The theoretical model for group-forced infragravity (IG) waves in shallow water is not well established for nonbreaking conditions. In the present study, analytical solutions of the group-forced IG waves at O(β₁) (β₁ = h_x/(Δkh), h_x = bottom slope, Δk = group wavenumber, h = depth) in intermediate water and at in shallow water are derived separately. In case of off-resonance [β₁μ⁻¹ = O(β₁), where is the resonant departure parameter, c_g = group speed] in intermediate water, additional IG waves in quadrature with the wave group forcing (hereinafter, the nonequilibrium response or component) are induced at O(β₁) relative to the equilibrium bound IG wave solution of Longuet–Higgins and Stewart (1962) in phase with the wave group. The present theory indicates that the nonequilibrium response is mainly attributed to the spatial variation of the equilibrium bound IG wave amplitude instead of group-forcing. In case of near-resonance [β₁μ⁻¹ = O(1)] in shallow water; however, both the equilibrium and nonequilibrium components are at the leading order. Based on the nearly-resonant solution, the shallow water limit of the local shoaling rate of bound IG waves over a plane sloping beach is derived to be ~h⁻¹ for the first time. The theoretical predictions compare favorably with the laboratory experiment by Van Noorloos (2003) and the present numerical model results generated using SWASH. Based on the proposed solution, the group-forced IG waves over a symmetric shoal are investigated. In case of off-resonance, the solution predicts a roughly symmetric reversible spatial evolution of the IG wave amplitude, while in cases of near to full resonance the IG wave is significantly amplified over the shoal with asymmetric irreversible spatial evolution.

The present paper aims to clarify the mechanism of infragravity wave (IGW) energy amplification over nearshore shoals reported in recent studies. Wave transformation and energy transfer between short waves (SWs) and IGWs were investigated using SWASH model for nonbreaking random waves propagating over trapezoid shoals with different bottom slopes. It was found that the time lag of IGWs relative to SW groups is the major mechanism for energy transfer from SWs to IGWs and the amplification of IGW energy over all segments of the shoal. The time lag is generated on the front slope and enlarged on the plateau of the shoal, decreases on the rear slope with higher decreasing rates on milder slopes. Over the rear slope, the evolution of IGWs depends on the relative importance of deshoaling and nonlinear energy transfer. It was found that nonlinear energy transfer dominates over the rear slope gentler than 1/60, causing the IGW energy to increase over the first half of the deshoaling process and decrease over the second half whereas deshoaling dominates for steeper rear slope and the IGW energy decay over the whole slope. It is demonstrated numerically and theoretically that the shoals with gentler bottom slopes amplify the IGW energy more effectively by providing longer distance for nonlinear energy transfer to build up. The persistent nonlinear energy transfer on the plateau indicates the important role of wave spatial evolution history in the subsequent IGWs evolution. Strong free IGWs were detected on leeward of the shoal, possibly due to release of topography‐induced additional bound IGWs.

A new definition of wave groupiness factor is proposed here based on wave-height history of wave trains. This new definition takes into account the dual roles of both zero-downcrossing wave height and wave period in the spatial and temporal evolution of the wave groupiness. It is demonstrated that the new groupiness factor is less sensitive to the operational definition and can describe the groupiness degree of not only linear wave trains but also highly nonlinear ones. The variation of the wave groupiness across a laboratory fringing reef was investigated. Results showed that in the nonlinear shoaling zone, the groupiness became more pronounced. Decreasing of the groupiness was triggered by wave breaking in the vicinity of the breakpoint. The groupiness decreased rapidly shortly after breaking, whereas it increased in the inner surf zone. Infragravity wave modulation of short-wave water depth was the main source of groupiness after breaking.