  We present numerical calculations of the parameters $C_{\nu}$, $C_{\epsilon}$
and $C_{\kappa}$ associated with the common closures for turbulence production,
dissipation and diffusion. In the case of homogeneous and isotropic turbulence,
these parameters are expected to be statistically scale-invariant within the
inertial subrange. In order to scrutinise this conjecture, we utilised a
generalisation of the Germano filtering formalism, which is applicable to
compressible flows as well. The filtering of data obtained from
three-dimensional direct numerical simulations of forced isotropic turbulence
with Mach numbers in the range $\sim 0.1...1$ then yielded values of the
closure parameters associated with different length scales. The results
indicate that the closure parameters are nearly universal for subsonic or
moderately transonic flows, although the resolution of $432^{3}$ grid cells in
our simulations is not quite sufficient to clearly establish scale invariance.
In addition, it was found that the customary assumption of a kinetic Prandtl
number of about unity for the gradient-diffusion closure is flawed due to the
misalignment between turbulent flux and the gradient of the turbulence energy.
Nevertheless, sound correlation can be achieved if the flux magnitude rather
than the flux vector is locally matched. This conclusion is particularly useful
for the family of subgrid scale models based on the turbulence energy equation.
Furthermore, the parameter of production $C_{\nu}$ was computed in the fashion
of dynamical procedures. Thereby, superior agreement between modelled and
explicitly evaluated turbulence stresses in comparison to the eddy-viscosity
closure with constant $C_{\nu}$ was verified.
