Quasiperiodic instabilities and their exchange of criticality with harmonic and subharmonic modes in temperature-modulated Rayleigh-Benard convection.

Abstract

Previous studies dealing with Floquet stability analysis of non-zero-mean time-modulated Rayleigh-Bénard convection have shown the existence of only harmonic and subharmonic instability modes. Here, we emphasize the existence of quasiperiodic instabilities that have not yet been reported in the literature. This is achieved through both a Floquet-based analysis of the basic state and direct numerical simulations of the linearized stability equations. Particular attention is devoted to highlighting the existence of kinks in the numerically computed marginal stability curves that render difficult the detection of the stability exchange between quasiperiodic instabilities and their harmonic and subharmonic counterparts. Depending on the Prandtl number of the working fluid, such instability exchanges set in via either bicritical states or the migration of complex-conjugate pairs Floquet multipliers which can be combined to produce subharmonic responses.