Numerical prediction of wave particle velocities in the coastal zone

Modelling wave particle kinematics in coastal regions remains challenging due to the complex and highly nonlinear physical processes involved. This study quantifies how sea-state steepness and bed slope affect phase-resolved horizontal velocities in coastal waters and evaluates the ability of existing kinematic theories to predict these velocities. Velocity profiles beneath extreme wave crests are obtained through extensive numerical simulations of long-crested irregular waves. The results reveal that steeper slopes accelerate shoaling, whereas milder slopes experience stronger breaking-induced reductions. These lead to variations of up to 48% in shallow-water velocities across bathymetries. The performance of commonly used wave theories is assessed to provide practical modelling guidance. Regular wave theories (Stokes and Stream Function) yield accurate estimates in intermediate depths but fail in shallow water where nonlinear interactions dominate. In such cases, the implementation of irregular wave theories is found to be increasingly important. In particular, the methods of Molin and Donelan perform very well due to their ability to capture spectral superposition. In intermediate water depths they produce an error of the order of 5%. However, underestimations of up to 40% are evident in shallower water. These findings highlight both the capabilities and the limitations of current kinematic models and underscore the need for improved formulations under breaking conditions. • Crest velocity distributions under uni-directional irregular waves over varying bed slopes. • Quantified the influence of sea-state steepness and bed slope on phase-resolved wave kinematics. • Assessment of regular and irregular wave theories and practical guidance for application.