Bifurcations and dynamo action in a Taylor–Green flow

Dubrulle, Bérengère; Blaineau, Pierre; Lopes, O. Mafra; Daviaud, François; Laval, Jean-Philippe; Dolganov, Rostislav

doi:10.1088/1367-2630/9/8/308

Cited by 27 publications

(30 citation statements)

References 37 publications

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“…It is currently believed that the mechanism responsible for this cycle is a magnetic dynamo operating in the convection zone (Parker, 1955;Solanki, 2003). The low dynamics produced by the dynamo action presents features, such as magnetic field reversal, that are also observed in recent laboratory dynamo experiments (Berhanu et al, 2007;Dubrulle et al, 2007). All solar physics areas have explored the solar cycle, ranging from helioseismology (e.g., Chaplin et al, 2007;Houdek et al, 2001;Libbrecht and Woodard, 1990) to irradiance changes, period variations, and neutrino flux (e.g., Usoskin and Mursula, 2003;Solanki and Krivova, 2005;Walther, 1999;Rogers and Richards, 2006;Schatten, 2003).…”

Section: Introductionsupporting

confidence: 70%

Phase Space Analysis: The Equilibrium of the Solar Magnetic Cycle

Passos¹,

Lopes

2008

Sol Phys

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We present the results of a statistical study of the solar cycle based on the analysis of the superficial toroidal magnetic field component phase space. The magnetic field component used to create the embedded phase space was constructed from monthly sunspot number observations since 1750. The phase space was split into 32 sections (or time instants) and the average values of the orbits on this phase space were calculated (giving the most probable cycle). In this phase space it is shown that the magnetic field on the Sun's surface evolves through a set of orbits that go around a mean orbit (i.e., the most probable magnetic cycle that we interpret as the equilibrium solution). It follows that the most probable cycle is well represented by a van der Pol oscillator limit curve (equilibrium solution), as can be derived from mean-field dynamo theory. This analysis also retrieves the empirical Gnevyshev -Ohl's rule between the first and second parts of the solar magnetic cycle. The sunspot number evolution corresponding to the most probable cycle (in phase space) is presented.

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Section: Introductionsupporting

confidence: 70%

Phase Space Analysis: The Equilibrium of the Solar Magnetic Cycle

Passos¹,

Lopes

2008

Sol Phys

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“…Priest (1984) showed that some of the dynamics of the solar dynamo can be explained in terms of dynamical systems analysis. Features, like magnetic field reversal, have also been recently observed in laboratory dynamo experiments ( Berhanu et al 2007;Dubrulle et al 2007) which indicate that, within certain approximations, some of these dynamics can be explained by low-order dynamo models (Mininni et al 2001;Pontieri et al 2003;WilmotSmith 2005).…”

Section: Introductionmentioning

confidence: 75%

A Low‐Order Solar Dynamo Model: Inferred Meridional Circulation Variations Since 1750

Passos¹,

Lopes²

2008

Astrophysical Journal

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In this work we present the possible variations that the meridional circulation of the Sun might have undergone during the last 250 years. In order to do this, we reduce an -dynamo to a low-order system that focuses on the time evolution of one of the solar magnetic field components. Afterward we used a method based on the analysis of phase space of the superficial toroidal magnetic field to infer changes in the superficial meridional circulation. We used sunspot numbers to build a time series that approximately represents the magnetic field behavior. After reconstructing the time series' phase space we assume equilibrium solutions for each solar cycle and we fit them to our model. The resulting fit parameters are shown to depend on background quantities of the theoretical model, such as magnetic diffusivity, differential rotation, meridional circulation, etc. The methodology presented here allows one to extract information about the meridional circulation average behavior, and possibly other parameters, from more that 250 years of sunspot number observations.

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“…To investigate the more realistic case of finite diffusivity, one may resort to numerical simulations. This has been done by Laval et al (2006) and Dubrulle et al (2007) for the case of the Taylor-Green flow, without inclusion of the non-linear term in the induction equation. Two kinds of noise were tested: shortly correlated noise, like in the analytical case, and Markovian noise, with finite correlation time τ c that can be varied from 0 to several eddy-turnover time.…”

Section: B Dubrullementioning

confidence: 99%

“…(1.1) for Taylor-Green forcing have been made in Ponty et al (2005), Laval et al (2006), Ponty et al (2007) and Dubrulle et al (2007). The dynamo threshold Rm c has been computed for different values of Re.…”

Section: Taylor-green Numerical Simulationsmentioning

confidence: 99%

“…One sees that the dynamo threshold increases with Re until a value of the order Re ∼ 100 where it seems to saturate. Dubrulle et al (2007) also performed computations at low Re but larger and larger Rm to try and detect a possible signature of the second laminar window of instability. At Re = 6, they detected a transition from an intermittent dynamo at Rm = 25, to a dynamo with a mean field at Rm = 100 (see Fig.…”

Section: Taylor-green Numerical Simulationsmentioning

confidence: 99%

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