  We investigate the behavior and consequences of the reverse shock that
terminates the supersonic expansion of the baryonic wind which is driven by
neutrino heating off the surface of (non-magnetized) new-born neutron stars in
supernova cores. To this end we perform long-time hydrodynamic simulations in
spherical symmetry. In agreement with previous relativistic wind studies, we
find that the neutrino-driven outflow accelerates to supersonic velocities and
in case of a compact, about 1.4 solar mass (gravitational mass) neutron star
with a radius of about 10 km, the wind reaches entropies of about 100 k_B per
nucleon. The wind, however, is strongly influenced by the environment of the
supernova core. It is decelerated and shock-heated abruptly by a termination
shock that forms when the supersonic outflow collides with the slower preceding
supernova ejecta. The radial position of this reverse shock varies with time
and depends on the strength of the neutrino wind and the different conditions
in progenitor stars with different masses and structure. Its basic properties
and behavior can be understood by simple analytic considerations. We
demonstrate that the entropy of matter going through the reverse shock can
increase to a multiple of the asymptotic wind value. Seconds after the onset of
the explosion it therefore can exceed 400 k_B per nucleon. The temperature of
the shocked wind has typically dropped to about or less than 10^9 K, and
density and temperature in the shock-decelerated matter continue to decrease
only very slowly. Such conditions might strongly affect the important phases of
supernova nucleosynthesis in a time and progenitor dependent way. (abridged)
