A grain boundary in cellular structures near the onset of convection

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Abstract
The structure of a grain boundary between parallel and perpendicular rolls is analysed by means of the amplitude equation. If ∊ is the (small) difference between the control parameter and its threshold value, this grain boundary is divided into an outer region of thickness of the order of ∊−½ and an inner region of thickness ∊−3/10. If the wavenumbers on both sides of the grain boundary are different, it moves with a constant velocity. This velocity ensures the balance by viscous loss of the energy gain due to the replacement of a less optimal structure by a more optimal one.