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Understanding directional spectra of infragravity (IG) waves composed of free and bound components is required due to their impacts on various coastal processes (e.g., coastal inundation and morphological change). However, conventional reconstruction methods of directional spectra relying on linear wave theory are not applicable to IG waves in intermediate water depths (20–30 m) due to the presence of bound waves. Herein, a novel method is proposed to reconstruct directional spectra of IG waves in intermediate depth based on weakly nonlinear wave theory. This method corrects cross‐spectra among observed wave signals by taking account of the nonlinearity of bound waves in order to reconstruct directional spectra of free IG waves. Numerical experiments using synthetic data representing various directional distributions show that the proposed method reconstructs free IG wave directional spectra more accurately than the conventional method. The method is subsequently applied to observations of severe sea‐states at two field sites. At these sites, free IG waves are not isotropic and have clear peak directions. Numerical modeling of the wave fields shows that these peak directions correspond to the reflection of IG waves from the shore and/or coastal structures. Additionally, the validity of the underlying weakly nonlinear wave theory of the present method is assessed by a newly proposed method employing bispectral analysis. The bound wave response generally agrees with the theory at the field sites but deviates slightly for energetic sea states. The applicability of the present method on a sloping bottom is further discussed by an analytical solution. Plain Language Summary: Infragravity (IG) waves, long waves whose wave period is much longer than sea and swells, are known to play important roles in coastal inundation and beach topographic change during high wave conditions. However, the magnitude of IG waves propagating to beaches is not well understood. This is because conventional methods to estimate directional distributions (wave energy propagating to each direction) of sea and swells are not applicable to IG waves that are composed of "free" and "bound" components. In this study, a novel method to estimate directional distributions of IG waves is proposed. The method estimates directional distributions of free IG waves by considering bound IG waves in observed wave data based on their theoretical solution. This method is tested in numerical experiments using synthetic wave data, and the results demonstrate its high applicability and superiority over the conventional method. Applying this method to field measurement data reveals that free IG waves are directionally focused owing to the reflection from the shore and coastal structures. These findings violate the assumption of uniform directional distributions of free IG waves implemented in recent numerical models. The new method will help future studies to elucidate the magnitude of IG waves propagating to beaches. Key Points: A new method to reconstruct directional spectra of free infragravity waves based on weakly nonlinear wave theory is proposedThe method is verified to accurately reconstruct directional spectra of free infragravity waves from synthetic dataDirectional distributions of free infragravity waves vary diversely owing to wave reflection from nearby beaches and coastal structures [ABSTRACT FROM AUTHOR]

Infragravity waves are low-frequency surface waves that can impact a variety of nearshore and oceanic processes. Recent measurements in the North Sea showed that significant bursts of infragravity energy occurred during storm events. Using a spectral wave model, we show that a substantial part of this energy was radiated from distant shorelines where it was generated by the incident sea-swell waves. These radiated infragravity waves can cross the North Sea basin and reach distant shorelines. The origin of the infragravity wave energy varied between the different storms, and particularly depends on where largest sea-swell waves made landfall. Along the coastlines of the North Sea, shoreward directed infragravity waves that originate from a remote source were non-negligible during storm events. This suggests that radiated infragravity waves can potentially contribute to coastal dynamics and hazards away from their region of generation. [ABSTRACT FROM AUTHOR]

Two-dimensional mean wave-driven flow and setup dynamics were investigated at a reef-lagoon system at Ningaloo Reef, Western Australia, using the numerical wave-flow model, SWASH. Phase-resolved numerical simulations of the wave and flow fields, validated with highly detailed field observations (including >10 sensors through the energetic surf zone), were used to quantify the main mechanisms that govern the mean momentum balances and resulting mean current and setup patterns, with particular attention to the role of nonlinear wave shapes. Momentum balances from the phaseresolved model indicated that onshore flows near the reef crest were primarily driven by the wave force (dominated by radiation stress gradients) due to intense breaking, whereas the flow over the reef flat and inside the lagoon and channels was primarily driven by a pressure gradient. Wave setup inside the lagoon was primarily controlled by the wave force and bottom stress. The bottom stress reduced the setup on the reef flat and inside the lagoon. Excluding the bottom stress contribution in the setup balance resulted in an over prediction of the wave-setup inside the lagoon by up to 200--370%. The bottom stress was found to be caused by the combined presence of onshore directed wave-driven currents and (nonlinear) waves. Exclusion of the bottom stress contribution from nonlinear wave shapes led to an over prediction of the setup inside the lagoon by approximately 20--40%. The inclusion of the nonlinear wave shape contribution to the bottom stress term was found to be particularly relevant in reef regions that experience a net onshore mass flux over the reef crest. [ABSTRACT FROM AUTHOR]

