Shearing rate of time-dependent E×B flow

Abstract

Theory of E؋B shear suppression of turbulence in toroidal geometry ͓Phys. Plasmas 2, 1648 ͑1995͔͒ is extended to include fast time variations of the E؋B flows often observed in nonlinear simulations of tokamak turbulence. It is shown that the quickly time varying components of the E؋B flows, while they typically contribute significantly to the instantaneous E؋B shearing rate, are less effective than the slowly time varying components in suppressing turbulence. This is because the shear flow pattern changes before eddies get distorted enough. The effective E؋B shearing rate capturing this important physics is analytically derived and estimated from zonal flow statistics of gyrofluid simulation. This provides new insights into understanding recent gyrofluid and gyrokinetic simulations that yield a reduced, but not completely quenched, level of turbulence in the presence of turbulence-driven zonal flows.

Long-distance correlation and zonal flow structures induced by mean E×B shear flows in the biasing H-mode at TEXTOR

“…Applying Ref. 23, we found however that in our case the reduction is negligible. The ZF is smaller than but comparable with dc .…”

Size Scaling of Turbulent Transport in Magnetically Confined Plasmas

“…Zonal flows are then generated through modulational instability [16,17] and saturate the toroidal ITG eigenmodes through random shearing [18]. Finally, the nonlinear coupling of ITG-zonal flows leads to a fully developed turbulence with a steady state transport level that is insensitive to initial conditions.…”

Quasilinear transport modelling at low magnetic shear

“…Indeed, the non-linear k y j max was also recovered by calculating maxðc eff =k 2 y Þ, where c eff is a quenched growth rate taken as c eff ¼ maxð0; c k À 0:3x ExB Þ. x ExB is the effective zonal flow ExB shear rate taken from the GENE non-linear simulations, including the effect of the autocorrelation time on the effective shearing time. 30 0.3 is a tuned coefficient, which provided a best fit to the non-linear flux spectra maxima throughout the set of simulations. k ?…”