by very well known authors.
Synopsis
This book offers a new approach to the modelling and analysis of turbulent flows dominated by coherent structures. Using techniques from probability theory and nonlinear dynamics, the authors show how the governing nonlinear equations of fluid mechanics may be reduced to simpler models which provide understanding of the basic mechanisms of turbulence generation.
Synopsis
'Turbulence has fascinated mankind and frustrated scientists for over 500 years. This book offers a new approach to the modelling and analysis of turbulent flows. Using techniques from probability theory and nonlinear dynamics, the authors show how the governing nonlinear equations of fluid mechanics may be reduced to simpler models which provide understanding of the basic mechanisms of turbulence generation. This book will be valuable to engineers (aerospace, chemical, civil, environmental and geophysical) as well as physicists and applied mathematicians concerned with turbulence.\n
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Synopsis
This book offers a new approach to the modeling and analysis of turbulent flows dominated by coherent structures: the concentrated and recurrent patterns of vorticity seen in aircraft contrails, eddies behind bridge piers and the wakes of moving cars and boats. Using techniques from probability theory and nonlinear dynamics, the authors show how the governing nonlinear equations of fluid mechanics may be reduced to simpler models that provide understanding of the basic mechanisms of turbulence generation.
Table of Contents
Preface; Part I. Turbulence: 1. Introduction; 2. Coherent structures; 3. Proper orthogonal decomposition; 4. Galerkin projection; Part II. Dynamical Systems: 5. Qualitative theory; 6. Symmetry; 7. One-dimensional âturbulenceâ; 8. Randomly perturbed systems; Part III. 9. Low-dimensional Models: 10. Behaviour of the models; Part IV. Other Applications and Related Work: 11. Some other fluid problems; 12. Review: prospects for rigor; Bibliography.