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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]

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]

Fast and accurate estimation of wave runup is needed for coral-reef islands, but most of the existing formulae are not applicable in this context. Tree-based models were applied to the comprehensive numerical database of Pearson et al. (J. Geophys. Res. Oceans. 122, 10099–10117) to identify the essential predictor parameters for runup in coral-reef environments and classify different runup regimes on which a set of runup formulae was developed. It was found that, wave conditions, reef roughness, and reef-flat length are generally crucial for predicting runup, while the importance of forereef and beach slopes depends on the relative reef submergence (reef submergence normalized by off-reef wave height). The forereef slope is more important than the beach slope when waves mainly break over the forereef at low relative reef submergences but less important when waves mainly break over the reef flat and the beach at middle and high relative reef submergences. The proposed formula set was validated against data from laboratory and field coral reefs, which implies that the formula set has the potential for fast prediction of runup along coral-reef islands at broad scales for flooding assessment. • Four regimes of wave runup over reef-lined beaches are identified. • An explicit runup formula set corresponding to the four regimes is derived. • The formula set is validated against data of laboratory and field coral reefs. • Beach slope is more important than forereef slope at high water levels. [ABSTRACT FROM AUTHOR]