## Rayleigh-B nard Convection: Structures and DynamicsThis 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-B nard 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. |

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### Contents

Introduction | 1 |

Basic Concepts | 9 |

Investigation Tools | 27 |

Basic Types of ConvectiveFlow Structures | 59 |

Convection Regimes | 99 |

Selection of the Wavenumbers of Convection Rolls | 119 |

Peculiarities of Stratification and Vertical Structure of Convection | 191 |

Conclusion | 215 |

239 | |

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### Common terms and phrases

amplitude equation analysis aspect ratio assumed axisymmetric behaviour bifurcation boundary conditions boundary layer Boussinesq approximation Boussinesq equations Busse calculated contraselective factors convection cells convection zone convective flows corresponding critical Rayleigh number Croquette curve decrease defects dependence discussed dislocation dynamics effect evolution experimental finite flow geometry fluid layer front grain boundaries heat hexagonal hexagonal cells horizontal increases infinite layer initial conditions investigation layer boundaries linear Lyapunov functional Manneville mantle marginal stability mean drift model equations motion nonlinear NWS equation observed obtained optimal wavenumber parameter particular phase planform possible Prandtl number preferred wavenumber problem ramp range Rayleigh-Benard convection readjustment regimes region roll flows roll pattern scale solution spatially periodic spiral stability steady steady-state structure studied subcritical sublayer supercritical temperature gradient theoretical thermal thermal conductivity three-dimensional transition two-dimensional roll umbilicus unperturbed temperature values variation velocity vertical viscosity wall wavevector width