Modeling Near-Shore Waves, Surface Rollers, and Undertow Velocity Profiles

TLDR

Near‑shore waves can be periodic or narrow‑banded random, and beaches may be plane or barred. The study develops a theoretical model to predict near‑shore hydrodynamics in the surf zone along long straight beaches. The model combines a wave model, a surface roller model, and a near‑shore mean current model based on energy‑balance equations and two‑layer 2DH momentum equations with a turbulent eddy viscosity closure, producing analytical vertical shear current profiles. The model’s undertow velocity predictions agree well with independent experimental data.

Abstract

This paper presents a theoretical model for the prediction of near-shore hydrodynamics in the surf zone along long straight beaches. The waves may be periodic or narrow-banded random waves, and the beach profile may be plane or barred. The theoretical model consists of three components: wave model, surface roller model, and near-shore mean current model. Both wave and surface roller models are based on simple energy balance equations and all the variables applied for the current model are determined in terms of wave energies. The near-shore mean current model consists of two-layer 2DH momentum equations, integrated above the wave trough level and over the entire depth, which determine mean shear stresses at the trough level and on the bottom, respectively. Coupled with a simple turbulent eddy viscosity model, analytical solutions are obtained for the vertical mean shear current profiles. The bottom boundary condition is specified by a wave–current bottom boundary layer model requiring knowledge of the equivalent bottom roughness. Model predictions of undertow velocity profiles compare favorably with experimental observations which were not used in the model's development.