Preliminary Numerical Investigation on Spatial Distribution of Triad Resonant Interaction for Steady Free-Surface Flow over Rippled Bottoms

Fan, J.; Tao, A.F., and Zheng, J.H., 2024. Preliminary numerical investigation on spatial distribution of triad resonant interaction for steady free-surface flow over rippled bottoms. In: Phillips, M.R.; Al-Naemi, S., and Duarte, C.M. (eds.), Coastlines under Global Change: Proceedings from the International Coastal Symposium (ICS) 2024 (Doha, Qatar). Journal of Coastal Research, Special Issue No. 113, pp. 675-679. Charlotte (North Carolina), ISSN 0749-0208. Due to the existence of submarine sandbars in estuarial and coastal areas, the hydrodynamics for flow over rippled bottoms have drawn increasing attention with the potential resonant interaction induced. For the triad resonant interaction induced by steady free-surface flow over rippled bottoms, the spatial distribution of the resonant wave amplitude could reflect the spatial wave energy transmission behaviors above the finite undulating patches. This paper adapts the numerical model based on the high-order spectral method (HOS) to simulate the spatial distribution behaviors of the triad resonant wave components. For the representative cases for the triad resonance corresponding to upstream-propagating waves, the numerical results reveal the nonlinear spatial exponential growth pattern of the resonant wave amplitudes, which compares well with the theoretical singular perturbation solutions by multiple-scale expansion.