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Nearshore rocky reefs with scales of order 10–100 m are common along the world's coastline and often shape wave‐driven hydrodynamics and shoreline morphology in their lee. The interaction of waves with these reefs generally results in either two or four‐cell mean circulation systems (2CC and 4CC, respectively), with diverging flows behind the reefs and at the shoreline in the 2CC case and flows that diverge in the lee and converge at the shoreline in the 4CC case. By applying a phase‐resolving wave‐flow model to conduct a detailed analysis of mean momentum balances for waves interacting with nearshore reefs, we develop an understanding of the drivers of 2CC and 4CC flow dynamics and how they vary for different reef geometries and wave and water level conditions. The 2CC or 4CC patterns were primarily driven by alongshore pressure gradients toward the exposed (nonreef fronted) or reef‐fronted beach. These alongshore pressure gradients were dependent on the cross‐shore setup dynamics governed by the balance between pressure (i.e., related to the setup) and radiation stress gradients, and mean bottom stresses exerted on the water column. If shoreline wave setup in the lee of the reef was less than the exposed beach, a 4CC pattern developed with convergent flow at the shoreline in the lee of the reef; otherwise, a 2CC emerged with divergent flow at the shoreline. Across the parameter space investigated, reef roughness, distance to the shoreline, and beach slope were the three parameters most likely to change the flow patterns between 2CC and 4CC. Small‐scale nearshore rocky reefs are found worldwide along a variety of sandy and rocky coastlines. Wave breaking over small reefs drives mean alongshore circulation patterns in their lee that may cause shoreline accretion or erosion. In this study, we apply a wave‐flow model to investigate the physical drivers of the mean currents in the lee of small reefs. The alongshore circulation was primarily driven by the differences of the mean water levels between the lee and the adjacent nonreef fronted beaches. Mean water levels increased by wave breaking; however, the onshore‐directed mean flows over the reef created offshore‐directed bottom stresses that reduced the mean water levels in the reef lee. If the shoreline mean water levels in the lee were less than the adjacent beach, alongshore currents that converged from the adjacent beaches toward the reefs were developed. If the shoreline mean water levels in the lee of the reef exceeded the adjacent beach, alongshore currents that diverged from the reef toward the adjacent beach occurred. The improved understanding of the circulation drivers developed in this study enhances our ability to characterize and predict wave‐driven flows in small‐scale nearshore reef systems. Phase‐resolved model simulations were used to understand circulation patterns that occur in the lee of small‐scale reefsTwo‐cell and four‐cell circulation patterns were primarily driven by alongshore pressure gradients, which depend on the setup dynamicsA four‐cell pattern generally developed if the shoreline wave setup in the lee of the reef was less than the adjacent nonreef fronted beach Phase‐resolved model simulations were used to understand circulation patterns that occur in the lee of small‐scale reefs Two‐cell and four‐cell circulation patterns were primarily driven by alongshore pressure gradients, which depend on the setup dynamics A four‐cell pattern generally developed if the shoreline wave setup in the lee of the reef was less than the adjacent nonreef fronted beach

Wave breaking on the steep fore‐reef slopes of shallow fringing reefs can be effective at dissipating incident sea‐swell waves prior to reaching reef shorelines. However, wave setup and free infragravity waves generated during the sea‐swell breaking process are often the largest contributors to wave‐driven water levels (wave runup) at the shoreline. Laboratory flume experiments and a two‐dimensional vertical phase‐resolving nonhydrostatic wave‐flow model, which includes a canopy model to predict drag forces generated by roughness elements, were used to investigate wave‐driven water levels for along‐shore uniform fringing reefs. In contrast to many previous studies, both the laboratory experiment and the numerical model account for the effects of large bottom roughness. The numerical model reproduced the observations of the wave transformation and runup over both smooth and rough reef profiles. The numerical model was then extended to quantify the influence of reef geometry and compared to simulations of plane beaches lacking a reef. For a fixed offshore forcing condition, the fore‐reef slope controlled wave runup on reef‐fronted beaches, whereas the beach slope controlled wave runup on plane beaches. As a result, the coastal protection utility of reefs is dependent on these slopes. For our examples, with a fore‐reef slope of 1/5 and a 500 m prototype reef flat length, a beach slope of ∼1/30 marked the transition between the reef providing runup reduction for steeper beach slopes and enhancing wave runup for milder slopes. Roughness coverage, spacing, dimensions, and drag coefficient were investigated, with results indicating the greatest runup reductions were due to tall roughness elements on the reef flat. Wave breaking and bottom friction are effective at reducing incident sea‐swell waves before they can reach the shoreline of reef‐fronted coastlines. However, globally, mass mortality of coral reef‐building organisms is causing coral reefs to become structurally flatter, a process that may lower wave dissipation. Laboratory flume experiments and a multilayer phase‐resolving wave‐flow model that includes drag forces generated by roughness elements (representing coral reef forms) were used to investigate wave‐driven water levels in the lee of fringing reefs and assess the influence of reef geometry and roughness characteristics. The numerical model was able to reproduce laboratory observations of waves and water levels over both smooth and rough reef profiles. Wave runup, the vertical extent of wave uprush on a beach, was sensitive to the presence and characteristics of roughness. Roughness coverage, spacing, and dimensions were investigated with results indicating the greatest runup reductions were due to tall roughness elements on the reef flat. SWASH reproduced laboratory observations of waves and runup over both smooth and rough fringing reefsFore‐reef slope controls wave runup on reef‐fringed coasts as opposed to beach slope on plane open coast beachesWave runup was sensitive to bottom roughness with tall roughness elements on the reef flat generating the greatest runup reduction SWASH reproduced laboratory observations of waves and runup over both smooth and rough fringing reefs Fore‐reef slope controls wave runup on reef‐fringed coasts as opposed to beach slope on plane open coast beaches Wave runup was sensitive to bottom roughness with tall roughness elements on the reef flat generating the greatest runup reduction

