Abstract
This paper considers the way in which a lateral boundary restricts the wavelength of convective rolls parallel to the boundary. Unlike previous theories of wave number selection, the present work allows for perpendicular cross rolls adjacent to the boundary, the existence of which is indicated by stability considerations. The present theory also incorporates forcing at the boundary, equivalent to a wall that is imperfectly insulated, as in many experimental investigations of Rayleigh-Benard convection. The results are based on weakly non-linear solutions of amplitude equations derived from the Swift-Hohenberg model and are compared with numerical solutions of the full non-linear Swift-Hohenberg equation.
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