This chapter presents a mathematical framework for describing convection patterns. On the horizontal diffusion time scale TH, 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 TH, 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 TH as their role is to adjust wavelength, although small adjustments of order ε2 will be made on the ε-2TH scale.
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