This paper presents a comprehensive numerical study into the infragravity‐wave dynamics at a field site, characterized by a gently sloping barred beach. The nonhydrostatic wave‐flow model SWASH was used to simulate the local wavefield for a range of wave conditions (including mild and storm conditions). The extensive spatial coverage of the model allowed us to analyze the infragravity‐wave dynamics at spatial scales not often covered before. Overall, the model predicted a wavefield that was representative of the natural conditions, supporting the model application to analyze the wave dynamics. The infragravity‐wave field was typically dominated by leaky waves, except near the outer bar where bar‐trapped edge waves were observed. Relative contributions of bar‐trapped waves peaked during mild conditions, when they explained up to 50% of the infragravity variance. Near the outer bar, the infragravity‐wave growth was partly explained by nonlinear energy transfers from short waves. This growth was strongest for mild conditions, and decreased for more energetic conditions when short waves were breaking at the outer bar. Further shoreward, infragravity waves lost most of their energy, due to a combination of nonlinear transfers, bottom friction, and infragravity‐wave breaking. Nonlinear transfers were only effective near the inner bar, whereas near the shoreline (where losses were strongest) the dissipation was caused by the combined effect of bottom friction and breaking. This study demonstrated the model's potential to study wave dynamics at field scales not easily covered by in situ observations. Nearshore infragravity waves are examined using a nonhydrostatic wave modelInfragravity losses are large near the shore, due breaking and bottom frictionBar‐trapped edge waves are generally energetic at the outer bar

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. 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. 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 A new method to reconstruct directional spectra of free infragravity waves based on weakly nonlinear wave theory is proposed The method is verified to accurately reconstruct directional spectra of free infragravity waves from synthetic data Directional distributions of free infragravity waves vary diversely owing to wave reflection from nearby beaches and coastal structures

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. Infragravity waves are long period surface waves that are small in the ocean but much larger in the shallow waters closer to the coast. In coastal regions, they are known to affect coastal safety assessments as they can, for example, impact the overtopping of coastal structures, enhance the erosion of dunes, and trigger the resonance of harbors. Recent observations in the North Sea showed that large infragravity waves occurred during storm events. By analyzing the measurements and using a wave model, we have shown that a substantial part of these waves was not generated locally but originated from distant shorelines. At such a distant shoreline, infragravity waves were generated by the breaking of sea‐swell waves at the beach. After generation, the infragravity waves radiate into the North Sea, and modeling shows that they are able to cross the North Sea basin and reach distant shorelines. This study suggests that these radiated infragravity waves can be non‐negligible along the borders of North Sea during storm events, and may contribute to coastal dynamics and nearshore hazards away from their region of generation. Significant bursts of free infragravity energy in the North Sea can be explained by radiation from distant shorelinesThe origin of the free infragravity waves depends on storm characteristics, and in particular on where large sea‐swell waves made landfallRadiated free infragravity waves may impact coastal environments away from their region of generation Significant bursts of free infragravity energy in the North Sea can be explained by radiation from distant shorelines The origin of the free infragravity waves depends on storm characteristics, and in particular on where large sea‐swell waves made landfall Radiated free infragravity waves may impact coastal environments away from their region of generation

