Three-dimensional simulations of the parallel velocity shear instability

Abstract

The nonlinear mode structure and anomalous momentum transport of the electrostatic parallel velocity shear instability in a uniformly magnetized slab were studied using three-dimensional (3-D) nonlinear fluid simulations. Within this simplified model, the system depends upon two dimensionless parameters α=2πqRρs/Lv2, which is a ratio of the sound transit time to the linear growth time of the mode and ρ̂=ρs/LV, which is a ratio of the ion Larmor radius and the radial scale length of the parallel velocity profile. In the limit of ρ̂=0, the mode structure evolved nonlinearly to a state with m=2/α and n=1 for α<1, and m=2 and n=α for α>1 where m is the poloidal mode number and n is the toroidal mode number. The transport had a value of D∼ρscs/2 for all α. For ρ̂≠0 the system displayed a different saturated state, evolving to m=1 and n=α/2 for all α. The transport remained D∼ρscs/2 for all α. The effect of the Larmor radius is this 3-D system is similar to the well known inverse cascade in a two-dimensional incompressible fluid.