Variation in flow characteristics of overtopping waves on dike crests

During severe storms, waves can overtop dikes, leading to erosion of the crest and landward slope, which may ultimately result in breaching. To accurately model this erosion, the overtopping flow needs to be described in a time-dependent manner for each individual wave overtopping event. The peak flow velocity ($u_{peak}$) and peak flow thickness ($h_{peak}$) are critical boundary conditions in this context. Previous studies have shown that these flow characteristics are related to the overtopping volume, yet often propose deterministic models that overlook the variability and interdependency between these characteristics.

The goal of this study is to address these gaps by explicitly quantifying the variation and interdependence of $u_{peak}$ and $h_{peak}$, using data from small-scale FlowDike experiments. We propose generalized distributions to describe the variation in these flow characteristics, with $u_{peak}$ varying by 13% to 23%, depending on the waterside slope angle, and $h_{peak}$ varying by approximately 20%. Furthermore, the interdependency between $u_{peak}$ and $h_{peak}$ is modeled using a Student-t copula ($\nu =9.361$, $\rho =-0.497$), revealing a moderate negative correlation. This suggests that overtopping events with a high $u_{peak}$ are less likely to have a large $h_{peak}$, and vice versa.

The findings of this study can be directly applied to improve models that describe the loading caused by overtopping waves and the resulting erosion. By incorporating the variation and interdependence of $u_{peak}$ and $h_{peak}$, these models can provide a more detailed representation of the peak flow characteristics of overtopping waves. Furthermore, these insights can be applied to the design of wave overtopping simulators, enabling the simulation of more realistic overtopping flows by incorporating more of their natural variation.