Saturation of Kelvin--Helmholtz fluctuations in a sheared magnetic field

Kelvin--Helmholtz unstable flows are numerically investigated in the context of a sheared E x B flow profile and a sheared magnetic field in the collisional, electrostatic limit. In the extreme form of this limit, density fluctuations are small and the system is described by the nonlinear E x B vorticity dynamics. In order to focus on the role of magnetic shear localization, the computations are confined to two dimensions. For weak magnetic shear the fluctuations become turbulent and saturate by nonlinear cascade to small (dissipative) scales. In a strong magnetic shear regime near the linear stability boundary, nonlinear spatial broadening allows direct access to resistive shear dissipation, leading to saturation at small amplitude with nearly all the fluctuation energy in the longest-wavelength mode. This is in accordance with previous investigation using a statistical closure analysis [Phys. Fluids 29, 231 (1986)]. The amount of broadening is proportional to the linear growth rate. The fluctuation amplitude scaling with magnetic shear is found to agree closely with the theory