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Spatial inhomogeneity of heating of fluids in the gravity field is the cause of all motions in nature: in the atmosphere and the oceans on Earth, in astrophysical and planetary objects. All natural objects rotate and convective motions in rotating fluids are of interest in many geophysical and astrophysical phenomena. In many industrial applications, too (crystal growth, semiconductor manufacturing), heating and rotation are the main mechanisms defining the structure and quality of the material.
Depending on the geometry of the systems and the mutual orientation of temperature and gravity field, a variety of phenomena will arise in rotating fluids, such as regular and oscillating waves, intensive solitary vortices and regular vortex grids, interacting vortices and turbulent mixing. In this book the authors elucidate the physical essence of these phenomena, determining and classifying flow regimes in the space of similarity numbers. The theoretical and computational results are presented only when the results help to explain basic qualitative motion characteristics.
The book will be of interest to researchers and graduate students in fluid mechanics, meteorology, oceanography and astrophysics, crystallography, heat and mass transfer.
List of contents
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.
