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.

Engineered and natural submerged coastal structures (e.g., submerged breakwaters and reefs) modify incident wave fields and thus can alter hydrodynamic processes adjacent to coastlines. Although submerged structures are generally assumed to promote beach protection by dissipating waves offshore and creating sheltered conditions in their lee, their interaction with waves can result in mean wave-driven circulation patterns that may either promote shoreline accretion or erosion. Here, we analyse the mean flow patterns and shoreline water levels (wave runup) in the lee of idealised impermeable submerged structures with a phase-resolved nonhydrostatic numerical model. Waves propagating over submerged structures can drive either a 2-cell mean (wave-averaged) circulation, which is characterised by diverging flows behind the structure and at the shoreline, or 4-cell circulation, with converging flows at the shoreline and diverging flows in the immediate lee of the structure. The numerical results show that the mode of circulation can be predicted with a set of relationships depending on the incoming wave heights, the structure crest level, and distance to the shoreline (or structure depth). Qualitative agreement between the mean flow and proxies for the sediment transport using an energetics approach suggest that the mean flow can be a robust proxy for inferring sediment transport patterns. For the cases considered, the submerged structures had a minimal influence on shoreline wave setup and wave runup despite the wave energy dissipation by the structures due to alongshore wave energy fluxes in the lee. Consequently, these results suggest that the coastal protection provided by the range of impermeable submerged structures we modelled is primarily due to their capacity to promote beach accretion.

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.

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.

Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free-long-wave generation, through breakpoint forcing and bound-wave release mechanisms, we highlight the importance of an additional free-long-wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free-long-wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.

Analysis of the mean (wave-averaged) momentum balance is a common approach used to explain the physical forcing driving wave set-up and mean currents in the nearshore zone. Traditionally this approach has been applied to phase-averaged models but has more recently been applied to phase-resolving models using post-processing, whereby model output is used to calculate each of the momentum terms. While phase-resolving models have the advantage of capturing the nonlinear properties of waves propagating in the nearshore (making them advantageous to enhance understanding of nearshore processes), the post-processing calculation of the momentum terms does not guarantee that the momentum balance closes. We show that this is largely due to the difficulty (or impossibility) of being consistent with the numerical approach. If the residual is of a similar magnitude as any of the relevant momentum terms (which is common with post-processing methods as we show), the analysis is largely compromised. Here we present a new method to internally calculate and extract the depth-integrated, mean momentum terms in the phase-resolving non-hydrostatic wave-flow model SWASH in a manner that is consistent with the numerical implementation. Further, we demonstrate the utility of the new method with two existing physical model studies. By being consistent with the numerical framework, the internal method calculates the momentum terms with a much lower residual at computer precision, combined with greatly reduced calculation time and output storage requirements compared to post-processing techniques. The method developed here allows the accurate evaluation of the depth-integrated, mean momentum terms of wave-driven flows while taking advantage of the more complete representation of the wave dynamics offered by phase-resolving models. Furthermore, it provides an opportunity for advances in the understanding of nearshore processes particularly at more complex sites where wave nonlinearity and energy transfers are important.

In this study we assess the capabilities of the mesh-free, Lagrangian particle method (Smooth Particle Hydrodynamics, SPH) method to simulate the detailed hydrodynamic processes generated by both spilling and plunging breaking waves within the surf zone, and present how the approach can be used to predict a broad spectrum of hydrodynamic processes relevant to coastal applications where wave breaking is important. The weakly-compressible SPH code DualSPHysics was applied to simulate wave breaking over two bathymetric profiles (a plane beach and fringing reef) and compared to experimental flume measurements of waves, currents, and mean water levels. We demonstrate how the model can accurately reproduce a broad range of relevant hydrodynamic processes, ranging from the nonlinear evolution of wave shapes across the surfzone, wave setup distributions, mean current profiles and wave runup. We compare the surfzone predictions with results from other classes of wave models, and illustrate some of the advantages of the SPH approach (particularly in resolving the hydrodynamics above the wave trough). Overall, the results reveal how the mesh-free SPH approach can accurately reproduce the detailed wave breaking processes with comparable skill to state-of-the-art mesh-based Computational Fluid Dynamic models, and how it can be used as a valuable tool to develop new physical insight into surf zone processes.

