Wave Height Reduction Research Articles

Near-reef and nearshore tropical cyclone wave climate in the Great Barrier Reef with and without reef structure

The Great Barrier Reef (GBR) coral coverage is in rapid decline from severe and sustained pressures from lagoon water quality, crown-of-thorns starfish (COTS), coral bleaching, tropical cyclones, pollution and diseases. The two recent GBR coral bleaching events (2016–2017) lead to Great Barrier Reef Marine Park Authority (GBRMPA) shifting their focus from passive management to active intervention (Great Barrier Reef Blueprint for resilience by GBRMPA). These active interventions, potentially able to increase GBR resilience, as there are reefs that, due to their physical location relative to all other reefs, river and estuary entrances, ocean currents, have favourable coral growth conditions. To undertake such interventions, various information is required including tropical cyclone wave climates. This paper develops tropical cyclone wave climates for the entire GBR. These wave climates were developed by simulating several thousand synthetic cyclones derived from the “HadGEM” general circulation model with RCP8.5 climate change scenario. The synthetic cyclones adopted herein include the following climate changes assessed by comparing averages of key forcing parameters between 1950 to 1999 and 2050 to 2099. Their average arrival rate increases from 2.25 to 2.41 cyclones/year and their average maximum wind speed increases from 24 to 28 m/s. Their average radius to maximum winds remains constant at 51 km. Two key challenges were resolved, namely, long runtimes and large files (600 m grid increment covering 1800 km by 280 km). Runtimes were reduced by excluding cyclones where their wind speeds over the entire event never exceeded 10 m/s within GBR itself or within 100 km of the GBR over water. Maximum wave heights were compared with an extended fetch empirical expression, which was based on satellite data of tropical cyclones in open waters, when cyclones were outside the GBR lagoon. These comparisons indicate that predicted wave heights have a lower bias using default wave generation parameters when compared with the extended fetch empirical expression. Prediction uncertainty was estimated at no more than 10% from various cyclonic wind-field models. The existing GBR reefs reduce nearshore wave or runup height by between 1.5 and 2 times compared to the no reef case. The reduction in wave or runup height was found to be minimal for 1 m sea level rise. These two findings indicate that there is more flooding potential from coral removal than SLR within the GBR lagoon.

Physical Model of Natural Coastal Protection System: Wave Transmission Over Mangrove Seedling Trees

Yuanita, N.; Kurniawan, A.; Setiawan, H.; Hasan, F., and Khasanah, M., 2019. Physical model of natural coastal protection system: Wave transmission over mangrove seedling trees. In: Lee, J.L.; Yoon, J.-S.; Cho, W.C.; Muin, M., and Lee, J. (eds.), The 3rd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 91, pp. 176-180. Coconut Creek (Florida), ISSN 0749-0208.Erosion is one of main problem in coastal area. In order to solve erosion problem, currently natural coastal protection using vegetation such as mangrove is preferable in many places in the world. However, there are challenges in development of this natural coastal protection, e.g. mangrove-seedling-trees have been damaged by the waves or current, before they are growth strongly which required at least 2 years of plantation. To solve this problem, a natural coastal protection system consists of combination of main natural protection and temporary manmade structures is proposed. The study aimed to quantify the wave height reduction with various mangrove densities as well as the influence of mangrove seedling trees arrangements on wave reduction. The laboratory experiments were conducted in a narrow wave flume using model of mangrove as main natural protection and geotextile-geobag models as temporary manmade structure. Various wave conditions were generated during this laboratory test. This paper focus on the experiment results of wave transmission over mangrove seedling trees in order to determine the most effective configuration of mangrove trees plantation against wave. The results showed that the wave height reduction in area with mangroves was about two times larger compared to that in bare land. The wave reduction difference between tandem and staggered arrangements of trees was less than 20 %. It is also found that the temporary structure is significantly reduce wave height and protect mangrove seeds grow from waves attack.

WHTO: A methodology of calculating the energy extraction of wave energy convertors based on wave height reduction

Wave energy has significant worldwide exploitable resource and its exploitation has attracted renewable energy investigator’ attention. Great progress on calculating device performance has been made by means of theoretical, numerical and model tests. This paper presents a method of calculating the energy extraction of a wave energy converter (WEC) based on Wave Height Take-off (WHTO). The method provides a means to improve the capture efficiency of designs, including demonstrating how well different kinds of WEC are optimized for certain wave conditions. Numerical simulations of a heaving buoy and a bottom-hinged pendulum in a 2D wave flume with different damping types (linear and nonlinear) are presented. The results show that the difference between the calculated energy extraction from the wave height reduction and from the model power take-off (PTO) was not significant in a 2D flume. Physical model tests were conducted using a simplified PTO consisting of a system of lifting weights, used to measure the energy extraction directly. Based on both numerical and physical model analyses, the article defines WHTO, which is equivalent to energy extracted by PTO, but determined without taking direct measurements. This paper aims to promote and validate the concept of the WHTO.

