Spiral defect chaos in Rayleigh-Bénard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals

Spiral defect chaos appears near the onset of Rayleigh-B\'enard convection for a low Prandtl number fluid. In this state, rotating spirals are continuously nucleated and eliminated, yielding a persistent dynamics. Here we derive an equation for the azimuthal flow induced by an effective body force originating from rotating spirals. This result is verified numerically using a two-dimensional generalized Swift-Hohenberg model and the three-dimensional Boussinesq equations. We identify a correlation between the appearance of spiral defect chaos and the balance between mean-flow advection and diffusive dynamics related to roll unwinding.