  Properties of the turbulent cascade of kinetic energy are studied using
direct numerical simulations of three-dimensional hydrodynamic decaying
turbulence with a moderate Reynolds number and the initial Mach number $M=1$.
Compressible and incompressible versions of the Karman-Howarth-Monin (KHM) and
low-pass filtering/coarse-graining approaches are compared. In the simulation
the total energy is well conserved; the scale dependent KHM and coarse-grained
energy equations are also well conserved; the two approaches show similar
results, the system does not have an inertial range for the cascade of kinetic
energy, the region where this cascade dominates also have a non-negligible
contribution of the kinetic-energy decay, dissipation, and pressure-dilatation
effects. While the two approaches give semi-quantitatively similar results for
the kinetic energy cascade, dissipation and pressure-dilatation rates, they
differ in the increment separation and filtering scales; these scales are not
simply related. The two approaches may be used to find the inertial range and
to determine the cascade/dissipation rate of the kinetic energy.
