Spiral defect chaos in Rayleigh-B\'enard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals

TL;DR

This study investigates how azimuthal flows induced by rotating spirals in Rayleigh-Bénard convection influence spiral interactions and chaos, combining asymptotic analysis with numerical simulations to reveal flow behaviors and their role in spiral defect chaos.

Contribution

The paper provides the first analytical and numerical analysis of azimuthal flows caused by rotating spirals in Rayleigh-Bénard convection, elucidating their asymptotic behavior and impact on spiral interactions.

Findings

Azimuthal flow velocity depends logarithmically on distance from the spiral core.

Flow damping transitions from logarithmic to approximately 1/r with boundary conditions.

Correlation found between spiral defect chaos and the balance of mean-flow advection and diffusive dynamics.

Abstract

Rotating spiral patterns in Rayleigh-B\'enard 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.