| |
| |
Preface | |
| |
| |
| |
Introduction and Preliminaries | |
| |
| |
| |
The topics to be discussed | |
| |
| |
| |
Equilibrium and departures from it | |
| |
| |
| |
The equations of motion and various approximations | |
| |
| |
| |
Basic parameters of heterogeneous flows | |
| |
| |
| |
Linear Internal Waves | |
| |
| |
| |
Waves at a boundary between homogeneous layers | |
| |
| |
Progressive waves in deep water | |
| |
| |
Waves between layers of finite thickness | |
| |
| |
Standing waves | |
| |
| |
| |
Waves in a continuously stratified fluid | |
| |
| |
Description in terms of modes | |
| |
| |
Description in terms of rays | |
| |
| |
Laboratory experiments on waves in bounded regions | |
| |
| |
| |
Waves in a moving stratified fluid | |
| |
| |
Velocity constant with height | |
| |
| |
Lee waves with varying properties in the vertical | |
| |
| |
Reversals of velocity and critical layers | |
| |
| |
| |
Weak non-linearities: interactions between waves | |
| |
| |
The mechanism of resonant interaction | |
| |
| |
Interactions of interfacial waves | |
| |
| |
Interactions with continuous stratification | |
| |
| |
| |
Finite Amplitude Motions in Stably Stratified Fluids | |
| |
| |
| |
Internal waves of finite amplitude | |
| |
| |
Interfacial waves | |
| |
| |
Cnoidal and solitary waves | |
| |
| |
Waves and flows in a density gradient | |
| |
| |
Finite amplitude lee waves | |
| |
| |
| |
Internal hydraulics and related problems | |
| |
| |
Steady frictionless flow of a thin layer | |
| |
| |
Internal hydraulic jumps | |
| |
| |
Flow down a slope | |
| |
| |
The 'lock exchange' problem | |
| |
| |
Gravity currents and noses | |
| |
| |
| |
Slow motions in a stratified fluid | |
| |
| |
The problem of selective withdrawal | |
| |
| |
Blocking ahead of an obstacle | |
| |
| |
Upstream wakes and boundary layers | |
| |
| |
Viscous diffusive flows | |
| |
| |
| |
Instability and the Production of Turbulence | |
| |
| |
| |
The stability of a free shear layer | |
| |
| |
The various types of instability | |
| |
| |
The Kelvin-Helmholtz mechanism | |
| |
| |
Interfaces of finite thickness | |
| |
| |
Observations of the breakdown of parallel stratified flows | |
| |
| |
| |
The combined effects of viscosity and stratification | |
| |
| |
Viscous effects at an interface | |
| |
| |
Thermally stratified plane Poiseuille flow | |
| |
| |
Flows along a sloping boundary | |
| |
| |
Transition to turbulence | |
| |
| |
| |
Mechanisms for the generation of turbulence | |
| |
| |
Classification of the various mechanisms | |
| |
| |
Flows near boundaries | |
| |
| |
Shear instabilities produced by interfacial waves | |
| |
| |
The interaction between wave modes | |
| |
| |
Internal instabilities with continuous stratification | |
| |
| |
| |
Turbulent Shear Flows in a Stratified Fluid | |
| |
| |
| |
Velocity and density profiles near a horizontal boundary | |
| |
| |
The logarithmic boundary layer | |
| |
| |
The effect of a buoyancy flux | |
| |
| |
Forced and free convection | |
| |
| |
Constant-flux layers in stable stratification | |
| |
| |
| |
Theories of turbulence in a stratified shear flow | |
| |
| |
Similarity theories of turbulence and diffusion | |
| |
| |
The spectrum of nearly inertial turbulence | |
| |
| |
Arguments based on the governing equations | |
| |
| |
| |
Observations and experiments on stratified shear flows | |
| |
| |
The generation and collapse of turbulent wakes | |
| |
| |
The suppression of turbulence at an interior shear layer | |
| |
| |
Stratified flows in pipes, channels and estuaries | |
| |
| |
Longitudinal mixing and advection | |
| |
| |
| |
Buoyant Convection from Isolated Sources | |
| |
| |
| |
Plumes in a uniform environment | |
| |
