Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz,...
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Book Review BOOK REVIEWS published in this section reflect the opinions of their individual authors. They are not necessarily the opinions of the Editors of this journal or of AIAA. Turbulence, Coherent Structures, Dynamical Systems and Symmetry P. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England, U.K., 2012, 386 pp., $90 DOI: 10.2514/1.J052557 This book is a valuable (almost necessary) addition to the library of students and researchers working on reduced- order models (ROMs) of fluid flows. I find it on practically all bookshelves of corresponding researchers and students. The first edition of this book was written in 1996 by P. Holmes, J. L. Lumley, and G. Berkooz, the pioneers of modern low-dimensional dynamical models of turbulence, and it has become one of the classics in its field. The second edition has C. W. Rowley as new author, a pioneer in control-oriented modeling. This edition contains a new chapter on balanced proper orthogonal decomposition (POD) targeting control-design applications. Otherwise, the main structure of the book has not been changed, while various sections have been updated. Reduced-order modeling is emerging as a new discipline besides experimental and theoretical fluid mechanics. ROM translates data or high-dimensional Navier–Stokes discretizations into low-dimensional dynamical models as a testbed for the understanding of key physical processes, as a computationally inexpensive surrogate model for optimization, and as a dynamical plant for closed-loop flow control. ROM is a difficult interdisciplinary subject because it requires a solid understanding of fluid mechanics, a good mastery of computational methods, and a working knowledge of dynamical systems theory. I have taught the subject on numerous occasions from summer schools to a two-semester course (120 h) at Berlin Institute of Technology and have learned to appreciate the teaching challenge. The authors have elegantly addressed this challenge by an unconventional structure and exposition. The book comprises four parts. The first part focusses on fluid mechanics: simplifications of the Navier–Stokes equation, the phenomenology of coherent structures, (balanced) POD as low-order kinematics, and the Galerkin projection leading to low-order dynamical models. The second part recapitulates dynamical systems theory from a more mathematical perspective. The third part describes their first pioneering model of the turbulent boundary layer in detail, building on the previous chapters. And the last part addresses various progresses of ROM for other flows as well as open challenges. The book contains rigorous textbook chapters for the methodology, simple analytical examples that invite the reader to explore the field, and additional sections closing up to the state of the art (i.e., invitations to additional reading). A single book cannot describe the vast knowledge of rapidly evolving ROM in fluid mechanics, as the authors correctly emphasize in the preface. Several other books have been written on this subject, focusing, for instance, on mathematical system reduction, computational Galerkin models, control-oriented models, etc. Yet the current book will remain a standing classic in POD-based Galerkin models of turbulent flows. Bernd R. Noack Institute PPRIME/CNRS 2991 AIAA JOURNAL Vol. 51, No. 12, December 2013 Downloaded by CASE WESTERN RESERVE UNIVERSITY on May 10, 2014 | http://arc.aiaa.org | DOI: 10.2514/1.J052557
Transcript of Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz,...
Book ReviewBOOK REVIEWS published in this section reflect the opinions of their individual authors. They are not necessarily the opinions of the Editors ofthis journal or of AIAA.
Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England,
U.K., 2012, 386 pp., $90
DOI: 10.2514/1.J052557
This book is a valuable (almost necessary) addition to thelibrary of students and researchers working on reduced-ordermodels (ROMs) of fluid flows. I find it onpractically allbookshelves of corresponding researchers and students.The first edition of this book was written in 1996 by P.Holmes, J. L. Lumley, and G. Berkooz, the pioneers ofmodern low-dimensional dynamical models of turbulence,and it has becomeoneof the classics in its field. The secondedition has C. W. Rowley as new author, a pioneer incontrol-oriented modeling. This edition contains a newchapter on balanced proper orthogonal decomposition(POD) targeting control-design applications. Otherwise,themain structure of the book has not been changed,whilevarious sections have been updated.Reduced-ordermodeling is emerging as a new discipline
besides experimental and theoretical fluid mechanics.ROM translates data or high-dimensional Navier–Stokesdiscretizations into low-dimensional dynamicalmodels as atestbed for the understanding of key physical processes, asa computationally inexpensive surrogate model foroptimization, and as a dynamical plant for closed-loopflow control. ROM is a difficult interdisciplinary subjectbecause it requires a solid understanding of fluidmechanics, a good mastery of computational methods,and a working knowledge of dynamical systems theory. Ihave taught the subject on numerous occasions fromsummer schools to a two-semester course (120 h) at BerlinInstitute of Technology and have learned to appreciate theteaching challenge.
The authors have elegantly addressed this challenge byan unconventional structure and exposition. The bookcomprises four parts. The first part focusses on fluidmechanics: simplifications of the Navier–Stokes equation,the phenomenology of coherent structures, (balanced)POD as low-order kinematics, and the Galerkin projectionleading to low-order dynamical models. The second partrecapitulates dynamical systems theory from a moremathematical perspective. The third part describes theirfirst pioneering model of the turbulent boundary layer indetail, building on the previous chapters. And the last partaddresses various progresses of ROM for other flows aswell as open challenges. The book contains rigoroustextbook chapters for the methodology, simple analyticalexamples that invite the reader to explore the field, andadditional sections closing up to the state of the art (i.e.,invitations to additional reading).
A single book cannot describe the vast knowledge ofrapidly evolving ROM in fluid mechanics, as the authorscorrectly emphasize in the preface. Several other bookshave beenwrittenon this subject, focusing, for instance, onmathematical system reduction, computational Galerkinmodels, control-orientedmodels, etc. Yet the current bookwill remain a standing classic in POD-based Galerkinmodels of turbulent flows.
Bernd R. NoackInstitute PPRIME/CNRS
2991
AIAA JOURNAL
Vol. 51, No. 12, December 2013
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