Spiral Dynamics in Pattern-Forming Systems: Mean Flow Effects

Mean flow effects are discussed for two different pattern-forming systems: RayleighBénard convection and Faraday instability in viscous fluid. In both systems spirals are observed in certain parameter regions. In the Rayleigh-Bénard convection, the spiral core instability and subsequent generation of upand downflow hexagons are shown to occur due to the mean flow generated by the curved rolls near the core. In the Faraday instability, the mean flow which is generated by rapidly decaying surface waves near the wall, causes wavenumber frustration which leads to a rigidbody spiral rotation. In both cases we use phenomenological Swift-Hohenberg-type equations for the order parameter coupled to a large-scale mean flow. Numerical simulations are compared to recently reported experimental results.