The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.

This volume, containing twenty papers, includes the majority of those presented at the third IMA conference on stably stratified flows, held in Leeds in December 1989. The theme of the conference was waves and turbulence in stably stratified flows, although papers covering other aspects ofstably stratified flows are also included. A wide variety of techniques are described, ranging from numerical simulation, through laboratory studies, to field observations of the atmosphere. Some papers address fundamental aspects of turbulence in stably stratfied flows such as turbulence collapseand local scaling. Six of the papers report investigations motivated by Antarctic field studies, reflecting the importance of that region for research on the stably stratified atmosphere. Eight papers deal with aspects of mixing in stably stratified flows, of which four are directly concerned withindustrial applications. Observations of atmospheric internal gravity waves are discussed in two papers whilst a further two report studies of rotating, stratified flows with application to large-scale atmospheric and oceanic dynamics.

Gravity pervades the whole universe; hence buoyancy drives fluids everywhere including those in the atmospheres and interiors of planets and stars. Prime examples of such flows are mantle convection, atmospheric flows, solar convection, dynamo process, heat exchangers, airships and hot air balloons. In this book we present fundamentals and applications of thermal convection and stratified flows.Buoyancy brings in extremely rich phenomena including waves and instabilities, patterns, chaos, and turbulence. In this book we present these topics in a systematic manner. First we present a unified treatment of linear theory that yields waves and thermal instability for stably and unstably-stratified flows respectively. We extend this analysis to include rotation and magnetic field. We also describe nonlinear saturation and pattern formation in Rayleigh-Bénard convection.The second half of the book is dedicated to buoyancy-driven turbulence, both in stably-stratified flow and in thermal convection. We describe the spectral theory including energy flux and show that the thermally-driven turbulence is similar to hydrodynamic turbulence. We also describe large-scale quantities like Reynolds and Nusselt numbers, flow anisotropy, and the dynamics of flow structures, namely flow reversals. Thus, this book presents all the major aspects of the buoyancy-driven flows in a coherent manner that would appeal to advanced graduate students and researchers.

A towing tank system was used to study the structure of turbulence in stably stratified fluids. Turbulence is generated by moving an obstacle (a grid or a cylinder) in a tank of stratified salt water. Recent improved shadowgraph pictures of these laboratory generated stratified flows are shown in the paper. They give further support to Pao's observation that (1) internal waves and turbulence coexist in turbulent stratified flows, with internal waves at the large scales and turbulence at the small scales; (2) turbulence decays much more rapidly than internal waves; and (3) the turbulent-nonturbulent interfaces are not necessarily sharp, and the transition region may consist of mostly internal waves. Diagnostic methods to distinguish internal waves from turbulence with two probe measurements are proposed. (Author).

This volume contains the papers presented at the workshop on Statistical The ories and Computational Approaches to Turbulence: Modern Perspectives and Applications to Global-Scale Flows, held October 10-13, 2001, at Nagoya Uni versity, Nagoya, Japan. Because of recent developments in computational capabilities, the compu tational approach is showing the potential to resolve a much wider range of length and time scales in turbulent physical systems. Nevertheless, even with the largest supercomputers of the foreseeable future, development of adequate modeling techniques for at least some scales of motion will be necessary for practical computations of important problems such as weather forecasting and the prediction and control of global pollution. The more powerful the available machines become, the more demand there will be for precise prediction of the systems. This means that more precise and reliable knowledge of the underlying dynamics will become important, and that more efficient and precise numerical methods best adapted to the new generation of computers will be necessary. The understanding of the nature of unresolved scales then will playa key role in the modeling of turbulent motion. The challenge to turbulence theory here is to elucidate the physics or dynamics of those scales, in particular their sta tistical aspects, and thereby develop models on sound bases to reduce modeling ambiguity. The challenge to the computational method is to develop efficient algorithms suitable for the problems, the machines, and the developed models.