A self-consistent theory of nonlinear zonal flows amidst complex background of ion temperature gradient (ITG) turbulence is presented. Starting with a reactive fluid model, a set of coupled nonlinear equations has been obtained in the form of Zakharov-like equations using the reductive perturbation method. These equations represent dynamical evolution of nonlinearly excited zonal flows and potential fluctuations of ITG turbulence. The derived equations have the potential to provide a qualitative explanation of the evolution of zonal flows and drift wave turbulence and their mutual interaction, which have been observed in recent gyrokinetic simulations [A. Dimits et al., Phys. Plasmas 7, 969 (2000)]. The nonlinear coupling coefficients are studied and show that the excitation of zonal flows is due to a resonance in the energy nonlinearity. The resonance turns out to be sensitive to fluid closure.
Direct numerical simulations of pressure-driven flow between two infinite horizontal plates with a stabilizing temperature difference imposed on the plates are presented, for different Grashof numbers. A thermocline-like solution is obtained. The thermocline decorrelates velocity fluctuations which results in a high mean flow velocity. Temperature fluctuations decorrelate from the vertical velocity fluctuations and it is found that although ͗TЈ 2 ͘ and ͗Ј 2 ͘ increase with Grashof number, ͗ЈTЈ͘ decreases. It is argued from the simulations that this behavior is due to internal gravity waves. It is also found that the demands on the size of the computational box increase with Grashof number.
It is pointed out that close to the edge of tokamak plasmas
the fluid equations can support one high frequency mode and one low
frequency mode associated with drift motions. The high frequency
mode is stable in H mode while the low frequency mode can remain at
short wavelengths. We study different regimes of the low frequency
mode including different ratios of density and temperature
lengthscales. The low frequency mode can drive a particle pinch on
the H mode barrier.
A nonlinear instability due to zonal flows and magnetic islands has been found. The instability has the character of a dissipative drift instability due to an anomalous resistivity. The anomalous resistivity is typically two orders of magnitude larger than the classical at the edge.
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