Wave Energy Transfer in Shallow Water: Numerical Investigation of Slope and Offshore Wave Condition Effects

Abstract

This study advances the understanding of nonlinear wave interactions in shallow water by numerically quantifying how foreshore slope and offshore conditions influence energy transfer and wave evolution over a broad range of conditions. Two non-hydrostatic models, SWASH and XBeach, are validated against physical experiments and applied across a wide range of conditions. The two-layer SWASH model accurately reproduces wave parameters, third-order statistics, and nonlinear energy transfer. Results show that the relative water depth $\left(kh\right)$, the offshore wave steepness $\left(s_{m-1,0,\mathrm{deep}}\right)$ and the Iribarren number $\left(\xi \right)$ are key parameters for describing the interaction strength and biphase behavior. The slope mainly affects high-frequency biphase behavior, whereas for the other nonlinear interactions it primarily alters the magnitude of the energy transfer. For $\xi$ smaller than 0.2, low-frequency energy is redistributed toward higher frequencies within the surf zone, while low-frequencies at steeper slopes only receive energy. In shallow water , energy transfer to higher and lower frequencies is not dominated solely by primary wave interactions. Triads involving two high-frequency components $\left(f>1.5f_p\right)$ and one low-frequency component play a major role, alongside interactions of one low-frequency component with two primary components. Consequently, milder slopes increase low-frequency wave height contributions up to 60%, whereas steeper slopes result in 20%–40% for the studied conditions. High-frequency contributions remain relatively stable across profiles and offshore conditions, accounting for approximately 60%–70% of total wave height in shallow water.