Transverse instabilities of uprising planar jets formed by wave impacts on vertical walls

When a steep breaking wave hits a vertical sea wall, in shallow water, a rapidly ascending planar jet forms. This jet is ejected with high acceleration due to pressure created by the violent wave impact on the wall, creating a so-called ‘flip-through’ event. Previous studies have focussed on the impulsive pressures on, and within, the wall and on the velocity of the jet. Here, in contrast, we consider the formation and break-up of the jet itself. Experiments show that during flip-through a fluid sheet, bounded by a rim, forms. This sheet has unstable transitional behaviours and organising jets; undulations in the thickness of the fluid sheet are rapidly amplified and ruptured into an array of vertical ligaments. Lateral undulations of the rim lead to the formation of finger-jets, which subsequently break up to form droplets and spray.

We present, a linear stability analysis of the rim sheet systems that highlights the contributions of rim retraction and sheet stretching to the breakup process. The mechanisms for the sequential surface deformations in the rim-sheet system are also described. Multiple, distinct, instability modes are identified during the rim deceleration, sheet stretch attenuation and rim retraction processes. The wave numbers (and deformation length scales) associated with these instability modes are shown to lead to the characteristic double peak spectrum of surface displacement observed in the experiments. These mechanisms help to explain the columnar structures often seen in photographs of violent wave impacts on harbour walls.