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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 = hx/(Δkh), hx = bottom slope, Δk = group wavenumber, h = depth) in intermediate water and at O ⁡ (β 1 − 1 ) in shallow water are derived separately. In case of off-resonance [β1μ−1 = O(β1), where μ = 1 − c g 2 / (g h) is the resonant departure parameter, cg = 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 ~ O ⁡ (β 1 − 1 ) 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. [ABSTRACT FROM AUTHOR]

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. Key Points: Wave spatial evolution history has significant effects on the subsequent evolution of infragravity wavesInfragravity wave energy is significantly amplified in the direction of wave propagation by a near shore shoalShort waves continually transfer energy to infragravity waves when propagating across the shoal even in the deshoaling zone [ABSTRACT FROM AUTHOR]

Infragravity waves (IGWs) play a crucial role in nearshore hydrodynamics and are the primary drivers of coastal hazards such as harbor resonance and overtopping over seawalls. Field observations show that during five storm events in Fall 2013, the IGW heights at the landward side were significantly larger than those at the seaward side of an isolated shoal near Cape Canaveral, Florida, USA. The concurrent offshore incident waves were energetic with directions nearly perpendicular to the shoal. The maximum wave height-to-depth ratio was below 0.3, indicating no wave breaking. Here, we propose a semi-analytical model in combination with field observations to investigate the shoal-induced increase in the cross-shoal IGW energy flux. The model was proposed based on the theory of spatial evolution of nonlinear energy transfer from primary waves to IGWs over an idealized trapezoidal topography under nonbreaking conditions, and was calibrated using a numerical dataset of 21 test cases generated by the non-hydrostatic numerical wave model Simulating Waves till SHore (SWASH). The predicted increase in the cross-shoal IGW energy fluxes are in reasonable agreement with field observations, with 78 % data variability explained by the model. Also, the IGW energy flux increase calculated from the observed IGW height increase was found to coincide with the observed IGW energy flux increase in the cross-shoal direction. The results strongly indicate that the observed amplification of IGWs near Cape Canaveral in Fall 2013 is largely attributed to the topography-induced nonlinear energy transfers from sea-swells to IGWs. [ABSTRACT FROM AUTHOR]

Widespread flooding of reef-fringed islands demonstrates the insufficient protection provided by reef topographies and suggests the necessity of artificial structures for hazard prevention and mitigation. As an indicator of the structural protection efficiency, the wave overtopping rate is difficult to estimate in reef environments because hydrodynamics over reefs violate the application conditions of standard overtopping formulas. A combined physical and numerical modeling was performed to investigate wave transformations over reefs of different topographies and overtopping at vertical seawalls on the reefs. Results showed that, in addition to the off-reef wave height and still water level, the off-reef wave period also played significant roles. The intensity of short-wave motions and the level of wave setup near the seawall were positively correlated with the off-reef wave period, and the intensity of infragravity-wave motions depended largely on it. Steeper fore-reef slopes would lead to more intensive wave motions and higher setup on reef flats and, consequently, higher overtopping rates. Furthermore, the overtopping rate exponentially decreased with the distance between the seawall and reef edge, primarily due to the decay of short waves in the surf zone. • A laboratory experiment on random wave transformation and overtopping in reef environments was conducted. • The ability of SWASH model was validated against the experimental data. • Installation of a seawall on a reef flat could significantly modify the wave field. • Influences of hydrodynamic and reef topography on the physical drivers of flooding were studied. [ABSTRACT FROM AUTHOR]