Fragmentation of Colliding Liquid Rims

Wave splashing is an important pathway through which sea sprays are generated, which are crucial for enhancing the transfer of mass, momentum and energy at the air-sea interface. We investigate the transverse collision of two liquid rims as a possible model for understanding the wave splashing phenomena. Interfacial perturbations with fixed maximum wavenumbers and amplitudes 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. We first show the self-similar evolution of the interfacial and velocity profiles of the expanding lamellae forming between the two rims, and develop scaling laws for the evolution of liquid rims at their border. We then analyse the formation and growth of transverse ligaments on top of the rims, which we find to originate from the initial corrugated geometry of the perturbed rim surface rather than hydrodynamic instabilities acting on the decelerating lamella rims. Novel scaling models are proposed for predicting the decay of the ligament number density due to the ongoing ligament merging cascade. Lastly, we present the size and velocity statistics of the rim collision fragments and discuss their possible connections with the drop statistics of breaking waves.