Wave-induced mean currents and setup over barred and steep sandy beaches

Wind-generated surface waves breaking in the nearshore cause an increase in mean water levels, the wave setup, which can represent a significant fraction of storm surges developing both along open coasts and over sheltered areas such as coastal lagoons and estuaries. A common way to simulate the wave setup is to assume a balance between the barotropic gradient and the divergence of the depth-integrated wave-averaged momentum flux (radiation stress) associated with breaking waves in the surf zone. Field observations collected at several sandy beaches revealed that this depth-integrated approach could largely underestimate the wave setup close to the shoreline. The present study builds on Guerin et al. (2018) and further investigates how representing the depth-varying wave forcing in modelling systems can improve the prediction of wave setup across the surf zone. We use data collected during two major field campaigns at Duck, N.C., combined with simulations with SCHISM, a three-dimensional (3D) phase-averaged modelling system employing the vortex-force formalism to represent the effects of waves on currents. The ability of SCHISM to reproduce the surf zone circulation is first assessed with data collected during October 1994 (Duck94), which serve as a classical benchmark for 3D hydrostatic oceanic circulation models. The wave setup dynamics are then analysed during a storm event that occurred during SandyDuck. Consistent with the results of Guerin et al. (2018), we find that resolving the depth-varying nearshore circulation results in increased and improved wave setup predictions across the surf zone. At the shoreline, depth-integrated approaches based on the vortex-force formalism or the radiation stress concept underestimate the maximal wave setup by 10%-15% and 30% on the 1:14 foreshore slope, respectively. An analysis of the 3D cross-shore momentum balance reveals that the vertical mixing is the second most important contributor (10%-15% across the surf zone) to the simulated wave setup after the wave forces (80%-90%), followed by the vertical advection whose contribution increases with the beach slope (up to 10% at the shoreline). Simulations performed with a phase-resolving numerical model suggest that the largest discrepancies observed at the shoreline in past studies likely originate from swash-related processes, highlighting the difficulties to disentangle wave and swash processes on steep foreshores in the field.

Automated summary

Wind-generated surface waves can cause an increase in mean water levels, known as wave setup. A common way to simulate wave setup is by assuming a balance between the barotropic gradient and the radiation stress associated with breaking waves. However, field observations suggest that this approach underestimates wave setup near the shoreline. This study investigates the effects of depth-varying wave forcing on wave setup prediction, leading to improved accuracy in the surf zone.