Dislocation Dynamics in Rayleigh-B\'enard Convection

Theoretical results on the dynamics of dislocations in Rayleigh-B\'enard convection are reported both for Swift-Hohenberg models and the Boussinesq equations. For intermediate Prandtl numbers the motion of dislocations is found to be driven by the superposition of two independent contributions: (i) the Peach-Koehler force derived from the change of a Lyapunov potential with pattern wave number; (ii) a non-potential advection force on the dislocation core by its self-generated mean flow. Their competition allows for the first time to understand the experimentally observed bound dislocation pairs.