Scale selection and feedback loops for patterns in drift wave-zonal flow turbulence

Abstract

The scale selection and feedback loops for the formation and sustainment of a mesoscopic staircase profile structure are investigated for drift wave-zonal flow turbulence. A mean field model derived from the Hasegawa-Wakatani system and including the evolution of mean density, mean vorticity and perturbed potential enstrophy (PE), is used. It is found that a quasi-periodic zonal staircase forms from self-sharpening of modulation. The principle feedback loop is through the nonlinear dependence of mixing length on electron density gradient, which enters by way of the potential vorticity (PV) gradient. Counterintuitively, ⃑ × ⃑ shearing is not effective. Moreover, the number of steps in the staircase is sensitive to both the drive (production rate of PE and initial density gradient) and damping (flow viscosity and collisional diffusivity) factors. The minimal step scale is selected by competition a Author to whom any correspondence should be addressed.

Non-local transport nature revealed by the research in transient phenomena of toroidal plasma

“…Finite turbulence spreading is necessary to smooth the staircase structure's curvature at the corners of the jump and step. However, the enhancement of turbulence spreading tends to wash out the pattern (Guo et al 2019). Mesoscale transport events, such as avalanches or turbulence pulses (i.e., spreading), drive inhomogeneous mixing and transport of potential vorticity.…”

Wave trapping and E × B staircases

“…In this regard, it is interesting to establish a connection with previous staircase models. It was found that feedback via density gradient plays a more important role than E × B shearing in models based on an Hasegawa-Wakatani model combined with a bistable mixing length [38,39,35]. Temperature relaxation plays also a central role in the model [20] since it is responsible for the onset of zonal flows, production of small scale eddies and subsequent avalanches via a transient realignment of the eddies.…”

“…Several open issues subsist in the understanding of staircase pattern formation and sustainment, which were identified and summarised in [35]. One pending issue is the pattern selection processes that determine the intensity and width of the shear layers, and their spatial period.…”

“…The formation of shear layer is merely a consequence of temperature corrugations. An alternative model has been proposed in [38,39,35]. In this line of research, a set of reduced 1D PDEs has been developed that describes the dynamics of drift waves coupled to zonal flows.…”

Zonal profile corrugations and staircase formation: Role of the transport crossphase

“…Patterns are ubiquitous in non-equilibrium systems [5]. The most common radial pattern first observed in gyrokinetic simulations of ion-temperature gradient driven (ITG) turbulence has been dubbed 'E × B staircase' [6,7,8], due to its quasi-periodic nature, for which the leading explanation is that zonal flows are responsible for the pattern, and that the density and temperature profile corrugations and hence transport modulation are a consequence of the zonal flow pattern directly suppressing the turbulence intensity [9,10]. Similar patterns were observed in the KSTAR tokamak and reproduced by global δf gyrokinetic simulations of collisionless trapped-electron modes (CTEM) [11,12].…”