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Nonlinear dynamics and statistical theories for basic geophysical flows. (English) Zbl 1141.86001
Cambridge: Cambridge University Press (ISBN 0-521-83441-4/hbk). xii, 551 p. (2006).
Starting from introductory descriptions of barotropic and two-dimensional geophysical flows and the related exact mathematical solutions, the authors proceed to problems of the non-linear stability and decay of flows in presence of external forcing mechanisms. Two next chapters are devoted to nonlinear flow instabilities as well as to the limiting regime with chaotic solutions. Several chapters deal with information and statistical theories applied to flow configurations including vortex motions, and with their predictability properties. As a special case, the authors apply the equilibrium statistical mechanics theory to predict jets and spots on Jupiter utilizing the quasi-geostrophic flow model. The book concludes by a chapter on generalization to the non-flat geometry where barotropic quasi-geostrophic flows on a sphere are analyzed in detail.
The book thus offers a comprehensive insight into complexity of the nonlinear geophysical flow dynamics and the corresponding statistical theories, and it is written eloquently as one of the authors, A. J. Majda, was lecturing on the subject for years at the Courant Institute, New York. Throughout the book, physical processes of considered numerous geophysical flow configurations are described and treated both by rigorous mathematical derivations as well as by numerical procedures of solving flow equations. This book is therefore valuable both for professional researchers and graduate students in geophysics who are interested not only in physical phenomena as such but also in details concerning mathematical and numerical procedures of finding solutions to the involved equations.

86-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
76E20 Stability and instability of geophysical and astrophysical flows