Fundamentals of Geophysical Hydrodynamics
Authors: Dolzhansky, Felix V.
Editors: Gledzer, A.E., Gledzer, E.B. (Eds.)
 Comprehensive treatment of the fundamentals of geophysical hydrodynamics
 Fairly systematic exposition
 Broad range of topics
 Based on graduate and undergraduate courses at the Moscow Institute of Physics and Technology
 Ideal companion to the complexities of the topic for students and researchers in mathematics, physics, meteorology and engineering
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 About this book

This newlytranslated 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 RossbyObukhov invariants, quasigeostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the NavierStokes 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 userfriendly in engaging and exploring the broad range of topics for students and researchers in mathematics, physics, meteorology and engineering.
 About the authors

Preface. Part I Main Principles and Laws of Motion of an Ideal Fluid: 1 Equations of motion of an ideal incompressible fluid; Kelvin's circulation theorem. 2 Potential vorticity and the conservation laws of energy and momentum for a stratified incompressible fluid. 3 Helicity, equations of gas dynamics, and the Ertel invariant. 4 The RossbyObukhov potential vortex; energy and momentum of a compressible fluid; hydrodynamic approximation of equations of gas dynamics. Part II Quasigeostrophic Approximations of the Equations of Motion of Rotating Barotropic and Baroclinic Fluids: 5 Equations of motion of a rotating fluid and the notion of a geophysical flow. 6 What is geophysical hydrodynamics?. 7 The ObukhovCharney equation; Rossby waves. 8 Resonant interaction of Rossby waves, Helmholtz and Obukhov singular vortices, and the Kirchhoff equations. 9 Equations of quasigeostrophic baroclinic motion. 10 The energy balance, available potential energy, and Rossby waves in a baroclinic atmosphere. 11 Important remarks on the description of baroclinic geophysical flows. Part III Hydrodynamic Stability and Atmospheric Dynamics: 12 The notion of dynamical stability via the example of motion of a rigid body with a fixed point. 13 Stating the linear stability problem for planeparallel flows of ideal homogeneous and nonhomogeneous fluids. 14 The method of normal modes and its simplest applications in the theory of linear stability of planeparallel flows. 15 The Taylor problem of stability of motion of a stratified fluid with a linear velocity profile. 16 Applications of integral relations and conservation laws in the theory of hydrodynamic stability. 17 Stability of zonal flows of a barotropic atmosphere; the notion of barotropic instability. 18 The concept of baroclinic instability; the Eady model. Part IV Friction in Geophysical Boundary Layers and Their Models: 19 Equations of motion of a viscous fluid; the boundary conditions. 20 Friction mechanisms in global geophysical flows; quasigeostrophic equation for transformation of potential vorticity. 21 Kolmogorov flow and the role of surface friction. 22 Stability of quasitwodimensional shear flows with arbitrary velocity profiles. 23 Friction in a turbulent boundary layer. Part V Mechanical Prototypes of Equations of Motion of a Rotating Stratified Fluid and a Toy Model of Atmospheric Circulation: 24 Hydrodynamic interpretation of the Euler equations of motion of a classical gyroscope and their invariants. 25 Mechanical interpretation of the OberbeckBoussinesq equations of motion of an incompressible stratifed fluid in a gravitational field. 26 Motion of barotropic and baroclinic tops as mechanical prototypes for the general circulation of barotropic and baroclinic inviscid atmospheres. 27 Toy model for general circulation of a viscous atmosphere. Part VI Appendices: A1 On a certain boundary condition. A2 Stability of the Kolmogorov flow with an external friction. Index
 Reviews

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 Čadež, 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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Bibliographic Information
 Bibliographic Information

 Book Title
 Fundamentals of Geophysical Hydrodynamics
 Authors

 Felix V. Dolzhansky
 Editors

 A.E. Gledzer
 E.B. Gledzer
 Translated by
 Khesin, B.
 Series Title
 Encyclopaedia of Mathematical Sciences
 Series Volume
 103
 Copyright
 2013
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783642310348
 DOI
 10.1007/9783642310348
 Hardcover ISBN
 9783642310331
 Softcover ISBN
 9783642440052
 Series ISSN
 09380396
 Edition Number
 1
 Number of Pages
 XIV, 274
 Topics