Wavelength selection in convection near a lateral boundary

^** Corresponding author. This paper considers the way in which a lateral boundary restrictsthe wavelength of convective rolls parallel to the boundary.Unlike previous theories of wave number selection, the presentwork 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 manyexperimental investigations of Rayleigh–Bénardconvection. The results are based on weakly non-linear solutionsof amplitude equations derived from the Swift–Hohenbergmodel and are compared with numerical solutions of the fullnon-linear Swift–Hohenberg equation.