Parametrizing nonlinearity in orbital velocity at fetch-limited, low-energy beaches

Wave nonlinearity plays an important role in cross-shore beach morphodynamics and is often parameterized in engineering-type morphodynamic models through a nonlinear relationship with the Ursell number. It is not evident that the relationship established in previous studies also holds for sheltered sites with fetch-limited seas as they are more prone to effects of local winds and currents, the waves are generally steeper, and the beaches are typically reflective. This study investigates near-bed orbital velocity nonlinearity from wave records collected at two sheltered beaches in The Netherlands and contrasts them to earlier observations made along the exposed, wave-dominated North Sea coast. Our observations at sheltered beaches show that the Ursell number has comparable skill in predicting wave nonlinearity as it has on previously studied exposed coasts. However, the orbital velocities at sheltered coasts are more asymmetric for the same Ursell number than on exposed coasts. When exposed coast data were examined for moments with comparable high-steepness waves, a similar effect on asymmetry was observed. In addition, following and opposing winds were found to have a clear relationship with total nonlinearity, while they did not affect the phase between skewness and asymmetry at the sheltered beaches. Refitting the free parameters of an Ursell-based predictor improved the bias for the asymmetry parameterization. Whether this has implications for modeling of the magnitude of wave-nonlinearity-driven sediment transport using engineering type models is strongly dependent on the sediment transport formulation used, as these formulations depend on additional calibration coefficients too.