Assessing Empirical Components in Wave Breaking and Rollers Through Model Comparison of Radiation Stress and Vortex Force

As incoming waves approach shallow water, they break and result in nearshore currents. The assessment of the wave-induced nearshore currents often relies on the application of radiation stress (RS) and vortex force (VF) in circulation models, both of which incorporate empirical components to describe wave breaking and wave rollers. In this study, we compared a recent 3D RS formulation and a VF formulation by assessing the modeled cross-shore velocities against the measured counterparts from the LIP11D and Duck'94 experiments. The comparison results indicate that the RS model performs better in LIP11D, whereas the VF model exhibits better with respect to Duck'94. Using momentum balance analysis, we found that the cross-shore velocities were dominated by the breaking term (representing the RS terms and non-conservative breaking term in the RS and VF models, respectively) and the roller term. The breaking term generates undertow currents across the entire surf zone. The roller term cooperates with the breaking term in the inner surf zone, but counteracts the breaking term and tends to trigger unrealistic offshore currents at the water surface in the outer surf zone. Further analysis reveals that the RS and VF formulations can simulate almost identical velocity results by adjusting the vertical distribution of the breaking and roller terms. Overall, this study indicates that both the RS and VF formulations are effective in evaluating wave effects on the cross-shore currents, and empirical components in the breaking and roller terms are important for modeling cross-shore velocities. When waves come close to the shore, they break and generate currents. The assessment of these currents in circulation models often relies on two methods named radiation stress (RS) and vortex force (VF), both of which include empirical components to describe wave breaking and wave rollers. We compared the two methods using data from two experiments and found that the RS performed better in one experiment, while the VF showed better results in the other. The results indicated that the breaking and roller terms in the two methods play significant roles, and the relative strength and directional variation of the two terms control the direction of current velocity. We indicate that both the RS and VF methods are effective in evaluating wave effects on the cross-shore currents, and empirical components in the breaking and roller terms are important for modeling cross-shore velocities. A recent radiation stress formulation based on Lagrangian wave solutions is compared with the vortex force formulationBreaking and roller terms dominate the cross-shore velocity and result in main differences between the two formulationsRoller term leads to unrealistic offshore currents in outer surf zone in the radiation stress model due to the relatively weak breaking term