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Fundamentals of Geophysical Hydrodynamics

  • Fester Einband
  • 274 Seiten
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Beschreibung

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.


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.



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



Autorentext

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 Rossby-Obukhov potential vortex; energy and momentum of a compressible fluid; hydrodynamic approximation of equations of gas dynamics.- Part II Quasi-geostrophic 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 Obukhov-Charney equation; Rossby waves.- 8 Resonant interaction of Rossby waves, Helmholtz and Obukhov singular vortices, and the Kirchhoff equations.- 9 Equations of quasi-geostrophic 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 plane-parallel flows of ideal homogeneous and nonhomogeneous fluids.- 14 The method of normal modes and its simplest applications in the theory of linear stability of plane-parallel 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; quasi-geostrophic equation for transformation of potential vorticity.- 21 Kolmogorov flow and the role of surface friction.- 22 Stability of quasi-two-dimensional 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 Oberbeck-Boussinesq 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



Inhalt

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

Produktinformationen

Titel: Fundamentals of Geophysical Hydrodynamics
Autor:
Übersetzer:
Schöpfer:
EAN: 9783642310331
ISBN: 978-3-642-31033-1
Format: Fester Einband
Herausgeber: Springer, Berlin
Genre: Mathematik
Anzahl Seiten: 274
Gewicht: 578g
Größe: H20mm x B235mm x T161mm
Jahr: 2012
Auflage: 2013

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