  We present direct numerical simulations of the splashing process between two
cylindrical liquid rims. This belongs to a class of impact and collision
problems with a wide range of applications in science and engineering, and
motivated here by splashing of breaking ocean waves. Interfacial perturbations
with a truncated white noise frequency profile are introduced to the rims
before their collision, whose subsequent morphological development is simulated
by solving the two-phase incompressible Navier-Stokes equation with the
adaptive mesh refinement (AMR) technique, within the Basilisk software
environment. We first derive analytical solutions predicting the unsteady
interfacial and velocity profiles of the expanding sheet forming between the
two rims, and develop scaling laws for the evolution of the lamella rim under
capillary deceleration. We then analyse the formation and growth of transverse
ligaments ejected from the lamella rims, which we find to originate from the
initial corrugated geometry of the perturbed rim surface. Novel scaling models
are proposed for predicting the decay of the ligament number density due to the
ongoing ligament merging phenomenon, and found to agree well with the numerical
results presented here. The role of the mechanism in breaking waves is
discussed further and necessary next steps in the problem are identified.
