We investigate the properties of turbulent adiabatic shock waves resulting
from the self-consistent inclusion of finite Alfven-wave pressure in the sh
ock balance equations. We demonstrate (i) the absence of a switch-on shock;
(ii) the existence of two separated domains where the Mach number is great
er than unity that have gas compression, and an associated domain where the
gas compression ratio is less than unity (i.e. a rarefaction domain); (iii
) the difference between the scattering-centre compression ratio and the ga
s compression ratio for all upstream wave cross-helicity values except for
the isolated case of zero helicity; (iv) the presence of anomalous domains
where the cosmic-ray particle spectral index can be negative. All of these
results are brought about by including the upstream and downstream turbulen
t wave energies in the shock balance structure. Without the waves, none of
the effects persists.