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Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.

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., Environmental Fluid Mechanics

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., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics

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., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics

To be commercially viable, wave energy converters (WECs) will need to be deployed in arrays or “wave farms” to generate significant amounts of energy and to have the costs of these farms minimised. However, when designing a wave farm, there are a number of trade-offs to be made between competing objectives; for example, between the power production potential and installation costs, with the optimal design for one objective not necessarily favourable for the other. In this study, we developed a multi-objective optimisation methodology to allow rigorous evaluation of the trade-offs amongst multiple objectives. We demonstrate the methodology for four objectives: (1) maximising power production, (2) minimising the foundation loads, (3) minimising the number of foundations and (4) minimising the total export cable length required. However, the method is flexible and can be used for optimising a range of other parameters. A case study examining multi-objective optimisation of a wave farm using the developed probability-based evolutionary strategy was conducted for a proposed development site in Albany, Western Australia. The wave farms were composed of 5, 10 and 20 fully submerged cylindrical point-absorber type WECs similar to Carnegie Clean Energy's CETO-6 device. Simulations show that the optimal layouts preferring maximum power formed a single line perpendicular to the predominant wave direction; the optimal layouts preferring minimum cable length and a minimum number of foundations form multiple lines; whereas the optimal layouts preferring minimum foundation loads formed multiple lines in line with the predominant wave direction. By applying a cost model and non-dominated sorting, the methodology allowed us to quantify the trade-offs between power production and cost., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics

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 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 e, Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics

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., Environmental Fluid Mechanics

Author Posting. © American Geophysical Union, 2017. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 3451–3460, doi:10.1002/2016JC012319., The causes of surf zone morphologic changes observed along a sandy beach onshore of a submarine canyon were investigated using field observations and a numerical model (Delft3D/SWAN). Numerically simulated morphologic changes using four different sediment transport formulae reproduce the temporal and spatial patterns of net cross-shore integrated (between 0 and 6.5 m water depths) accretion and erosion observed in a ∼300 m alongshore region, a few hundred meters from the canyon head. The observations and simulations indicate that the accretion or erosion results from converging or diverging alongshore currents driven primarily by breaking waves and alongshore pressure gradients. The location of convergence or divergence depends on the direction of the offshore waves that refract over the canyon, suggesting that bathymetric features on the inner shelf can have first-order effects on short-term nearshore morphologic change., WHOI-USGS postdoctoral scholarship, NSF, ONR, 2017-10-29

Author Posting. © American Geophysical Union, 2015. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 120 (2015): 1887–1903, doi:10.1002/2014JC010555., Alongshore force balances, including the role of nonlinear advection, in the shoaling and surf zones onshore of a submarine canyon are investigated using a numerical modeling system (Delft3D/SWAN). The model is calibrated with waves and alongshore flows recorded over a period of 1.5 months at 26 sites along the 1.0, 2.5, and 5.0 m depth contours spanning about 2 km of coast. Field observation-based estimates of the alongshore pressure and radiation-stress gradients are reproduced well by the model. Model simulations suggest that the alongshore momentum balance is between the sum of the pressure and radiation-stress gradients and the sum of the nonlinear advective terms and bottom stress, with the remaining terms (e.g., wind stress and turbulent mixing) being negligible. The simulations also indicate that unexplained residuals in previous field-based estimates of the momentum balance may be owing to the neglect of the nonlinear advective terms, which are similar in magnitude to the sum of the forcing (pressure and radiations stress gradients) and to the bottom stress., Funding was provided by a joint WHOI-USGS postdoctoral scholarship, NSF, ONR, and ASD(R&E)., 2015-09-23