Rotating spiral patterns in Rayleigh-Bénard convection are known to induce azimuthal flows, which raises the question of how different neighboring spirals interact with each other in spiral chaos and the role of hydrodynamics in this regime. Far from the core, we show that spiral rotations lead to an azimuthal body force that is irrotational and of magnitude proportional to the topological index of the spiral and its angular frequency. The force, although irrotational, cannot be included in the pressure field as it would lead to a nonphysical multivalued pressure. We calculate the asymptotic dependence of the resulting flow and show that it leads to a logarithmic dependence of the azimuthal velocity on distance r away from the spiral core in the limit of negligible damping coefficient. This solution dampens to approximately 1/r when accounting for no-slip boundary conditions for the convection cell's plate. This flow component can provide additional hydrodynamic interactions among spirals including those observed in spiral defect chaos. We show that the analytic prediction for the azimuthal velocity agrees with numerical results obtained from both two-dimensional generalized Swift-Hohenberg and three-dimensional Boussinesq models and find that the velocity field is affected by the size and charges of neighboring spirals. Numerically, we identify a correlation between the appearance of spiral defect chaos and the balancing between the mean-flow advection and the diffusive dynamics related to roll unwinding.
Bibliographical noteFunding Information:
This research was supported by the Minnesota Supercomputing Institute and the Extreme Science and Engineering Discovery Environment , which is supported by the National Science Foundation under Grant No. ACI 1548562. E.V. acknowledges a Doctoral Dissertation Fellowship from the University of Minnesota and support from the Department of Aerospace Engineering and Mechanics. The research of J.V. was supported by the National Science Foundation under Grant No. DMR-1838977. M.R.P. and S.M. acknowledge support for computing resources from the Advanced Research Computing Center at Virginia Tech. Z.-F.H. acknowledges support from the National Science Foundation under Grant No. DMR-1609625.