  We study the formation and dynamics of shock waves initiated by a repulsive
potential in a superfluid unitary Fermi gas by using the order-parameter
equation. In the theoretical framework, the regularization process of shock
waves mediated by the quantum pressure term is purely dispersive. Our results
show good agreement with the experiment of Joseph {\it et al}. [Phys. Rev.
Lett. {\bf 106}, 150401 (2011)]. We reveal that the boxlike-shaped density peak
observed in the experiment consists of many vortex rings due to the transverse
instability of the dispersive shock wave. In addition, we study the transition
from a sound wave to subsonic shock waves by increasing the strength of the
repulsive potential and show a strong qualitative change in the propagation
speed of the wavefronts. In the relatively small strength regime, the speed
decreases below the sound speed with increasing the strength as a scaling
behavior, while in the large regime the speed remains almost unchanged, which
is found to be the same expansion speed of the proliferation of the vortex
rings.