Predictions of the wave-induced response of floating structures that are moored in a harbour or coastal waters require an accurate description of the (nonlinear) evolution of waves over variable bottom topography, the interactions of the waves with the structure, and the dynamics of the mooring system. In this paper, we present a new advanced numerical model to simulate the wave-induced response of a floating structure that is moored in an arbitrary nearshore region. The model is based on the non-hydrostatic approach, and implemented in the open-source model SWASH, which provides an efficient numerical framework to simulate the nonlinear wave evolution over variable bottom topographies. The model is extended with a solution to the rigid body equations (governing the motions of the floating structure) that is tightly coupled to the hydrodynamic equations (governing the water motion). The model was validated for two test cases that consider different floating structures of increasing geometrical complexity: a cylindrical geometry that is representative of a wave-energy-converter, and a vessel with a more complex shaped hull. A range of wave conditions were considered, varying from monochromatic to short-crested sea states. Model predictions of the excitation forces, added mass, radiation damping, and the wave-induced response agreed well with benchmark solutions to the potential flow equations. Besides the response to the primary wave (sea-swell) components, the model was also able to capture the second-order difference-frequency forcing and response of the moored vessel. Importantly, the model captured the wave-induced response with a relatively coarse vertical resolution, allowing for applications at the scale of a realistic harbour or coastal region. The proposed model thereby provides a new tool to seamlessly simulate the nonlinear evolution of waves over complex bottom topography and the wave-induced response of a floating structure that is moored in coastal waters. • New numerical tool to predict the wave-induced response of moored floating structures. • Comparison to solutions to the potential flow equations for a variety of sea-states. • The model captures the first and second-order response induced by irregular waves. • Model can predict the motions of a moored structure based on an offshore sea state. [ABSTRACT FROM AUTHOR]

Coastal safety assessments with wave-resolving storm impact models require a proper offshore description for the incoming infragravity (IG) waves. This boundary condition is generally obtained by assuming a local equilibrium between the directionally-spread incident sea-swell wave forcing and the bound IG waves. The contribution of the free incident IG waves is thus ignored. Here, in-situ observations of IG waves with wave periods between 100 s and 200 s at three measurement stations in the North Sea in water depths of O (30) m are analyzed to explore the potential contribution of the free and bound IG waves to the total IG wave height for the period from 2010 to 2018. The bound IG wave height is computed with the equilibrium theory of Hasselmann using the measured frequency-directional sea-swell spectra as input. The largest IG waves are observed in the open sea with a maximum significant IG wave height of O (0.3) m at 32 m water depth during storm Xaver (December 2013) with a concurrent significant sea-swell wave height in excess of 9 m. Along the northern part of the Dutch coast, this maximum has reduced to O (0.2) m at a water depth of 28 m with a significant sea-swell wave height of 7 m and to O (0.1) m at the most southern location at a water depth of 34 m with a significant sea-swell wave height of 5 m. These appreciable IG wave heights in O (30) m water depth represent a lower bound for the expected maximum IG wave heights given the fact that in the present analysis only a fraction of the full IG frequency range is considered. Comparisons with the predicted bound IG waves show that these can contribute substantially to the observed total IG wave height during storm conditions. The ratio between the predicted bound- and observed total IG variance ranges from 10% to 100% depending on the location of the observations and the timing during the storm. The ratio is typically high at the peak of the storm and is lower at both the onset and waning of the storm. There is significant spatial variability in this ratio between the stations. It is shown that differences in the directional spreading can play a significant role in this. Furthermore, the observed variability along the Dutch coast, with a substantially decreased contribution of the bound IG waves in the south compared to the northern part of the Dutch coast, are shown to be partly related to changes in the mean sea-swell wave period. For the southern part of the Dutch coast this corresponds to an increased difference with the typically assumed equilibrium boundary condition although it is not clear how much of the free IG-energy is onshore directed barring more sophisticated observations and/or modeling. [ABSTRACT FROM AUTHOR]