Foundations of Convection with Density Stratification

TL;DR

This paper systematically reviews the theory of convection with density stratification, covering weakly and strongly stratified cases, and provides detailed derivations and descriptions of different convective stages for educational and reference purposes.

Contribution

It offers a comprehensive and systematic description of both weakly and strongly stratified convection, including derivations and analysis of all convective stages, filling a gap in existing literature.

Findings

Detailed derivation of stratified convection stages

Systematic comparison of weakly and strongly stratified convection

Practical reference for educational and research use

Abstract

The phenomenon of thermal and compositional (chemical) convection is very common in nature and therefore of great importance from the point of view of understanding of many fundamental aspects of the environment and universe. A number of books have been written on the topic, such as e.g. the seminal work of Chandrasekhar (1961) on Hydrodynamic and Hydromagnetic Stability, a large portion of which is devoted to the convective instability near its onset or the outstanding book of Getling (1998) where systematization of the knowledge on convection has been continued with a thorough description of the weakly nonlinear stages. Most of the works, however, considered weakly stratified, that is the so-called Boussinesq convection. It is the aim of this book to continue the process of systematization. It seems important to put the current knowledge on weakly and strongly stratified convection in order and provide a comprehensive description of the marginal, weakly nonlinear and fully developed stages of convective flow in both cases. To that end the book provides a short compendium of knowledge on the linear and weakly nonlinear limits of the Boussinesq convection, as a useful reference for a reader and than proceeds with a review of the theory on fully developed, weakly stratified convection. The entire third chapter is devoted to a detailed derivation and a study of the three aforementioned stages of stratified (anelastic) convection. The description of stratified convection requires extreme care, since many aspects have to be considered simultaneously for full consistency. Detailed and systematic explanations are therefore provided. This book is meant as a textbook for courses on hydrodynamics and convective flows, for the use of lecturers and students, however, it may also be of use for the entire scientific community as a practical reference.