Formation of walls of water in ‘fully’ nonlinear simulations

Abstract This paper analyses the spatial evolution of steep directionally spread transient wave groups on deep water and identifies key nonlinear dynamic processes in their formation. Sightings and field measurements of unexpectedly large ‘freak’ waves on the open ocean appear inconsistent with standard statistical distributions, but it has only recently become practical to study them via numerical experiments. The frequency focusing of many wave components, spread in both frequency and direction, provides a sufficient concentration of energy to trigger nonlinear effects. The evolution of these waves, based on a realistic model for the peak of an ocean spectrum, is computed by a ‘fully’ nonlinear pseudospectral scheme. The steepest wave groups form a prominent peak crest, which could be considered to be a ‘wall of water’. The formation of this structure is controlled by the group properties of the wave field and results in rapid changes to the group shape relative to a linear solution. There is a dramatic contraction of the group along the mean wave direction, which appears to be balanced by a dramatic expansion of the group in the transverse direction. These processes appear to be consistent with third-order nonlinear wave–wave interactions.