(Color online) Primary instabilities generate turbulence from a potential energy reservoir, secondary instabilities lead to the growth of shear or zonal flows at the expense of turbulence kinetic energy, and tertiary instabilities may destabilize the shear or zonal flows. Zig-zag green arrows represent dissipative channels.
(Color online) Primary stability boundary in the plane and plane.
(Color online) Contour plot of in the saturated state. Zonally elongated structure of the electrostatic potential is clearly visible in the modified HW model (a), while isotropic vortices are generated in the HW model (b).
(Color online) Time evolution plots of total kinetic energy, zonal flow kinetic energy, and transport of MHW and HW models.
(Color online) Parameter dependence of the zonal kinetic energy normalized by the total kinetic energy. Transitions from a zonal-flow-dominated state to a turbulence-dominated state occur.
(Color online) Average zonal flow wavenumber versus and .
(Color online) Zonal flow amplitude vs and .
(Color online) Growth rates for flow in the hydrodynamic limit as described in the text.
(Color online) Growth rate in the adiabatic limit (, ). (a) dependence, (b) dependence.
(Color online) Growth rates for the HW case as described in the text.
(Color online) Bifurcation diagram showing the correlation between the linearized stability estimates described in the text and the regimes observed in our turbulence simulations.
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