1303.5052 (Greg Salvesen et al.)

Energetics and dissipation in the magnetised Kelvin-Helmholtz instability: the non-linear regime    [PDF]

Greg Salvesen, Kris Beckwith, Jacob B. Simon, Sean M. O'Neill, Mitchell C. Begelman

We perform a suite of 2D/3D MHD simulations of the Kelvin-Helmholtz instability (KHI) in the subsonic, weak magnetic field limit and study the non-linear development leading to magnetic field growth, saturation, and subsequent turbulent decay. 2D KHI simulations do not converge beyond the linear growth stage, while their 3D counterparts converge across all stages of evolution. Appealing to spectral energy transfer function analysis, we quantify energy transfer on a scale-by-scale basis and identify the physical mechanisms responsible for energy exchange. At late times when the fluid is in a state of MHD turbulence, magnetic tension mediates the dominant mode of energy injection into the magnetic reservoir, whereby turbulent fluid motions twist and stretch the magnetic field lines. This generated magnetic energy turbulently cascades to smaller scales, while being exchanged backwards and forwards with the kinetic energy reservoir, until finally being dissipated. Extending the ideal MHD treatment to include explicit viscous and resistive terms, we demonstrate that physical dissipation terms, as opposed to numerical effects, determine the dissipation scale. For ideal MHD simulations, the dissipation scale shifts to progressively smaller scales as numerical resolution is increased; however, the inclusion of physical dissipation reduces the importance of numerical dissipation and acts to move the dissipation scale to larger spatial scales. This is because physical dissipation acts across all scales, while numerical dissipation operates preferentially on the dissipation scale imposed by the grid resolution; therefore, incorporating explicit dissipation pushes the dissipation scale to larger scales than if the dissipation were entirely numerical. For scales larger than the dissipation scale, we show that the physics of energy transfer in decaying MHD turbulence are robust to numerical effects.

View original: http://arxiv.org/abs/1303.5052