## Convection and Chaos in FluidsThe book describes the progress made in understanding the phenomena of various hydrodynamic instabilities over the last thirty years. Exact results for the onset of Rayleigh-Benard convection in different systems are presented and approximation techniques like amplitude equations and few-mode truncations are treated at length. Routes to chaos and the characteristics of the chaotic state are reviewed. Certain features of the Taylor-Couette flow and the effect of parametric modulation on hydrodynamic instabilities are discussed. The theory is supplemented by experimental results. |

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### Contents

Onset of Convection | 1 |

Near the Onset | 14 |

Lorenz Model | 37 |

On Experiments | 101 |

Thermohaline Convection | 145 |

Binary Liquids | 175 |

CouetteTaylor Flow | 203 |

Modulated Systems | 219 |

Fully Developed Turbulence | 239 |

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### Common terms and phrases

Ahlers amplitude equation aspect ratio attractor Behringer boundary conditions Cantor set chaotic behaviour Chapter codimension-2 point coefficient conduction corresponds COSTTZ Couette flow cylindrical defined determined differential equations diffusion discuss dynamical systems effect eigenvalue flow Fluid Mech fractal dimension free boundary conditions frequency function hence Hopf bifurcation hydrodynamic hydrodynamic equations Im(p initial conditions intermittency iterations leads Lett Libchaber limit cycle linear stability analysis Lorenz model Lorenz system Lyapunov exponent Lyapunov number magnetic field modulation nonlinear terms Nusselt obtained onset of convection oscillation oscillatory instability period-doubling period-doubling bifurcations perturbation theory Phys plates Prandtl number quasiperiodic region rigid boundaries route to chaos scale schematic shown in Fig sinh siniTz solution solvability stationary bifurcation stationary convection stationary instability Steinberg temperature difference threshold trajectories travelling wave tricritical point truncated system unstable manifold vanish vector velocity field wavenumber yields zero