Bistability and chaos in the Taylor-Green dynamo

Abstract

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

Dynamo transition in a five-mode helical model

“…4, where we show the variation of f c with Pm on the log-log scale. The critical forcing decreases continuously with increasing Pm and hence our model indicates that the dynamo transition becomes easier as we increase the Pm, in accordance with the observations from DNS 12,29 . Hence, even though our model shows that a decrease in Pm decreases the Rm c , it still captures the fact that it is difficult to initiate dynamo for low Pm as the critical forcing amplitude f c increases sharply.…”

“…However, DNS results for low Pm have shown the bifurcation to be subcritical. 29 Krstulovic et al 30 reported the dynamo transition through a supercritical bifurcation for large Pm, whereas for small Pm it was through a subcritical one. They attributed the subcritical dynamo transition to the presence of a hydrodynamic instability which affects the growing magnetic modes.…”

Scaling laws in spherical shell dynamos with free-slip boundaries

“…Sasaki et al (2011), Schrinner et al (2012, and have also observed bistability in their dynamo simulations with free-slip boundaries. Dynamos in box geometry with periodic boundaries also show bistability (Yadav et al, 2012); in fact, even tristable and quadstable solutions were observed in such simulations. Bistable dynamo solutions have rarely been observed in dynamos with rigid boundaries, e.g.…”

Dynamo theories

“…2009; Monchaux et al. 2009; Yadav, Verma & Wahi 2012; Verma & Yadav 2013), and more recently stellar magnetism (Browning 2008; Morin et al. 2011; Gastine et al.…”

“…Subcritical dynamo transitions like this have been discussed for many years in the context of geo-dynamo and planetary dynamo problems (e.g. Roberts & Soward 1978;Roberts 1988;Christensen et al 1999;Kuang, Jiang & Wang 2008;Goudard & Dormy 2008;Simitev & Busse 2009;Morin & Dormy 2009;Sreenivasan & Jones 2011;Dormy, Oruba & Petitdemange 2018, see also Dormy (2011 for an accessible introductory review), but have also drawn attention in the context of laboratory experiments (Fuchs, Rädler & Rheinhardt 2001;Ponty et al 2007;Berhanu et al 2009;Monchaux et al 2009;Yadav, Verma & Wahi 2012;Verma & Yadav 2013), and more recently stellar magnetism (Browning 2008;Morin et al 2011;Gastine et al 2012Gastine et al , 2013.…”