Flow–Vegetation Interaction in a Living Shoreline Restoration and Potential Effect to Mangrove Recruitment

Hydrodynamic differences among shorelines with no vegetation, reference vegetation (mature mangrove), and vegetation planted on restored shoreline (marsh grass and young mangrove) were compared based on field observations 6.5 years after living shoreline restoration. Mean current velocities and waves were more strongly attenuated in vegetation (from channel to shoreline: 80–98% velocity decrease and 35–36% wave height reduction) than in bare shoreline (36–72% velocity decrease, 7% wave height reduction, ANOVA: p < 0.001). Normalized turbulent kinetic energy dissipation rates were significantly higher in reference vegetation (0.16 ± 0.03 m−1) than in restored (0.08 ± 0.02 m−1) or bare shoreline (0.02 ± 0.01 m−1, p < 0.001). Significant differences in the current attenuation and turbulence dissipation rates for the reference and planted vegetation are attributed to the observed differences in vegetation array and morphology. Although the hydrodynamic analyses did not suggest limitations to recruitment, mangrove seedlings were not observed in restored vegetation, while four recruited seedlings/m were counted in the reference vegetation. The lack of recruitment in the restored shoreline may suggest a lag in morphological habitat suitability (slope, sediment texture, organic matter content) after restoration. Although hydrodynamics suggest that the restored site should be functionally similar to a reference condition, thresholds in habitat suitability may emerge over longer timescales.

IMPLEMENTATION AND TESTING OF A POWER MATRIX-BASED WAVE ENERGY CONVERSION MODEL AND THE EFFECT SIMULATED ON THE WAVE FIELD — CASE STUDY OF LAGUNA, SC, BRAZIL

Electrical energy has become an essential resource for mankind and, as the population and technological dependency grow, also does the electricity demand. This necessity boosted numerous studies which focus on clean and renewable energy sources. Ocean wave energy is one of the most environmentally friendly sources of energy since it does not emit pollutants to the atmosphere and does not produce harmful waste. Another positive point about ocean waves is that they are inexhaustible, therefore a power plant could, potentially, provide energy indefinitely. Hence the object of this study is to estimate the wave energy reduction caused by the presence of wave energy conversion (WEC) devices near the coastline of Laguna, Brazil. In order to study the coastal impact of a WEC farm, the third generation sea state model TOMAWAC was used to simulate the waves on the Southern Brazilian Shelf under two different conditions, with and without the presence of an array of WECs. The results show that the mean significant wave height in the blockaded area undergoes a slight drop, caused by the presence of the WECs, which do not appear in the other scenario. But this reduction of the significant wave height is negligible compared to the order of magnitude of the wave height itself.

Wake Effect Assessment in Long- and Short-Crested Seas of Heaving-Point Absorber and Oscillating Wave Surge WEC Arrays

In the recent years, the potential impact of wave energy converter (WEC) arrays on the surrounding wave field has been studied using both phase-averaging and phase-resolving wave propagation models. Obtaining understanding of this impact is important because it may affect other users in the sea or on the coastline. However, in these models a parametrization of the WEC power absorption is often adopted. This may lead to an overestimation or underestimation of the overall WEC array power absorption, and thus to an unrealistic estimation of the potential WEC array impact. WEC array power absorption is a result of energy extraction from the incoming waves, and thus wave height decrease is generally observed downwave at large distances (the so-called “wake” or “far-field” effects). Moreover, the power absorption depends on the mutual interactions between the WECs of an array (the so-called “near field” effects). To deal with the limitations posed by wave propagation models, coupled models of recent years, which are nesting wave-structure interaction solvers into wave propagation models, have been used. Wave-structure interaction solvers can generally provide detailed hydrodynamic information around the WECs and a more realistic representation of wave power absorption. Coupled models have shown a lower WEC array impact in terms of wake effects compared to wave propagation models. However, all studies to date in which coupled models are employed have been performed using idealized long-crested waves. Ocean waves propagate with a certain directional spreading that affects the redistribution of wave energy in the lee of WEC arrays, and thus gaining insight wake effect for irregular short-crested sea states is crucial. In our research, a new methodology is introduced for the assessment of WEC array wake effects for realistic sea states. A coupled model is developed between the wave-structure interaction solver NEMOH and the wave propagation model MILDwave. A parametric study is performed showing a comparison between WEC array wake effects for regular, long-crested irregular, and short-crested irregular waves. For this investigation, a nine heaving-point absorber array is used for which the wave height reduction is found to be up to 8% lower at 1.0 km downwave the WEC array when changing from long-crested to short-crested irregular waves. Also, an oscillating wave surge WEC array is simulated and the overestimation of the wake effects in this case is up to 5%. These differences in wake effects between different wave types indicates the need to consider short-crested irregular waves to avoid overestimating the WEC array potential impacts. The MILDwave-NEMOH coupled model has proven to be a reliable numerical tool, with an efficient computational effort for simulating the wake effects of two different WEC arrays under the action of a range of different sea states.

