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The third-order law for magnetohydrodynamic turbulence with shear: Numerical investigation
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10.1063/1.3398481
/content/aip/journal/pop/17/5/10.1063/1.3398481
http://aip.metastore.ingenta.com/content/aip/journal/pop/17/5/10.1063/1.3398481

Figures

Image of FIG. 1.
FIG. 1.

Time evolution of the kinetic (dotted red line), magnetic (dashed green line), and total (full blue line) energy for the isotropic MHD simulation (run 1). See Table I for more details on the simulation.

Image of FIG. 2.
FIG. 2.

Time-averaged omnidirectional energy spectrum for the isotropic MHD simulation (full red line). For comparison, the Kolmogorov prediction is also shown (dashed black line).

Image of FIG. 3.
FIG. 3.

The scaling of mixed third-order structure functions for the isotropic MHD simulation (blue dashed and red solid line). The prediction of the inertial range scaling is also reported (dotted black line). See text for more details.

Image of FIG. 4.
FIG. 4.

Slope as a function of the increment for the scaling of the mixed third-order structure functions (red solid and blue dashed lines). The slope of the third-order moment computed with the absolute value is also reported (filled green squares).

Image of FIG. 5.
FIG. 5.

Scaling of mixed third-order structure functions with absolute sign. For comparison, the scaling (black dashed line) is reported as well.

Image of FIG. 6.
FIG. 6.

(a) Shear velocity profile ; (b) shear profile of ; (c) the averaged (in the -direction) dissipation as a function of . Clearly, the buffer regions at and introduce local anisotropy in the energy transfer rate. Regions A and B delimit quasihomogeneous parts of the domain.

Image of FIG. 7.
FIG. 7.

Time evolution of the kinetic (dotted red line), magnetic (dashed green line), and total energy (full blue line) for the shear MHD simulation (run 2).

Image of FIG. 8.
FIG. 8.

Time-averaged omnidirectional energy spectrum for the shear MHD simulation; for comparison, is plotted as a dashed line.

Image of FIG. 9.
FIG. 9.

Color map of the magnetic current for the shear MHD simulation (run 2). The shear produces anisotropy, with the structures stretched along the -direction. Scale (right) indicates values of the current density .

Image of FIG. 10.
FIG. 10.

Modal total energy spectrum, showing the anisotropy that develops due to the presence of velocity shear. The logarithmic color scale (right) indicates the energy spectrum level in each region.

Image of FIG. 11.
FIG. 11.

Scaling of the individual terms in the third-order law: (full red line), (dashed green line), and (dashed-dot blue line). Their sum (long-dashed red line), (dashed-dot-dot black line), and the prediction given by Eqs. (9) and (14) (dotted black line) are also shown.

Image of FIG. 12.
FIG. 12.

Slope of the mixed third-order structure functions as a function of the increment for run 2. See caption of Fig. 11.

Image of FIG. 13.
FIG. 13.

The scaling of the individual third-order terms , , and , their sum , and , using data from region B. See caption of Fig. 11 for more details.

Image of FIG. 14.
FIG. 14.

Slope for the scaling of mixed third-order structure function, and terms contributing to it, using data from region “B.”

Image of FIG. 15.
FIG. 15.

A typical fluctuation velocity component (full red line) as a function of , extracted from the central region of the periodic domain in which there is a nearly constant shear (see Fig. 6), here compared with the total velocity component (dashed green line).

Image of FIG. 16.
FIG. 16.

Total third-order moment , defined in Eq. (21) (full blue line), using data from the whole field (top) and data from region A (bottom). For comparison, the prediction [see Eq. (20)] is plotted (dashed black line).

Tables

Generic image for table
Table I.

Parameters for the isotropic and anisotropic simulations, where are the Kolmogorov scales, and are the Taylor microscales.

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/content/aip/journal/pop/17/5/10.1063/1.3398481
2010-05-12
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The third-order law for magnetohydrodynamic turbulence with shear: Numerical investigation
http://aip.metastore.ingenta.com/content/aip/journal/pop/17/5/10.1063/1.3398481
10.1063/1.3398481
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