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This newly translated addition to the literature provides a comprehensive treatment of the fundamentals of geophysical hydrodynamics -as expressed in Dolzhansky´s four decades of ground-breaking work at the Moscow Institute of Physics and Technology.

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This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation. Among the topics covered are the Kelvin, Ertel and Rossby-Obukhov invariants, quasi-geostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the Navier-Stokes equation, Kolmogorov´s flow, hydrodynamic stability, and geophysical boundary layers. Generalizing V. Arnold´s approach to hydrodynamics, the author ingeniously brings in an analogy of Coriolis forces acting on fluid with motion of the Euler heavy top and shows how this is used in the analysis of general atmospheric circulation.

This book is based on popular graduate and undergraduate courses given by F.V.Dolzhansky at the Moscow Institute of Physics and Technology, and is the result of the author´s highly acclaimed work in Moscow´s Laboratory of Geophysical Hydrodynamics. Each chapter is full of examples and figures, exercises and hints, motivating and illustrating both theoretical and experimental results. The exposition is comprehensive yet user-friendly in engaging and exploring the broad range of topics for students and researchers in mathematics, physics, meteorology and engineering.

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Preface.- Part I Main Principles and Laws of Motion of an Ideal Fluid.- Part II Quasi-geostrophic Approximations of the Equations of Motion of Rotating Barotropic and Baroclinic Fluids.- Part III Hydrodynamic Stability and Atmospheric Dynamics.- Part IV Friction in Geophysical Boundary Layers and Their Models.- Part V Mechanical Prototypes of Equations of Motion of a Rotating Stratified Fluid and a Toy Model of Atmospheric Circulation.- Part VI Appendices.- Index

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From the reviews:

"This is a clearly written and pedagogically well balanced book on numerous aspects of geophysical hydrodynamic processes that can be useful not only for teachers and graduate students but also for researchers as a good general reference literature." (Vladimir Cadez, zbMATH, Vol. 1286, 2014)
"One may find a complete undergraduate and graduate course of geophysical hydrodynamics in this book. Moreover, the reading of this textbook is quite pleasant even from the literary viewpoint. ... Every chapter ends with some very concrete exercises." (Catherine Choquet, Mathematical Reviews, November, 2013)

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