A laboratory experiment was conducted to investigate the dynamics of cross-shore sediment transport across a fringing coral reef. The aim was to quantify how a highly bimodal spectrum of high-frequency (sea-swell) and low-frequency (infragravity and seiching) waves that is typically present on coral reef flats, influences the various sediment transport mechanisms. The experiments were conducted in a 55. m wave flume, using a 1:15 scale fringing reef model that had a 1:5 forereef slope, a 14. m long reef flat, and a 1:12 sloping beach. The initial 7. m of reef flat had a fixed bed, whereas the back 7. m of the reef and the beach had a moveable sandy bed. Four seven-hour irregular wave cases were conducted both with and without bottom roughness elements (schematically representing bottom friction by coral roughness), as well as for both low and high still water levels. We observed that the wave energy on the reef flat was partitioned between two primary frequency bands (high and low), and the proportion of energy within each band varied substantially across the reef flat, with the low-frequency waves becoming increasingly important near the shore. The offshore transport of suspended sediment by the Eulerian mean flow was the dominant transport mechanism near the reef crest, but a wide region of onshore transport prevailed on the reef flat where low-frequency waves were very important to the overall transport. Ripples developed over the movable bed and their properties were consistent with the local high-frequency wave orbital excursion lengths despite substantial low-frequency wave motions also present on the reef flat. This study demonstrated that while a proportion of the sediment was transported by bedload and mean flow, the greatest contributions to cross-shore transport were due to the skewness and asymmetry of the high and low-frequency waves.

Low-frequency (infragravity) wave dynamics on a fringing coral reef were investigated using the numerical model XBeach (Roelvink et al., 2009). First, the skill of the model was evaluated in one- and two-dimensions based on its predictions of short waves (0.04-0.2. Hz), infragravity waves (0.004-0.04. Hz) and water level measurements (tidal and wave setup) obtained during a 2009 field study at Ningaloo Reef in Western Australia. The model calibration was sensitive to friction coefficients for short waves and current/infragravity bed friction, which were assumed independent in this model study. Although the one-dimensional cross-shore model captured the gradients in the dominant hydrodynamic processes at the site, a high current/IG bed friction coefficient was required. This resulted in an overestimation and a phase lag between the observed and predicted wave setup signal. In the two-dimensional model, a lower (more realistic) current/infragravity wave friction coefficient was required to achieve optimum performance due to the presence of significant reef and lagoon mean flows in the model, which led to reduced setup across the reef. The infragravity waves were found to propagate from the surf zone across the reef in a dominantly cross-shore direction towards the shore, but with substantial frictional damping. The infragravity waves were strongly modulated also over the reef by tidal depth variations, primarily due to the variability in frictional dissipation rates when the total water depth over the reef varied. Two mean wave-driven circulation cells were observed in the study area, with cross-shore flow becoming more alongshore-dominated before exiting the system via the two channels in the reef. The results reveal that short waves dominated bottom stresses on the forereef and near the reef crest; however, inside the lagoon, infragravity waves become increasingly dominant, accounting up to 50% of the combined bottom stresses.

Low-frequency (infragravity) wave dynamics on a fringing coral reef were investigated using the numerical model XBeach (Roelvink et al, 2009). First, the skill of the one-dimensional model was evaluated based on its predictions of short waves (0.04-0.2 Hz), infragravity waves (0.004-0.04 Hz) and water level measurements (tidal elevation and wave setup) obtained during a 2009 field study at Ningaloo Reef in Western Australia. The model calibration was sensitive to friction coefficients for short waves and current / infragravity bed friction, which were assumed independent in this model study. The infragravity waves were found to be generated primarily in the surf zone through the breakpoint generation mechanism rather than through offshore forcing. The infragravity waves were also strongly modulated over the reef by tidal depth variations, primarily due to the variability in frictional dissipation rates when the total water depth over the reef varied. The results revealed that short waves dominated bottom stresses on the forereef and near the reef crest; however, inside the lagoon, infragravity waves become increasingly dominant, accounting up to 50% of the combined bottom stresses.