A modelling study of nonlinearity of the cross-shore flow under breaking waves

Abstract A new process-based modelling framework is used to simulate wave-driven flows over a bar in the large-scale SINBAD and LIP11-1C experiments, representing high- and low-wave conditions, respectively. The framework couples an open-source Boussinesq wave model with a one-dimensional vertical (1-DV) column model. Model-data comparisons show good model skill, with discrepancies less than 10 $$\%$$ for waves and hydrodynamics, providing a robust basis for analysing higher-order velocity moments. The corresponding results demonstrate that the cross-shore evolution of the free-stream velocity skewness and asymmetry depends strongly on the breaker type, especially in the surf zone. In both tests, the skewness and asymmetry increase during shoaling. Under a spilling breaker, the intrawave velocity shapes reach peak nonlinearities near the breaking point and then decay gradually through the surf zone. In the plunging breaker, peak nonlinearities occur around the bar crest, decrease sharply at the bar crest, and recover within the splashing and plunging points. Inside the surf zone, the velocity signals evolve toward a strongly skewed-asymmetrical form. A very consistent pattern is found in the vertical direction across all cross-shore regions. The velocity skewness systematically increases towards the bed, while the asymmetry decreases, resulting in a more skewed, less asymmetric near-bed velocity. Boundary-layer filtering, phase shift, and undertow contribute to the velocity transformation inside the wave boundary layer. The bispectral analysis shows that, despite spectral energy decay with depth, strong triad coupling and a coherent biphase pattern persist, and at some locations, intensify within the wave boundary layer, demonstrating breaking influences on the re-organised harmonic interactions rather than making the flows random. These associated findings imply that sediment transport formulations based on free-stream skewness and asymmetry may misrepresent near-bed sediment transport.