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.
Author(s): Felix V. Dolzhansky (auth.)
Series: Encyclopaedia of Mathematical Sciences 103
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2013
Language: English
Pages: 274
Tags: Mathematical Applications in the Physical Sciences;Geophysics and Environmental Physics;Hydrogeology;Theoretical, Mathematical and Computational Physics;Fluid- and Aerodynamics
Front Matter....Pages I-XIV
Front Matter....Pages 1-1
Equations of Motion of an Ideal Incompressible Fluid; Kelvin’s Circulation Theorem....Pages 3-11
Potential Vorticity and the Conservation Laws of Energy and Momentum for a Stratified Incompressible Fluid....Pages 13-21
Helicity; Equations of Gas Dynamics; The Ertel Invariant....Pages 23-30
The Rossby–Obukhov Potential Vortex; Energy and Momentum of a Compressible Fluid; Hydrodynamic Approximation of Equations of Gas Dynamics....Pages 31-39
Front Matter....Pages 41-41
Equations of Motion of a Rotating Fluid; The Notion of a Geophysical Flow....Pages 43-50
What is Geophysical Hydrodynamics?....Pages 51-60
The Obukhov–Charney Equation; Rossby Waves....Pages 61-70
Resonant Interaction of Rossby Waves; Helmholtz and Obukhov Singular Vortices; The Kirchhoff Equations....Pages 71-82
Equations of Quasi-geostrophic Baroclinic Motion....Pages 83-92
The Energy Balance, Available Potential Energy, and Rossby Waves in a Baroclinic Atmosphere....Pages 93-99
Important Remarks on the Description of Baroclinic Geophysical Flows....Pages 101-106
Front Matter....Pages 107-107
The Notion of Dynamical Stability via the Example of Motion of a Rigid Body with a Fixed Point....Pages 109-115
Stating the Linear Stability Problem for Plane-Parallel Flows of Ideal Homogeneous and Nonhomogeneous Fluids....Pages 117-123
The Method of Normal Modes and Its Simplest Applications in the Theory of Linear Stability of Plane-Parallel Flows....Pages 125-131
The Taylor Problem of Stability of Motion of a Stratified Fluid with a Linear Velocity Profile....Pages 133-139
Applications of Integral Relations and Conservation Laws in the Theory of Hydrodynamic Stability....Pages 141-150
Stability of Zonal Flows of a Barotropic Atmosphere; The Notion of Barotropic Instability....Pages 151-157
The Concept of Baroclinic Instability; The Eady Model....Pages 159-167
Front Matter....Pages 169-169
Equations of Motion of a Viscous Fluid; The Boundary Conditions....Pages 171-179
Friction Mechanisms in Global Geophysical Flows; Quasi-geostrophic Equation for Transformation of Potential Vorticity....Pages 181-188
Front Matter....Pages 169-169
Kolmogorov Flow and the Role of Surface Friction....Pages 189-194
Stability of Quasi-two-dimensional Shear Flows with Arbitrary Velocity Profiles....Pages 195-204
Friction in a Turbulent Boundary Layer....Pages 205-213
Front Matter....Pages 215-215
Hydrodynamic Interpretation of the Euler Equations of Motion of a Classical Gyroscope and Their Invariants....Pages 217-224
Mechanical Interpretation of the Oberbeck–Boussinesq Equations of Motion of an Incompressible Stratified Fluid in a Gravitational Field....Pages 225-233
Motion of Barotropic and Baroclinic Tops as Mechanical Prototypes for the General Circulation of Barotropic and Baroclinic Inviscid Atmospheres....Pages 235-244
Toy Model for General Circulation of a Viscous Atmosphere....Pages 245-257
Back Matter....Pages 259-272
