Spectral modeling of magnetohydrodynamic turbulent flows

Baerenzung, Julien; Politano, H.; Ponty, Yannick; Pouquet, A.

doi:10.1103/physreve.78.026310

Cited by 32 publications

(47 citation statements)

References 32 publications

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“…It is desirable, then, to alter the model in such a way to prevent the formation of rigid bodies. Truncation of the SFS stress tensor, (4), to the first term results in the Clark-α model [8],…”

Section: The Influence Of Circulation On Rigid Bodiesmentioning

confidence: 99%

“…A DNS of MHD is computed at a resolution of 1024 3 . The initial conditions for v and b are a superposition of ABC modes [16] with random phases and wavenumbers k ∈ [1,4]. No external forcing is applied and the total energy is allowed to freely decay.…”

Section: Lamhd-α As a Sfs Modelmentioning

confidence: 99%

“…Some limited case MHD LES include the cross-helicity model [44] assuming alignment between the fields and the low magnetic Re LES [30,49]. Extensions of spectral models to MHD based on two-point closure formulations of the dynamical equations proposed recently look promising in the analysis of turbulent flows and of the dynamo mechanism [4]. Approximate deconvolution models for MHD [32] are theoretically appealing, but have yet to be tested on non-laminar flows.…”

Section: Mhd: Circulation and Outlook For Lesmentioning

confidence: 99%

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The Effect of Subfilter-Scale Physics on Regularization Models

et al. 2010

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The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations' performance as SFS models. Suppression of spectrally local SFS interactions and conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes α-model (LANS-α) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k +1 as the SFS spectra is resolved. The Clark-α and Leray-α models, truncations of LANS-α, do not conserve small-scale circulation and do not develop rigid bodies. LANS-α, however, is closest to Navier-Stokes in intermittency properties. All three models are found to be stable at high Reynolds number. Differences between L 2 and H 1 norm models are clarified. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangianaveraged MHD (LAMHD-α). LAMHD-α performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. It may prove generally applicable as a MHD-LES.

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Section: The Influence Of Circulation On Rigid Bodiesmentioning

confidence: 99%

Section: Lamhd-α As a Sfs Modelmentioning

confidence: 99%

Section: Mhd: Circulation and Outlook For Lesmentioning

confidence: 99%

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The Effect of Subfilter-Scale Physics on Regularization Models

et al. 2010

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“…Other restricted-case MHD-LES are applicable to low magnetic Reynolds number [21,22,23]. Extensions of spectral models to MHD based on two-point closure formulations of the dynamical equations proposed recently look promising in the analysis of turbulent flows and of the dynamo mechanism [5]. Finally, though technically not an LES, there are also hyper-resistive models for MHD which require rescaling of the length (wavenumber) scales to a known direct numerical simulation (DNS) [18].…”

Section: Introductionmentioning

confidence: 99%

“…One problem with extending the LES methodology for hydrodynamic turbulence to MHD is that most LES are based upon eddy-viscosity concepts [1], which can be related to a known power law of the energy spectrum [4] (although generalizations can be devised, see e.g. [5]), or upon self-similarity. For MHD, the underlying assumption of locality of interactions in Fourier space is not necessarily valid [6,7] (a contradiction of self-similarity) and spectral eddy-viscosity concepts [8] cannot be applied in a straightforward manner as neither kinetic nor magnetic energy is a conserved quantity and the general expression of the energy spectrum is not known at this time [9,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks

2009

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We demonstrate that, for the case of quasi-equipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics α−model (LAMHD) reproduces well both the large-scale and small-scale properties of turbulent flows; in particular, it displays no increased (super-filter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the sub-filter-scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes α−model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of super-filter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally non-local energy transfer (associated to Alfvén waves), it is responsible for the absence of a viscous bottleneck in MHD, as compared to the fluid case.As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (super-filter) bottleneck found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of ≈ 200 when compared to a direct numerical simulation on a large grid of 1536 3 points at the same Reynolds number.

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Bayesian inversion for the filtered flow at the Earth's core‐mantle boundary

2014

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The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field.

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Spectral modeling of magnetohydrodynamic turbulent flows

Cited by 32 publications

References 32 publications

The Effect of Subfilter-Scale Physics on Regularization Models

The Effect of Subfilter-Scale Physics on Regularization Models

Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks

Bayesian inversion for the filtered flow at the Earth's core‐mantle boundary

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