Evolution of secondary whirls in thermoconvective vortices: Strengthening, weakening, and disappearance in the route to chaos

Abstract

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.

Four-Frequency Solution in a Magnetohydrodynamic Couette Flow as a Consequence of Azimuthal Symmetry Breaking

“…Understanding how systems become chaotic is of fundamental importance in many applications. Biological systems [1,2], financial models [3], road traffic modelling [4], laser physics [5], neural networks [6], and simulations in fluid dynamics [7], or magnetohydrodynamics [8], exhibit transitions from regular oscillatory behaviour to a chaotic regime. Quite often, this transition follows the Newhouse-Ruelle-Takens (NRT) [9] scenario in which after a few bifurcations, involving quasiperiodic states, chaos emerges.…”

Dynamics of a trapped vortex in rotating convection

“…Though remarked upon, they offer no discussion or explanation for this. Oscillations have also been observed in models of dust devils by Castaño et al [16]. In this case the oscillations are asymmetric and occur through a sequence of Hopf bifurcations.…”

Four-frequency solution in a magnetohydrodynamic Couette flow as a consequence of azimuthal symmetry breaking

“…Understanding how systems become chaotic is of fundamental importance in many applications. Biological systems [1,2], financial models [3], road traffic modelling [4], laser physics [5], neural networks [6], and simulations in fluid dynamics [7], or magnetohydrodynamics [8], exhibit transitions from regular oscillatory behaviour to a chaotic regime. Quite often, this transition follows the Newhouse-Ruelle-Takens (NRT) [9] scenario in which after a few bifurcations, involving quasiperiodic states, chaos emerges.…”