Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

Abstract

We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh-Bénard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense these modes behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear mode may provide an explanation for the strong zonal flows observed recently in simulations and experiments on rapidly rotating convection at high Rayleigh number. †

Transition from non-swirling to swirling axisymmetric turbulence

“…The model predicts two nontrivial branches beyond the bifurcation, suggesting a subcritical transition with hysteresis. Such behavior with a subcritical transition between two different turbulent states was recently also observed in a different system, thin-layer rotating Rayleigh-Bénard convection [21]. The model prediction of subcriticality in the present case is in particular visible in the zoom in Fig.…”

Bistability in Rayleigh-Bénard convection with a melting boundary

“…This thermodynamical effect is nevertheless the starting point when deriving a diffuse-interface method called the phase-field method [6]. The problem described above is solved numerically by using a mixed pseudo-spectral fourth-order finite-difference method [22,24] and the particular phase-field model which has been discussed and validated in [23]. For several cases, we also checked our results by using the open-source pseudo-spectral solver Dedalus [9,10] (more information at http://dedalus-project.org).…”

Near-resonant instability of geostrophic modes: beyond Greenspan's theorem

“…Asymptotic theories describing rotating turbulence in the limit of vanishing forcing amplitude and dissipation also suggest that waves could dominate over geostrophic modes in such a regime (Bellet et al 2006;Sagaut & Cambon 2018). Hence, although bi-dimensionalisation in the form of geostrophic eddies has been commonly observed, it may not be the only equilibrium state of rotating turbulence, be it at moderate (Yokoyama & Takaoka 2017;Favier, Guervilly & Knobloch 2019) as well as small (van Kan & Alexakis 2019) forcing amplitudes. In addition, the nature of the forcing seems fundamental in determining the equilibrium state of rotating turbulence.…”