Fundamentals of Geophysical Hydrodynamics

- 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

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 mechanismsin

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)