by A V Getling (M V Lomonosov Moscow State University)

This invaluable book presents a concise but systematic account of the formation of spatial flow structures in a horizontal fluid layer heated from below. Flows of this type, known as Rayleigh-Bénard convection, show important features of behaviour inherent not only in various hydrodynamic-instability phenomena but also in nonlinear pattern-forming processes in other contexts. The book describes the basic methods of investigating convection patterns, and the types of two- and three-dimensional flows, pattern defects, and sequences of convection-regime changes.

The author pays special attention to the question of how various factors (mainly reducible to initial and boundary conditions) determine the shapes and sizes of the structures which develop. In this way, the role of order and disorder in flow patterns, as a factor strongly affecting the character of the evolution of structures, is revealed. The presentation emphasizes the physical picture of these phenomena, without excessive mathematical detail.

• Basic Concepts:
  • The Boussinesq Approximation
  • The Rayleigh-Bénard Problem
  • Linear Analysis
  • Nonlinear Regimes and Bifurcations
  • Planforms of Convection Cells
• Investigation Tools:
  • Experiment
  • Theoretical Approaches
• Basic Types of Convective-Flow Structures:
  • Two-Dimensional Rolls and Three-Dimensional Cells
  • Patterns of Quasi-Two-Dimensional Rolls
  • Convection Textures. Roll-Pattern Defects
• Convection-Regimes:
  • Regime Diagram
  • Phase Turbulence
  • Spiral-Defect Chaos
• Selection of the Wavenumbers of Convection Rolls:
  • Wavenumbers in Experiments with Random Initial Disturbances
  • Searches for Universal Selection Criteria
  • Stability of Two-Dimensional Roll Flows
  • Lyapunov Functional and Selection
  • “Selection Mechanisms”
• Peculiarities of Stratification and Vertical Structure of Convection:
  • Effects of Strong Temperature Dependence of Viscosity
  • Penetrative Convection
  • Small-Scale Motions in a Globally Unstable Layer
  • Astro- and Geophysical Applications