A Reduced Magnetohydrodynamic Model of Coronal Heating in Open Magnetic Regions Driven by Reflected Low‐Frequency Alfven Waves

A reduced magnetohydrodynamic (RMHD) description is employed to examine a suggestion made by W. H. Matthaeus and colleagues in 1999 that coronal heating might be sustained by a cascade of low-frequency MHD turbulence. Here RMHD simulations show that the low-frequency cascade to high transverse wavenumbers can be driven by an externally maintained flux of low-frequency propagating Alfvén waves, in combination with reflection caused by an inhomogeneous background medium. The simulations show that the suggestions made previously on the basis of a phenomenology are indeed realizable. In addition, the effect is seen to sensitively depend on the presence of reflection, as the background turbulence level needed to maintain the cascade can be sustained only when reflection is imposed. The steady level of turbulence is insensitive to the initial seed turbulence level (provided it is nonzero). Consequences of this model for realistic models of coronal heating in open field-line regions are discussed.