The application of spectral methods in simulating compressible fluid and magnetofluid turbulence

Ghosh, S.; Hossain, Murshed; Matthaeus, W. H.

doi:10.1016/0010-4655(93)90103-j

Cited by 62 publications

(48 citation statements)

References 33 publications

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“…We use a pseudospectral code to solve the set of equations (9) uated using the standard pseudospectral procedure [28]. The runs are freely evolved for 10 time units (the initial eddy turnover time is defined in terms of the initial rms velocity fluctuation and unit length).…”

Section: B Numerical Codesmentioning

confidence: 99%

Energy spectrum, dissipation, and spatial structures in reduced Hall magnetohydrodynamic

2012

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We analyze the effect of the Hall term in the magnetohydrodynamic turbulence under a strong externally supported magnetic field, seeing how this changes the energy cascade, the characteristic scales of the flow and the dynamics of global magnitudes, with particular interest in the dissipation. Hall effect modifies the transfer of energy across scales, slowing down the transfer of energy from the large scales up to the Hall scale (ion skin depth) and carrying faster the energy from the Hall scale to smaller scales. The final outcome is an effective shift of the dissipation scale to larger scales but also a development of smaller scales. Current sheets (fundamental structures for energy dissipation) are affected in two ways by increasing the Hall effect, with a widening but at the same time generating an internal structure within them. In the case where the Hall term is sufficiently intense, the current sheet is fully delocalized. The effect appears to reduce impulsive effects in the flow, making it less intermittent.

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Section: B Numerical Codesmentioning

confidence: 99%

Energy spectrum, dissipation, and spatial structures in reduced Hall magnetohydrodynamic

2012

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“…As described in Sect. 2, we make use of spectral method simulations, with N Fourier modes in each Cartesian direction (Ghosh et al, 1993;Canuto et al, 1988) Figure 18 displays the number of reconnection sites C × as a function of k max /k diss . It is evident that under-resolved runs include many additional X-points that are not found in the well-resolved cases.…”

Section: Warning About the Accuracy Of Simulationsmentioning

confidence: 99%

“…(1)- (2) are solved in a periodic Cartesian geometry (x,y), using a well tested dealiased (2/3 rule) pseudo-spectral code (Ghosh et al, 1993). We employ a standard Laplacian dissipation term with constant dissipation coefficients.…”

Section: Overview On 2-d Mhd Turbulencementioning

confidence: 99%

Magnetic reconnection as an element of turbulence

Servidio

Dmitruk

Greco

et al. 2011

Nonlin. Processes Geophys.

107

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Abstract. In this work, recent advances on the study of reconnection in turbulence are reviewed. Using direct numerical simulations of decaying incompressible two-dimensional magnetohydrodynamics (MHD), it was found that in fully developed turbulence complex processes of reconnection locally occur (Servidio et al., , 2010a. In this complex scenario, reconnection is spontaneous but locally driven by the fields, with the boundary conditions provided by the turbulence. Matching classical turbulence analysis with a generalized Sweet-Parker theory, the statistical features of these multiple-reconnection events have been identified. A discussion on the accuracy of our algorithms is provided, highlighting the necessity of adequate spatial resolution. Applications to the study of solar wind discontinuities are reviewed, comparing simulations to spacecraft observations. New results are shown, studying the time evolution of these local reconnection events. A preliminary study on the comparison between MHD and Hall MHD is reported. Our new approach to the study of reconnection as an element of turbulence has broad applications to space plasmas, shedding a new light on the study of magnetic reconnection in nature.

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“…All the fluctuations are initialized isotropically (no mean fields are assumed) with random phases and amplitudes in Fourier space and evolved further by integration of Eqs. (1) and (4) using a fully de-aliased pseudospectral numerical scheme (Gottlieb et al, 1977). This algorithm conserves energy in terms of the dynamical fluid variables rather than using a separate energy equation written in a conservative form (Ghosh et al, 1993).…”

Section: Nonlinear Three-dimensional Simulationsmentioning

confidence: 99%

“…(1) and (4) using a fully de-aliased pseudospectral numerical scheme (Gottlieb et al, 1977). This algorithm conserves energy in terms of the dynamical fluid variables rather than using a separate energy equation written in a conservative form (Ghosh et al, 1993). The evolution variables are discretized in Fourier space and we use periodic boundary conditions.…”

Section: Nonlinear Three-dimensional Simulationsmentioning

confidence: 99%

Three-dimensional simulations of turbulent spectra in the local interstellar medium

Shaikh

Zank

2007

Nonlin. Processes Geophys.

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Abstract. Three-dimensional time dependent numerical simulations of compressible magnetohydrodynamic fluids describing super-Alfvénic, supersonic and strongly magnetized space and laboratory plasmas show a nonlinear relaxation towards a state of near incompressibility. The latter is characterized essentially by a subsonic turbulent Mach number. This transition is mediated dynamically by disparate spectral energy dissipation rates in compressible magnetosonic and shear Alfvénic modes. Nonlinear cascades lead to super-Alfvénic turbulent motions decaying to a subAlfvénic regime that couples weakly with (magneto)acoustic cascades. Consequently, the supersonic plasma motion is transformed into highly subsonic motion and density fluctuations experience a passive convection. This model provides a self-consistent explaination of the ubiquitous nature of incompressible magnetoplasma fluctuations in the solar wind and the interstellar medium.

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The application of spectral methods in simulating compressible fluid and magnetofluid turbulence

Cited by 62 publications

References 33 publications

Energy spectrum, dissipation, and spatial structures in reduced Hall magnetohydrodynamic

Energy spectrum, dissipation, and spatial structures in reduced Hall magnetohydrodynamic

Magnetic reconnection as an element of turbulence

Three-dimensional simulations of turbulent spectra in the local interstellar medium

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