Flower patterns in drop impact on thin liquid films.

We describe experimentally the formation of a pattern for drop impacts on thin liquid films for a large range of impact parameters. Using the shallow-water approximation, we are able to explain the main mechanisms leading to these patterns: it consists in the linear instability of the self-similar axisymmetric radial solution of the equations. Agreement between the experiments and the theory is remarkably good, leading, in particular, to the prediction that the most unstable fold number scales like (We/h∞)2/7.