Speaker
Description
The nature of the turbulent energy cascade of various simple two-dimensional fluid models of ion temperature gradient driven turbulence is studied in some detail. In order to clarify the mechanisms of injection and dissipation, on top of which a nonlinear cascade picture can be developed, linear terms related to finite Larmor radius corrections, and small and large-scale dissipation terms are considered, and their effects on growth rate and the mixing length are characterized.
First, it is observed that for a minimal two-field model of toroidal ITG, the behavior is qualitatively different with or without the diamagnetic nonlinearity. In its absence, it is observed that the zonal flows always dominate and the system never reaches a high transport state. In contrast, when it is retained, they dominate only near marginality (per Dimits shift), while far from marginality, an inverse cascade with high levels of streamers is observed, requiring large-scale dissipation (hypoviscosity) in order to saturate.
Furthermore, a more complete model with four nonlinearities that conserve potential vorticity is proposed. Unlike the simpler model, this system exhibits a well-behaved heat flux with proper zonal flow dynamics (and destabilization) even in two dimensions. The turbulent cascade of this potential vorticity conserving model is analyzed and compared to the minimal model demonstrating the role of higher order terms in the pressure equation. Finally, the direction of nonlinear transfer due to the different nonlinearities (i.e. the diamagnetic nonlinearity in particular) is investigated by examining their contributions to the spectral energy transfer function and by considering the triadic instability assumption for each of these nonlinearities.