Three-dimensional simulations of the parallel velocity shear instability

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 alpha = 2 pi qR rho(s)/L(v)(2), which is a ratio of the sound transit time to the linear growth time of the mode and <(rho)over cap> = rho(s)/L(V), which is a ratio of the ion Larmor radius and the radial scale length of the parallel velocity profile. In the Limit of <(rho)over cap> = 0, the mode structure evolved nonlinearly to a state with m = 2/alpha and n = 1 for alpha < 1, and m = 2 and n = alpha for alpha > 1 where m is the poloidal mode number and n is the toroidal mode number. The transport had a value of D similar to rho(s)c(s)/2 for all alpha. For <(rho)over cap> not equal 0 the system displayed a different saturated state, evolving to m = 1 and n = alpha/2 for all alpha. The transport remained D similar to rho(s)c(s)/2 for all alpha. 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. (C) 1997 American Institute of Physics.