  In the problem of steady free-fall onto a standing shockwave around acentral
mass, the "antesonic" condition limits the regime of stable accretion to
$c_T^2/v_\mathrm{esc}^2\leq3/16$, where $c_T$ is the isothermal sound speed in
the subsonic post-shock flow, and $v_\mathrm{esc}$ is the escape velocity at
the shock radius. Above this limit, it is impossible to satisfy both the Euler
equation and theshock jump conditions, and the system transitions to a wind.
This physics explains the existence of a critical neutrino luminosity in
steady-state models ofaccretion in the context of core-collapse supernovae.
Here, we extend the antesonic condition to flows with rotation and turbulence
using a simple one-dimensional formalism. Both effects decrease the critical
post-shock sound speed required for explosion. While quite rapid rotation is
required for a significant change to the critical condition, we show that the
level of turbulence typically achieved in supernova simulations can greatly
impact the critical value of $c_T^2/v_\mathrm{esc}^2$. A core angular velocity
corresponding to a millisecond rotation period after contraction of the
proto-neutron star results in only a $\sim\!5$ per-cent reduction of the
critical curve. In contrast, near-sonic turbulence with specific turbulent
kinetic energy $K/c_T^2=0.5-1$, leads to a decrease in the critical value of
$c_T^2/v_{\rm esc}^2$ by $\sim\!20-40$ per-cent. This analysis provides a
framework for understanding the role of post-shock turbulence in instigating
explosions in models that would otherwise fail and helps explain why
multi-dimensional simulations explode more easily than their one-dimensional
counterparts.
