Numerical prediction of wave particle velocities in the coastal zone
File(s)
Published version
Author(s)
Al Khalili, Umniya
Christou, Marios
Karmpadakis, Ioannis
Type
Journal Article
Abstract
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.
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.
Date Issued
2026-05-01
Date Acceptance
2026-03-20
Citation
Applied Ocean Research, 2026, 170
ISSN
0141-1187
Publisher
Elsevier
Journal / Book Title
Applied Ocean Research
Volume
170
Copyright Statement
© 2026 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).
License URL
Identifier
10.1016/j.apor.2026.105039
Publication Status
Published
Article Number
105039
Date Publish Online
2026-03-24