### Abstract

This chapter presents a mathematical framework for describing convection patterns. On the horizontal diffusion time scale T_{H}, the convection field develops patches, of a circular nature surrounding a sink, in which the wavenumber is constant. The incompatibility of these patches is ironed out over the longer time scale of the aspect ratio times T_{H}, and the process involves a gliding motion in which roll dislocations move in a direction perpendicular to the roll axis. The climb motion, where the dislocations move along the roll axis, occur on the scale T_{H} as their role is to adjust wavelength, although small adjustments of order ε^{2} will be made on the ε^{-2}T_{H} scale.

Original language | English (US) |
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Pages (from-to) | 205-231 |

Number of pages | 27 |

Journal | North-Holland Mathematics Studies |

Volume | 81 |

Issue number | C |

DOIs | |

State | Published - Jan 1 1983 |

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### ASJC Scopus subject areas

- Mathematics(all)