  Drop impact experiments allow the modelling of a wide variety of natural
processes, from raindrop impacts to planetary impact craters. In particular,
interpreting the consequences of planetary impacts requires an accurate
description of the flow associated with the cratering process. In our
experiments, we release a liquid drop above a deep liquid pool to investigate
simultaneously the dynamics of the cavity and the velocity field produced
around the air-liquid interface. Using particle image velocimetry, we analyse
quantitatively the velocity field using a shifted Legendre polynomial
decomposition. We show that the velocity field is more complex than considered
in previous models, in relation to the non-hemispherical shape of the crater.
In particular, the velocity field is dominated by degrees 0 and 1, with
contributions from degree 2, and is independent of the Froude and the Weber
numbers when these numbers are large enough. We then derive a semi-analytical
model based on the Legendre polynomial expansion of an unsteady Bernoulli
equation coupled with a kinematic boundary condition at the crater boundary.
This model explains the experimental observations and can predict the time
evolution of both the velocity field and the shape of the crater, including the
initiation of the central jet.
