  Geometrical shock dynamics, also called CCW theory, yields approximate
equations for shock propagation in which only the conditions at the shock
appear explicitly; the post-shock flow is presumed approximately uniform and
enters implicitly via a Riemann invariant. The nonrelativistic theory,
formulated by G. B. Whitham and others, matches many experimental results
surprisingly well. Motivated by astrophysical applications, we adapt the theory
to ultra-relativistic shocks advancing into an ideal fluid whose pressure is
negligible ahead of the shock, but one third of its proper energy density
behind the shock. Exact results are recovered for some self-similar cylindrical
and spherical shocks with power-law pre-shock density profiles. Comparison is
made with numerical solutions of the full hydrodynamic equations. We review
relativistic vorticity and circulation. In an ultrarelativistic ideal fluid,
circulation can be defined so that it changes only at shocks, notwithstanding
entropy gradients in smooth parts of the flow.