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 phase‐resolved 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. Coral reefs that are located in close proximity to a coastline are typically characterized by a steep slope and reef crest that is connected to the coast or front a shallow lagoon. At the reef crest, waves break and drive onshore‐directed currents and elevate the mean (time‐averaged) water level in the lagoon. In this study, we combined measurements of waves, currents and water levels with simulations from an advanced computer model to understand the physical mechanisms that determine the current patterns and water level variations at a coral reef‐lagoon system in Western Australia. Friction generated by the water moving over the rough reef structures was found to reduce the mean water levels inside the lagoon. This friction was explained by the combined presence of both waves and mean currents. Furthermore, near the reef crest, the waves peak and pitch forward before they break, and this nonlinear wave shape was found to enhance the friction from the bottom. This contribution from nonlinear wave shapes however, is generally not accurately described in larger‐scale computer models and should be included in such computer models to provide more reliable simulations of the water motion in coral reefs. The numerical wave‐flow model, SWASH, reproduced highly detailed field measurements of waves and currents through the surf zone of a reef‐lagoon system (Ningaloo Reef, AU)Wave setup inside the lagoon was reduced by bottom stresses generated by the combined action of waves and currentsExclusion of the bottom stress contribution from nonlinear wave shapes resulted in a 20%–40% over prediction of the setup inside the lagoon The numerical wave‐flow model, SWASH, reproduced highly detailed field measurements of waves and currents through the surf zone of a reef‐lagoon system (Ningaloo Reef, AU) Wave setup inside the lagoon was reduced by bottom stresses generated by the combined action of waves and currents Exclusion of the bottom stress contribution from nonlinear wave shapes resulted in a 20%–40% over prediction of the setup inside the lagoon

The physical roughness (canopies) formed by organisms within aquatic ecosystems (e.g., seagrass, kelp, and mangroves) modifies the local wave‐driven hydrodynamics within coastal and estuarine regions. In wave‐dominated environments, an understanding of the mean wave‐driven flows generated within and above canopies is important, as it governs material transport (e.g., of nutrients, sediment, and biota). However, until recently the effect of submerged canopies on wave‐current interactions and the resulting mean (wave‐averaged) flow dynamics has received relatively little attention. In this study, a combination of wave flume experiments and numerical modeling is used to investigate the wave‐induced mean flow profiles in the presence of a submerged canopy. The measured velocities and vegetation forces were used to derive bulk drag and inertia coefficients, and to validate a nonhydrostatic 2DV wave‐flow model. The numerical model results were used to conduct an in‐depth analysis of the mean horizontal momentum terms responsible for driving the mean (horizontal) flow within and above the submerged canopies. We show that the mean canopy hydrodynamics are driven by vertical gradients in wave and turbulent Reynolds stresses, balanced by the mean canopy drag forces. The wave Reynolds stress gradient is the dominant force driving the in‐canopy mean flow and is directly related to the vorticity that is generated when the wave orbital motions become rotational near the canopy interface. This study provides new insight in the mechanisms responsible for wave‐driven mean flows within submerged canopies and guidance for how these hydrodynamics can be predicted in coastal wave‐circulation models. Aquatic plants that grow in estuaries and coastal oceans (such as seagrass, kelp, and mangroves) have a considerable influence on water flow (currents) and on waves propagating toward the shore. However, mean flows generated by the waves interacting with aquatic vegetation (with time scales much longer than the individual wave periods) have not been comprehensively studied. This study provides a description of how submerged vegetation alters the mean wave‐driven flow structure. A combination of detailed experiments conducted in a wave flume and numerical simulations are used to show that the mean flow just above the vegetation is relatively strong (up to 20% to 50% of the maximum wave velocity above the canopy), while it is considerably weaker inside the vegetation. We identified three forces that govern the mean current profile: the wave Reynolds stress gradient, the turbulent Reynolds stress gradient, and the vegetation drag force. These forces are usually not accurately described in larger‐scale computer simulations of coastal processes. However, reliable simulation of processes in the coastal ocean such as sediment transport and nutrient exchange requires an accurate prediction of mean flows, and thus these forces need to be properly incorporated in computer models when applied to regions with aquatic vegetation. Physical and numerical modeling is used to investigate the wave‐induced mean flow profiles in the presence of submerged vegetationThe multilayered phase‐resolving wave‐ flow model was able to accurately reproduce the depth variation of the wave‐driven mean flow profilesWave‐driven mean flows inside vegetation canopies are driven by vertical gradients in the wave and turbulent Reynolds stresses