  The dynamic renormalization group (RG) is used to study the large-distance
and long-time limits of viscous and resistive incompressible
magnetohydrodynamics subject to random forces and currents. The scale-dependent
viscosity and magnetic resistivity are derived and used for carrying out
RG-improved perturbation theory. This is applied to derive both the asymptotic
scaling and the overall proportionality coefficients for both the velocity and
magnetic field correlation functions as well as the kinetic and magnetic energy
density spectral functions. The Kolmogorov, Iroshnikov-Kraichnan, as well as
other energy spectra, formally can be obtained by suitable choice of injected
noise, although the method limits the validity of these energy spectra only to
the asymptotic regime . Injection of a random magnetic helicity is considered,
its RG-improved spectral density derived, and its contribution to the velocity
and magnetic field correlation functions determined. The RG scaling solutions
are used to determine information at asymptotic scales about energy and
helicity cascade directions and mixing between magnetic and kinetic energy.
Some of the results found here also are shown to be valid for the Navier-Stokes
hydrodynamic equation. The results have applicability to geomagnetism as well
as cosmic magnetic fields at astrophysical and cosmological scales.
