Self-consistent mean-field magnetohydrodynamics

Courvoisier, Alice; Hughes, David W.; Proctor, M. R. E.

doi:10.1098/rspa.2009.0384

Cited by 20 publications

(31 citation statements)

References 22 publications

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“…Similar results restricted to kinematic MHD have also been obtained in Vladimirov (2010) and Herreman and Lesaffre (2011). There remains the challenge of developing a self-consistent theory of the full MHD equations (Moffatt 1978), which may be viewed as a complementary approach to that of Courvoisier et al (2010).…”

Section: Discussionsupporting

confidence: 53%

Vortex Dynamics of Oscillating Flows

2015

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We employ the method of multiple scales (two-timing) to analyse the vortex dynamics of inviscid, incompressible flows that oscillate in time. Consideration of distinguished limits for Euler's equation of hydrodynamics shows the existence of two main asymptotic models for the averaged flows: strong vortex dynamics (SVD) and weak vortex dynamics (WVD). In SVD the averaged vorticity is 'frozen' into the averaged velocity field. By contrast, in WVD the averaged vorticity is 'frozen' into the 'averaged velocity + drift'. The derivation of the WVD recovers the Craik-Leibovich equation in a systematic and quite general manner. We show that the averaged equations and boundary conditions lead to an energy-type integral, with implications for stability.

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Section: Discussionsupporting

confidence: 53%

Vortex Dynamics of Oscillating Flows

2015

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“…In other words, our simulations do not posses a kinematic stage in which the influence of B would be negligible. The applicability of QKTF to such a situation has been questioned by Courvoisier et al (2010). We emphasize, however, that Eq.…”

Section: Calculation Of Turbulent Transport Coefficientsmentioning

confidence: 96%

Alpha effect due to buoyancy instability of a magnetic layer

Chatterjee

Mitra

Rheinhardt

et al. 2011

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Context. A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. Aims. We calculate the α effect due to helical motions caused by an unstable magnetic layer in a rotating density-stratified system with angular velocity Ω making an angle θ with the vertical. We also study the dependence of the α effect on θ and the strength of the initial magnetic field. Methods. We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent electromotive force (EMF) due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. Results. We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting α effect is non-uniform and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" α effect. The α effect is also nonlocal, i.e. scale dependent, requiring around 8-16 Fourier modes to reconstruct the actual mean EMF based on the actual mean field.

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“…Turbulent viscosity is by far not the only contribution to the Reynolds stress tensor. In addition to hydrodynamic contributions such as the Λ effect (Rüdiger 1980(Rüdiger , 1989, which is relevant to explaining stellar differential rotation (Rüdiger & Hollerbach 2004), and the anisotropic kinetic alpha effect (Frisch et al 1987), which provides an important test case in mean-field hydrodynamics (Brandenburg & von Rekowski 2001;Courvoisier et al 2010), there are magnetic contributions as well. One can think of them as a magnetic feedback on the hydrodynamic stress tensor (Rädler 1974;Rüdiger 1974) or, especially when magnetic fluctuations are also considered, as a mean-field contribution to the turbulent Lorentz force.…”

Section: Introductionmentioning

confidence: 99%

Properties of the negative effective magnetic pressure instability

et al. 2012

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As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter β characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter β . The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.

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Self-consistent mean-field magnetohydrodynamics

Cited by 20 publications

References 22 publications

Vortex Dynamics of Oscillating Flows

Vortex Dynamics of Oscillating Flows

Alpha effect due to buoyancy instability of a magnetic layer

Properties of the negative effective magnetic pressure instability

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