Direct numerical simulations of helical dynamo action: MHD and beyond

Gomez, Daniel Osvaldo; Mininni, Pablo D.

doi:10.5194/npg-11-619-2004

Cited by 14 publications

(10 citation statements)

References 68 publications

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“…The cosine of γ (the angle between µ and Ω) oscillates wildly in time, and the orientation of the dipole shows no preferred direction. The only difference between run D1 and D2 is the change in the forcing scale, and the result seems to indicate a separation of scales between the forcing and the largest scale in the system helps the dynamo, as indicated by the larger ratio E M /E V in run D2, and as also reported before in simulations with periodic boundary conditions [28,31,32]. In all these runs, the largest available scale is fixed and given by the inverse of the smallest |λ| (corresponding to λ ±1,1 ) and determined by the radius of the sphere (R = 1), while the separation between this scale and the forcing scale is controlled by the values of q and l in the forcing function (see Table 1).…”

Section: Dynamossupporting

confidence: 76%

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Mininni¹,

Montgomery²,

Turner³

2007

New J. Phys.

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Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached.

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Section: Dynamossupporting

confidence: 76%

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Mininni¹,

Montgomery²,

Turner³

2007

New J. Phys.

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“…The magnetic energy spectra shown in figure 7 appear to have a positive slope at small wave numbers. This is in contrast with the MHD simulations with order one Prandtl number for which at the saturated state most of the magnetic energy is concentrated close to the forcing scale [30,31]. The positive slope extends to larger wavenumbers as the magnetic Reynolds number is increased.…”

Section: A Archontis Flowcontrasting

confidence: 70%

Nonlinear dynamos at infinite magnetic Prandtl number

Alexakis¹

2011

Phys. Rev. E

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The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow, and the ABC flow forced at two different scales. The investigation covers roughly three orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration was almost force-free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior. Dynamo instability is considered to be the main mechanism for the generation and sustainment of magnetic field throughout the universe [1]. In this scenario an initially small magnetic field is amplified by currents induced solely by the motion of a conducting fluid. This process saturates when the magnetic field becomes strong enough for the Lorentz force to act back on the flow and reduce its ability to further amplify the magnetic energy. The exact effect the Lorentz force has on the flow and which property of the flow is altered to prevent further magnetic field amplification is the subject of many current investigations.One can in principle envision many scenarios for saturation especially in the presence of turbulence. For example, saturation can occur because the magnetic field suppresses the fluid flow thus reducing the magnetic Reynolds number of the flow to its critical value. This behavior is expected close to the dynamo onset for laminar flows. In another scenario, dynamo can saturate by suppressing the chaotic stretching of the magnetic field lines [2,3]; or the dynamo can saturate because the folding of the field lines is modified to be less constructive. Finally, saturation of the dynamo can be due to correlations between the velocity and the magnetic field without suppressing the ability of the flow to amplify an uncorrelated passive vector field thus in principle still be a dynamo flow (see for example [4][5][6]).In principle there is no unique answer to this question and the list above does not exhaust all possibilities. The exact mechanism can be a combination of different processes whose choice can depend on the type of forcing and the examined parameter range. Identifying the mechanisms in simple flows can help in unveiling the dependence of the amplitude of magnetic field saturation on the magnetic Reynolds number R m and the fluid Reynolds number Re. This dependence is important for astro...

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“…It was shown within the framework of the approximations made that magnetic helicity cascades inversely from small scales to large scales. Direct numerical simulations (DNSs; Pouquet & Patterson 1978;Meneguzzi et al 1981;Kida et al 1991;Brandenburg 2001;Maron & Blackman 2002;Gómez & Mininni 2004) have verified the inverse cascade of magnetic helicity including in the highly compressible case (Balsara & Pouquet 1999) and have shown the generation of large-scale magnetic fields from small-scale helical force. A detailed examination of the cascading process was investigated in Brandenburg (2001), in which the rate of transfer of magnetic energy among different scales was measured from DNSs.…”

Section: Introductionmentioning

confidence: 94%

“…Early studies using mean-field theory [11,12] and turbulent closure models [13,14] have shown within the framework of the approximations made that magnetic helicity cascades inversely from small scales to large scales. Direct numerical simulations (DNS) [15,16,17,18,19] have verified the inverse cascade of magnetic helicity and have shown the generation of large scale magnetic fields from small scale helical forcing. A detailed examination of the cascading process was investigated in [18], where the rate of transfer of magnetic energy among different scales was measured from DNS.…”

Section: Introductionmentioning

confidence: 97%

On the Inverse Cascade of Magnetic Helicity

Alexakis

Mininni

Pouquet

2006

ApJ

104

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We study the inverse cascade of magnetic helicity in conducting fluids, as pertinent to the generation and dynamics of magnetic fields as observed, e.g., in the solar corona, by investigating the detailed transfer of helicity between different spherical shells in Fourier space in direct numerical simulations of three-dimensional magnetohydrodynamics (MHD). Two different numerical simulations are used, one in which the system is forced with an electromotive force in the induction equation and one in which the system is forced mechanically with an ABC flow and the magnetic field is solely sustained by a dynamo action. The magnetic helicity cascade at the initial stages of both simulations is observed to be inverse and local (in scale space) at large scales and direct and local at small scales. When saturation is approached, most of the helicity is concentrated at large scales and the cascade is nonlocal. Helicity is transferred directly from the forced scales to the largest scales. At the same time, a smaller in amplitude direct cascade is observed from the largest scale to small scales.

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Direct numerical simulations of helical dynamo action: MHD and beyond

Cited by 14 publications

References 68 publications

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Nonlinear dynamos at infinite magnetic Prandtl number

On the Inverse Cascade of Magnetic Helicity

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