Physics of Buoyant Flows

From Instabilities to Turbulence

Mahendra K Verma

• Publisher: WSPC
• Year: 2018
• eBook ISBN: 9789813237810
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

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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.

--> Contents:

• Basic Formulation, Patterns, and Chaos:
  • Introduction
  • Basic Framework
  • Fourier Space Description
  • Energy Transfers in Buoyancy-Driven Flows
  • Waves in Stably-Stratified Flows
  • Instability in Thermal Convection
  • Nonlinear Saturation
  • Patterns and Chaos in Buoyancy-Driven Flows
  • Boundary Layer, Bulk, and Exact Relations in Thermal Convection
• Turbulent Buoyant Flows:
  • A Survey of Hydrodynamic Turbulence
  • Scaling of Large-Scale Quantities in RBC
  • Phenomenology of Stably Stratified TurbulenceC
  • Phenomenology for Turbulent Thermal Convection
  • Turbulence Phenomenology of Other Buoyancy-Driven Flows
  • Anisotropy in Thermally-Driven Turbulence
  • Shell Models for Buoyancy-Driven Turbulence
  • Structures and Flow Reversals in RBC
  • Turbulence Phenomenology for RBC
• Buoyant Flows with Rotation and Magnetic Field:
  • Rotating Flows
  • Buoyant and Rotating Flows
  • Magnetohydrodynamics and Rotating Flows
  • Buoyant Flows Under Magnetic Field
  • Buoyant and Rotating Flows Under Magnetic Field
  • Double Diffusive Convection
  • Conclusions
• Appendices:
  • Thermal Parameters of Common Fluids
  • Phase and Group Velocities of a Wave Packet
  • Buoyant and Rotating Flows Under Magnetic Field
  • Proper Orthogonal Decomposition of RBC

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--> Readership: Graduate students and researchers in fluid mechanics, nonlinear dynamical systems, and related fields. -->
Thermal Convection;Rayleigh-Bénard Convection;Buoyancy-Driven Flows;Stably-Stratified Flows;Thermal Instability;Gravity Waves;Thermally-Driven Turbulence;Flow Reversal0 Key Features:

• Starts from basic principles and develops advanced topics in simple ways
• Highlights varied phenomena of buoyancy-driven flows — waves, instability, patterns, and turbulence — in unified and systematic manner
• Covers current results in the field

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Reviews
• Foreword
• Preface
• Acknowledgments
• Notation
• Contents
• Basic Formulation, Patterns, and Chaos
• Turbulent Buoyant Flows
• Buoyant Flows with Rotation and Magnetic Field
• Appendix A Thermal Parameters of Common Fluids
• Appendix B Phase and Group Velocities of a Wave Packet
• Appendix C Proper Orthogonal Decomposition of RBC
• Bibliography
• Index