Foundations of Convection with Density Stratification

1. Front Matter

   Pages i-xvii

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2. The Equations of Hydrodynamics

   • Krzysztof A. Mizerski

   Pages 1-20

3. The Oberbeck-Boussinesq Convection

   • Krzysztof A. Mizerski

   Pages 21-85

4. Anelastic Convection

   • Krzysztof A. Mizerski

   Pages 87-197

5. Inclusion of Compositional Effects

   • Krzysztof A. Mizerski

   Pages 199-246

6. Back Matter

   Pages 247-248

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This book continues the process of systematization of knowledge about convection. It is 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. The book provides a short compendium of knowledge on the linear and weakly nonlinear limits of the Boussinesq convection, and a review of the theory on fully developed Boussinesq convection. The third chapter is devoted to a detailed derivation and a study of the three aforementioned stages of stratified (anelastic) convection, with a full solution in the marginal stage provided for the first time. Detailed and systematic explanations are given. The book is intended mainly as a textbook for courses on hydrodynamics and convective flows, for the use of lecturers and students; however, it also serves for the entire scientific community as a practical reference.

• Thermal Convection
• Compositional Convection
• Anelastic Approximation
• Fluid Dynamics
• Adiabatic Gradient
• Buoyancy Force
• Sound-proof Approximation
• Chemical Convection
• Binary Alloys
• Mathematical Fluid Mechanics

• Department of Magnetism, Institute of Geophysics, Warsaw, Poland

  Krzysztof A. Mizerski

Krzysztof Mizerski has experience in theoretical fluid mechanics in particular the theory of stratified convection and the hydromagnetic dynamo theory. All of his works have been concerned with analytic approaches to hydrodynamic and MHD problems supplied by numerical models. In collaboration with Professor Chris Jones from the University of Leeds, they have developed an effective theory of fully developed stratified convection and constructed a consistent dynamical picture of the phenomenon. The second main topic of the research conducted by Krzysztof Mizerski is the description of large-scale hydromagnetic dynamo effect in the fully nonlinear regime via the renormalization group method.

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