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 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