  In this paper we analyze the impact of a circular disc on a free surface
using experiments, potential flow numerical simulations and theory. We focus
our attention both on the study of the generation and possible breakup of the
splash wave created after the impact and on the calculation of the force on the
disc. We have experimentally found that drops are only ejected from the rim
located at the top part of the splash --giving rise to what is known as the
crown splash-- if the impact Weber number exceeds a threshold value
$\Weber_{crit}\simeq 140$. We explain this threshold by defining a local Bond
number $Bo_{tip}$ based on the rim deceleration and its radius of curvature,
with which we show using both numerical simulations and experiments that a
crown splash only occurs when $Bo_{tip}\gtrsim 1$, revealing that the rim
disrupts due to a Rayleigh-Taylor instability. Neglecting the effect of air, we
show that the flow in the region close to the disc edge possesses a
Weber-number-dependent self-similar structure for every Weber number. From this
we demonstrate that $\Bond_{tip}\propto\Weber$, explaining both why the
transition to crown splash can be characterized in terms of the impact Weber
number and why this transition occurs for $We_{crit}\simeq 140$.
  Next, including the effect of air, we have developed a theory which predicts
the time-varying thickness of the very thin air cushion that is entrapped
between the impacting solid and the liquid. Our analysis reveals that gas
critically affect the velocity of propagation of the splash wave as well as the
time-varying force on the disc, $F_D$. The existence of the air layer also
limits the range of times in which the self-similar solution is valid and,
accordingly, the maximum deceleration experienced by the liquid rim, what sets
the length scale of the splash drops ejected when $We>\Weber_{crit}$.
