Analytic derivation of the inertial range of compressible turbulence
  An analytic model for steady state turbulence is employed to obtain the
inertial range power spectrum of compressible turbulence. We assume that for
homogeneous turbulence, the timescales controlling the energy injected at a
given wavenumber from all smaller wave-numbers, are equal for each spatial
component. However, the longitudinal component energy is diverted into
compression, so the rate controlling the energy that is transferred to all
larger wave-numbers by the turbulent viscosity is reduced. The resulting
inertial range is a power law with index -2. Indeed such power spectra were
observed in various astrophysical settings and also in numerical simulations.