| |
Axisymmetric turbulent plumes | |
| |
| |
The entrainment assumption | |
| |
| |
Forced plumes | |
| |
| |
Vertical two-dimensional plumes | |
| |
| |
| |
Inclined plumes and turbulent gravity currents | |
| |
| |
A modified entrainment assumption | |
| |
| |
Slowly varying flows | |
| |
| |
Laboratory experiments and their applications | |
| |
| |
Detailed profile measurements | |
| |
| |
| |
Thermals in a uniform environment | |
| |
| |
Dimensional arguments and laboratory experiments | |
| |
| |
Buoyant vortex rings | |
| |
| |
'Starting plumes' | |
| |
| |
Line thermals and bent-over plumes | |
| |
| |
| |
The non-uniform environment | |
| |
| |
Motions in an unstable environment | |
| |
| |
Plumes in a stable environment | |
| |
| |
Forced plumes and vortex rings in a stable environment | |
| |
| |
Environmental turbulence | |
| |
| |
| |
Convection from Heated Surfaces | |
| |
| |
| |
The theory of convection between horizontal plates | |
| |
| |
The governing parameters | |
| |
| |
Linear stability theory | |
| |
| |
Finite amplitude convection | |
| |
| |
| |
Laboratory and numerical experiments on parallel plate convection | |
| |
| |
Observations of laminar convection | |
| |
| |
Measurements at larger Rayleigh numbers | |
| |
| |
Numerical experiments | |
| |
| |
| |
The interaction between convective elements and their environment | |
| |
| |
The formation of plumes or thermals near a horizontal boundary | |
| |
| |
The environment as an ensemble of convection elements | |
| |
| |
Convection from small sources in a confined region | |
| |
| |
Penetrative convection | |
| |
| |
| |
Convection with other shapes of boundary | |
| |
| |
A heated vertical wall | |
| |
| |
Buoyancy layers at vertical and sloping boundaries | |
| |
| |
Convection in a slot | |
| |
| |
| |
Double-Diffusive Convection | |
| |
| |
| |
The stability problem | |
| |
| |
The mechanism of instability | |
| |
| |
Linear stability analysis | |
| |
| |
The form of the convection cells | |
| |
| |
Finite amplitude calculations | |
| |
| |
| |
The formation of layers: experiments and observations | |
| |
| |
The 'diffusive' regime | |
| |
| |
The 'finger' regime | |
| |
| |
Side boundaries and horizontal gradients | |
| |
| |
Related observations in the ocean | |
| |
| |
| |
The fluxes across an interface | |
| |
| |
Measurements in the 'diffusive' regime | |
| |
| |
The time-history of several convecting layers | |
| |
| |
Fluxes and structure at a 'finger' interface | |
| |
| |
The thickness of a 'finger' interface | |
| |
| |
Convection in a region of variable depth | |
| |
| |
| |
Mixing Across Density Interfaces | |
| |
| |
| |
Laboratory experiments | |
| |
| |
Stirring with oscillating grids | |
| |
| |
Mixing driven by a surface stress | |
| |
| |
The influence of molecular processes | |
| |
| |
Comparison of various methods of stirring | |
| |
| |
| |
Geophysical applications | |
| |
| |
The wind-mixed surface layer | |
| |
| |
Seasonal changes of a thermocline | |
| |
| |
Mixing at an atmospheric inversion | |
| |
| |
Other factors limiting the depth of a mixed layer | |
| |
| |
| |
Internal mixing Processes | |
| |
| |
| |
The observational data | |
| |
| |
| |
Critical Richardson number criteria | |
| |
| |
Examples of equilibrium conditions | |
| |
| |
Non-equilibrium conditions: step formation | |
| |
| |
Energetics of a layered system | |
| |
| |
| |
Wave-induced mixing | |
| |
| |
Mixing at existing interfaces | |
| |
| |
Formation of layers from a smooth gradient | |
| |
| |
Statistical aspects of wave generation and breaking | |
| |
| |
Waves and turbulence in large scale flows | |
| |
| |
Bibliography and Author Index | |
| |
| |
Recent Publications | |
| |
| |
Subject Index | |