Parametric modulation of dynamo waves

Kitchatinov, L. L.; Nepomnyashchikh, Alexander

doi:10.1134/s1063773715070026

Cited by 5 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This nonresonant parametric amplification can also be of importance for long-term variations of magnetic activity as, for example, found in the solar dynamo models of Ref. [40].…”

Section: Discussionmentioning

confidence: 72%

Parametric instability in periodically perturbed dynamos

2017

View full text Add to dashboard Cite

We examine kinematic dynamo action driven by an axisymmetric large scale flow that is superimposed with an azimuthally propagating non-axisymmetric perturbation with a frequency $\omega$. Although we apply a rather simple large scale velocity field, our simulations exhibit a complex behavior with oscillating and azimuthally drifting eigenmodes as well as stationary regimes. Within these non-oscillating regimes we find parametric resonances characterized by a considerable enhancement of dynamo action and by a locking of the phase of the magnetic field to the pattern of the perturbation. We find an approximate fulfillment of the relationship between the resonant frequency $\omega_{\rm{res}}$ of the disturbed system and the eigenfrequency $\omega_0$ of the undisturbed system given by $\omega_{\rm{res}}=2\omega_0$ which is known from paradigmatic rotating mechanical systems and our prior study [Giesecke et al., Phys. Rev. E, 86, 066303 (2012)]. We find further -- broader -- regimes with weaker enhancement of the growth rates but without phase locking. However, this amplification regime arises only in case of a basic (i.e. unperturbed) state consisting of several different eigenmodes with rather close growth rates. Qualitatively, these observations can be explained in terms of a simple low dimensional model for the magnetic field amplitude that is derived using Floquet theory. The observed phenomena may be of fundamental importance in planetary dynamo models with the base flow being disturbed by periodic external forces like precession or tides and for the realization of dynamo action under laboratory conditions where imposed perturbations with the appropriate frequency might facilitate the occurrence of dynamo action.Comment: 25 pages, 19 Figures, minor corrections to match the published version published in Phys. Rev. Fluids 2, 053701 (2017

show abstract

“…This nonresonant parametric amplification can also be of importance for long-term variations of magnetic activity as, for example, found in the solar dynamo models of Ref. [40].…”

Section: Discussionmentioning

confidence: 72%

Parametric instability in periodically perturbed dynamos

2017

View full text Add to dashboard Cite

show abstract

“…We found that the consideration of a low-amplitude stochastic 'magnetic noise' as an additional poloidal source in the Babcock-Leighton model recovers the solar cycle every time the cycle is kicked into a grand minimum and reasonably mimics the occurrence statistics of the grand minima inferred from the cosmogenic radionuclides. It also exhibits bimodal distribution of toroidal magnetic energy (a proxy of sunspot number) implying the presence of two distinct modes of activity (Kitchatinov & Nepomnyashchikh 2015) and reproduces the phase space collapse, which is a signature of the only directly observed grand minimum, i.e. the Maunder minimum.…”

Section: Discussionmentioning

confidence: 77%

“…In other words, the grand minima cannot be considered as events that correspond to a tail of a single regular mode of solar activity. This bimodal nature in the probability density of smoothed SSN is actually due to the hysteresis present in the model (Kitchatinov & Nepomnyashchikh 2015). It should be noted that the hysteresis is a phenomenon where bistable solutions exist in a certain parameter regime and either of them is realized depending upon the system's initial conditions.…”

Section: 'Magnetic Noise' As a Possible Mechanism For The Recovery Fr...mentioning

confidence: 91%

Origin and Recovery from Grand Solar Minima in a Time Delay Dynamo Model with Magnetic Noise as an Additional Poloidal Source

Tripathi,

Nandy,

Banerjee

2018

Preprint

View full text Add to dashboard Cite

We explore a reduced Babcock-Leighton (BL) dynamo model based on delay differential equations using numerical bifurcation analysis. This model reveals hysteresis, seen in the recent mean-field dynamo model and the direct numerical simulations of turbulent dynamos. The BL model with 'magnetic noise' as an additional weak-source of the poloidal field recovers the solar cycle every time from grand minima, which BL source alone cannot do. The noise-incorporated model exhibits a bimodal distribution of toroidal field energy confirming two modes of solar activity. It also shows intermittency and reproduces phase space collapse, an experimental signature of the Maunder Minimum. The occurrence statistics of grand minima in our model agree reasonably well with the observed statistics in the reconstructed sunspot number. Finally, we demonstrate that the level of magnetic noise controls the duration of grand minima and even has a handle over its waiting period, suggesting a triggering effect of grand minima by the noise and thus shutting down the global dynamo. Therefore, we conclude that the 'magnetic noise' due to small-scale turbulent dynamo action (or other sources) plays a vital role even in Babcock-Leighton dynamo models.

show abstract

“…Thus this dependence of the magnetic field with the dynamo number exhibits a hysteresis behavior. Further, in a simplified model, Kitchatinov & Nepomnyashchikh (2015) demonstrated that transitions 266-2 V. Vashishth et al: Subcritical Dynamo and Hysteresis in a Babcock-Leighton Type Kinematic Dynamo Model between two modes (subcritical dynamo with finite magnetic field and supercritical dynamo) qualitatively reproduce two distinct modes in the distribution of solar activity as inferred from cosmogenic isotope content in natural archives (Usoskin et al 2014). This behavior was further supported by Karak et al (2015) in the turbulent dynamo simulations.…”

Section: Introductionmentioning

confidence: 65%

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

Vashishth

Karak

Kitchatinov

2021

Res. Astron. Astrophys.

View full text Add to dashboard Cite

In the Sun and Sun-like stars, it is believed that cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helicity in the plasma flows in their convection zones (CZs). Hence, it is expected that for each star, there is a critical dynamo number for the operation of a large-scale dynamo. As a star slows down, it is expected that the large-scale dynamo ceases to operate above a critical rotation period. In our study, we explore the possibility of the operation of the dynamo in the subcritical region using the Babcock–Leighton type kinematic dynamo model. In some parameter regimes, we find that the dynamo shows hysteresis behavior, i.e., two dynamo solutions are possible depending on the initial parameters—decaying solution if starting with weak field and strong oscillatory solution (subcritical dynamo) when starting with a strong field. However, under large fluctuations in the dynamo parameter, the subcritical dynamo mode is unstable in some parameter regimes. Therefore, our study supports the possible existence of subcritical dynamo in some stars which was previously demonstrated in a mean-field dynamo model with distributed α and MHD turbulent dynamo simulations.

show abstract

Parametric modulation of dynamo waves

Cited by 5 publications

References 21 publications

Parametric instability in periodically perturbed dynamos

Parametric instability in periodically perturbed dynamos

Origin and Recovery from Grand Solar Minima in a Time Delay Dynamo Model with Magnetic Noise as an Additional Poloidal Source

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

Contact Info

Product

Resources

About