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Role of stable modes in zonal flow regulated turbulence
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10.1063/1.4729906
/content/aip/journal/pop/19/6/10.1063/1.4729906
http://aip.metastore.ingenta.com/content/aip/journal/pop/19/6/10.1063/1.4729906

Figures

Image of FIG. 1.
FIG. 1.

The total turbulent energy in the ITG case is significantly reduced compared to the ETG case.

Image of FIG. 2.
FIG. 2.

The rate of change of energy in the ETG case, divided into various components as defined in Eq. (15).

Image of FIG. 3.
FIG. 3.

The net heat flux (drive) , the high k dissipation D, and the dissipation at zonal wavenumbers when the zonal flows are “turned on” at time . The zonal flows are turned on by changing from 1 to 0.

Image of FIG. 4.
FIG. 4.

The rate of change of energy in the ITG case, divided into various components as defined in Eq. (15).

Image of FIG. 5.
FIG. 5.

The rate of change of the unstable mode energy, , divided into the various coupling terms as a function of time. (a) is for ETG case and (b) is for ITG case. The legend is the same for both plots.

Image of FIG. 6.
FIG. 6.

The zonal field couplings of the unstable mode energy in ITG case.

Image of FIG. 7.
FIG. 7.

A cartoon showing the nonlinear energy transfer rates for the unstable mode (a) and the zonal flow (b).

Image of FIG. 8.
FIG. 8.

The rate of change of energy terms for the zonal pressure (a) and zonal flow (b) for ITG case.

Image of FIG. 9.
FIG. 9.

The rate of change of energy of the unstable mode in ITG, explicitly showing calculation of the energy transfer from the unstable to stable mode via zonal flows ().

Image of FIG. 10.
FIG. 10.

The nonlinear transfer function spectrum for modes at different wavenumbers.

Image of FIG. 11.
FIG. 11.

The nonlinear growth rate of the stable modes derived from the different nonlinear couplings of the stable mode which are similar to Eq. (17). The second panel is a continuation of the first panel with the y axis magnified and x axis shrunk.

Image of FIG. 12.
FIG. 12.

The frequency sum using linear frequencies, for k = (−0.08,0.2).

Image of FIG. 13.
FIG. 13.

The frequency sum using the nonlinear frequencies, for k = (−0.08,0.2).

Tables

Generic image for table
Table I.

Frequency sum for k = (−0.08,0.2) and k′ = (0.0,0.2).

Generic image for table
Table II.

Zonal field energy levels.

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/content/aip/journal/pop/19/6/10.1063/1.4729906
2012-06-29
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Role of stable modes in zonal flow regulated turbulence
http://aip.metastore.ingenta.com/content/aip/journal/pop/19/6/10.1063/1.4729906
10.1063/1.4729906
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