Numerical simulation of Alfvénic turbulence in the solar wind

Abstract

Low-frequency fluctuations in the solar wind magnetic field and plasma velocity are often highly correlated, so much so that the fluctuations can be thought of as nearly perfect Alfvén waves. Evidence from the Helios and Ulysses spacecraft suggest strongly that these fluctuations emanate from the solar corona with high correlation and flat power spectra (∼f⁻¹). These fluctuations constitute a source of free energy for a turbulent cascade of magnetic and kinetic energy to high wave numbers, a cascade that evolves most rapidly in the vicinity of velocity shears and the heliospheric current sheet. Numerical solutions of both the compressible and incompressible equations of magnetohydrodynamics (MHD) in Cartesian geometry showed that sharp gradients in velocity would decrease substantially the Alfvénicity of initially pure Alfvénic fluctuations; however, the effects of solar wind expansion on this turbulent evolution is, as yet, undetermined. We demonstrate that as was the case in Cartesian geometry, in an expanding volume, velocity shears and pressure-balanced flux tubes still reduce the Alfvénicity of parallel propagating wave packets. These three-dimensional spherically expanding simulations include velocity shears separating fast and slow flows, pressure-balanced flux tubes, and a central current sheet which is the site of magnetic reconnection. Two-dimensional spectra constructed in the r – θ plane resemble closely those resulting from similar initial conditions in Cartesian geometry.