Abstract
Abstract The situation of 90° grain boundaries in a pair of two-dimensional models of Rayleigh-Bénard convection is studied by perturbation analysis near threshold and by direct numerical simulation. In contrast to the work by Manneville and Pomeau (1983), a unique state is found in which the grain boundary is stationary, characterized by a unique wavenumber qs x of the rolls parallel to the boundary, and a unique wavenumber qs y of the rolls perpendicular to the boundary. Two different kinds of dynamical motion result from deviations from these unique values, and these modes have essentially separate dependences on qx and qy . For potential models, the values of the selected wavenumbers coincide with minimization of the potential and with marginal stability to the zig-zag instability, whereas no such agreement is found for non-potential models.
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