Convection in Rotating Fluids

1 General notions.- 1.1 Description of the rotating fluid motion. The Boussinesq approximation.- 1.2 The basic non-dimensional parameters.- 1.3 Some other approximations.- 1.4 Boundary layers.- 1.5 The efficiency of a convective system.- 1.6 Analogies between rotating and stratified fluids.- 2 Plane horizontal homogeneous layer.- 2.1 Convective motions in non-rotating fluids.- 2.2 The onset of convection in rotating fluids: Theory.- 2.3 The onset of convection in rotating fluids. Experiments.- 2.4 The structure of the convective motions and at small supercritical Rayleigh numbers.- 2.5 Spatial structure at large Rayleigh numbers.- 2.6 Convective rings.- 2.7 Thermal structure of regular convective motions.- 2.8 The velocity field in the regular convective regime.- 2.9 Turbulent convection in non-rotating fluids.- 2.10 Irregular convection regimes in rotating fluids.- 2.11 Heat transfer.- 2.12 Convection at a non-parallel rotation axis and gravity acceleration.- 2.13 The role of the velocity shear.- 3 Horizontally temperature-inhomogeneous rotating annuli.- 3.1 Classification of convective regimes in an annulus.- 3.2 The axisymmetrical regime and its stability.- 3.3 Non-axisymmetrical regimes.- 3.4 Temperature and velocity field structure.- 3.5 Heat and angular momentum transfer.- 3.6 Various Prandtl numbers.- 3.7 Some non-linear models.- 3.8 Thermal and topography inhomogeneities.- 3.9 Specific heating cases.- 4 Vertically and horizontally inhomogeneous heating.- 4.1 Temperature gradient at horizontal bottom.- 4.2 Stable vertical stratification in annuli.- 4.3 Baroclinic instability without hydrostatics and geostrophy.- 4.4 Unstable vertical stratification.- 4.5 Diffusion circulation.- 5 Convection from local sources.- 5.1 Local buoyancy source in a non-rotating fluid.-5.2 Geostrophic balance and local sources.- 5.3 Intense solitary vortices.- 6 Centrifugal effects.- 6.1 Narrow cylindrical layer of a constant depth.- 6.2 Layer with sloping boundaries.- 6.3 Shallow cylindrical layers.- 7 Convection in spheres and spherical shells.- 7.1 Spherically symmetric gravitation and heating.- 7.2 Thin spherical shells.- 8 Geophysical and astrophysical applications and analogies.- 8.1 Parameters and properties of some natural objects.- 8.2 Geostrophic convection.- 9 Bibliography.