Numerical simulation of Alfvenic turbulence in the solar wind

Low-frequency fluctuations in the solar wind magnetic field and plasma velo city are often highly correlated, so much so that the fluctuations can be t hought of as nearly perfect Alfven waves. Evidence from the Hellos and Ulys ses spacecraft suggest strongly that these fluctuations emanate from the so lar corona with high correlation and flat power spectra (similar to f(-1)) These fluctuations constitute a source of free energy for a turbulent casca de of magnetic and kinetic energy to high wave numbers, a cascade that evol ves most rapidly in the vicinity of velocity shears and the heliospheric cu rrent sheet. Numerical solutions of both the compressible and incompressibl e equations of magnetohydrodynamics (MHD) in Cartesian geometry showed that sharp gradients in velocity would decrease substantially the Alfvenicity o f initially pure Alfvenic fluctuations; however, the effects of solar wind expansion on this turbulent evolution is, as yet, undetermined. We demonstr ate that as was the case in Cartesian geometry, in an expanding volume, vel ocity shears and pressure-balanced flux tubes still reduce the Alfvenicity of parallel propagating wave packets. These three-dimensional spherically e xpanding simulations include velocity shears separating fast and slow flows , pressure-balanced flux tubes, and a central current sheet which is the si te of magnetic reconnection. Two-dimensional spectra constructed in the r - theta plane resemble closely those resulting from similar initial conditio ns in Cartesian geometry.