Numerical study on vertical structures of undertow inside and outside the surf zone

Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and the gradient of horizontal current velocity. A shear stress boundary condition at the wave trough level derived from the momentum balance equation combined with a no-slip condition at the sea bed were applied to solve the vertical structure of undertow. The turbulent eddy viscosity was assumed to be relevant to the breaking energy dissipation and linearly distributed over depth. The wave characteristics as inputs for the present model were obtained by solving an extended wave energy balance equation incorporating the surface roller effect. Numerical results showed generally good agreements with three series of experimental data for various bathymetries and wave conditions. Comparisons indicated that the formula proposed in this paper for the shear stress at wave trough level could reasonably improve the modeled undertow profiles especially outside the surf zone and a little distance shoreward of the breaking point, and revealed that the model performs well in simulating both vertical and horizontal distributions of undertow and is capable of providing hydrodynamic forcing for the cross-shore sediment transport.