DIRECT NUMERICAL SIMULATIONS OF REFLECTION-DRIVEN, REDUCED MAGNETOHYDRODYNAMIC TURBULENCE FROM THE SUN TO THE ALFVEN CRITICAL POINT

We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfven critical point. These are the first such simulations that take into account the solar-wind outflow velocity and the radial inhomogeneity of the background solar wind without approximating the nonlinear terms in the governing equations. RMHD turbulence is driven by outward-propagating Alfven waves (z(+) fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfven waves (z(-) fluctuations). We present 10 simulations with different values of the correlation time tau(+)(c circle dot) and perpendicular correlation length L-perpendicular to circle dot of outward-propagating Alfven waves at the coronal base. We find that between 15% and 33% of the z(+) energy launched into the corona dissipates between the coronal base and Alfven critical point. Between 33% and 40% of this input energy goes into work on the solar-wind outflow, and between 22% and 36% escapes as z(+) fluctuations through the simulation boundary at r = r(A). The z(+/-) power spectra scale like k(-alpha +/-), where k(perpendicular to) is the wavenumber in the plane perpendicular to B-0. In our simulation with the smallest value of t(c circle dot)(+) (similar to 2 minutes) and largest value of L-perpendicular to circle dot (2 x 10(4) km), we find that alpha(+) decreases approximately linearly with increasing ln(r), reaching a value of 1.3 at r = 11.1 R-circle dot. Our simulations with larger values of t(c circle dot)(+) exhibit alignment between the contours of constant phi(+), phi(-), Omega(+)(0), and Omega(-)(0), where phi(+/-) are the Elsasser potentials and Omega(+/-)(0) are the outer-scale parallel Elsasser vorticities.