  The piece-wise parabolic method (PPM) is applied to simulations of forced
isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state
is dominated by the Fermi pressure of an electron-degenerate fluid. The
dissipation in these simulations is of purely numerical origin. For the
dimensionless mean rate of dissipation, we find values in agreement with known
results from mostly incompressible turbulence simulations. The calculation of a
Smagorinsky length corresponding to the rate of numerical dissipation supports
the notion of the PPM supplying an implicit subgrid scale model. In the
turbulence energy spectra of various flow realisations, we find the so-called
bottleneck phenomenon, i.e., a flattening of the spectrum function near the
wavenumber of maximal dissipation. The shape of the bottleneck peak in the
compensated spectrum functions is comparable to what is found in turbulence
simulations with hyperviscosity. Although the bottleneck effect reduces the
range of nearly inertial length scales considerably, we are able to estimate
the value of the Kolmogorov constant. For steady turbulence with a balance
between energy injection and dissipation, it appears that $C\approx 1.7$.
However, a smaller value is found in the case of transonic turbulence with a
large fraction of compressive components in the driving force. Moreover, we
discuss length scales related to the dissipation, in particular, an effective
numerical length scale $\Delta_{\mathrm{eff}}$, which can be regarded as the
characteristic smoothing length of the implicit filter associated with the PPM.

Astrophysics;Fluid Dynamics