  The energy spectrum of tearing mode turbulence in a sheared background
magnetic field is studied in this work. We consider the scenario where the
nonlinear interaction of overlapping large-scale modes stirs up a broad
spectrum of small-scale modes, generating tearing mode turbulence. The spectrum
of such turbulence is of interest since it is relevant to the small-scale
back-reaction to the large-scale field. The turbulence we discuss here differs
from traditional MHD turbulence mainly in two aspects, one being the existence
of many linearly stable small-scale modes which cause an effective damping
during energy cascade; the other being the scale independent anisotropy induced
by the large scale modes tilting the sheared background field, as opposed to
the scale dependent anisotropy frequently encountered in traditional weak
turbulence or critically balanced turbulence theory. These two differences
result in the deviation of energy spectrum from a simple power law behavior,
taking the form of a power law multiplied by an exponential falloff. Numerical
simulation is carried out using viscous resistive MHD equations to verify our
theoretical prediction, and reasonable agreement is found between numerical
result and our model.