Linking management planning for coastal wetlands to potential future wave attenuation under a range of relative sea-level rise scenarios.

Understanding changes in wave attenuation by emergent vegetation as wetlands degrade or accrete over time is crucial for incorporation of wetlands into holistic coastal risk management. Linked SLAMM and XBeach models were used to investigate potential future changes in wave attenuation over a 50-year period in a degrading, subtropical wetland and a prograding, temperate wetland. These contrasting systems also have differing management contexts and were contrasted to demonstrate how the linked models can provide management-relevant insights. Morphological development of wetlands for different scenarios of sea-level rise and accretion was simulated with SLAMM and then coupled with different vegetation characteristics to predict the influence on future wave attenuation using XBeach. The geomorphological context, subsidence, and accretion resulted in large predicted reductions in the extent of vegetated land (e.g., wetland) and changes in wave height reduction potential across the wetland. These were exacerbated by increases in sea-level from +0.217 m to +0.386 m over a 50-year period, especially at the lowest accretion rates in the degrading wetland. Mangrove vegetation increased wave attenuation within the degrading, subtropical, saline wetland, while grazing reduced wave attenuation in the temperate, prograding wetland. Coastal management decisions and actions, related to coastal vegetation type and structure, have the potential to change future wave attenuation at a spatial scale relevant to coastal protection planning. Therefore, a coastal management approach that includes disaster risk reduction, biodiversity, and climate change, can be informed by coastal modeling tools, such as those demonstrated here for two contrasting case studies.

Wave energy converter geometry for coastal flooding mitigation

Wave farms, i.e., arrays of wave energy converters (WECs), have been proposed to fulfil the dual function of carbon-free energy generation and coastal protection. The objective of this work is to investigate, for the first time, how the coastal protection performance against flooding is affected by WEC geometry. This is done by means of a case study with WaveCat WECs (floating, overtopping WECs) deployed off the Playa Granada beach (Spain). To this end, two models of WaveCat WECs with different geometries are tested in a laboratory tank at a 1:30 scale under low-, mid- and high-energy sea states representative of the wave conditions of Playa Granada. The geometries differed in the angle between the twin hulls (wedge angle) of WaveCat: 30° and 60°. The reflection and transmission coefficients thus obtained are used in a coupled numerical modelling approach, combining wave and coastal processes models (SWAN and XBeach-G, respectively). We find that WECs with an angle of 60° provide more (less) protection for long (short) wave periods in terms of reductions in wave height and run-up on the beach. As for the flooded dry beach areas, they are generally smaller for WECs with 60°, with only some exceptions under mild conditions. Thus, considering that beach inundation usually occurs under high-energy, storm conditions, we conclude that the wave farm composed by WECs with a wedge angle of 60° is more efficient against coastal flooding.

Experimental Study on the Effectiveness of Emerged and Submerged Coastal Bio-Shield in Storm Surge Protection

Surges and waves induced by cyclones and other severe storms can cause devastating damage of property and loss of life in coastal areas of Bangladesh. Bio-shield in wetlands can reduce the energy of storm surges and cyclones. To study the effectiveness of emerged and submerged coastal bio-shield in storm surge protection, a laboratory experiment was carried out in a 22 m long, 0.75 m wide and 0.75 m deep wave flume in the Hydraulics and River Engineering Laboratory of Bangladesh University of Engineering and Technology (BUET). Experiments were carried out for investigating the performance of the bio-shields in submerged as well as emerged conditions. Bio-shields were represented by cylindrical bamboo sticks as rigid bio-shield and polyethylene as flexible bio-shield whose diameter was 6 mm. There were a total of 51 experimental runs covering 3 different wave periods of 1.6, 1.8 and 2.0 seconds. Time-series of water surface elevations for vegetated (with bio-shield) and non-vegetated (without bio-shield condition) were compared to identify the influence of bio-shield on wave height reduction. It is found for emerged and submerged conditions of bio-shield that the maximum wave height reductions are 71% and 52% at a location which is 3.5 m away from the embankment for wave periods of 2.0 sec at bio-shield spacing of 50 mm c/c and 25 mm c/c respectively. These reductions of wave heights occur when bio-shield of 2 m width (1 m Rigid + 1 m Flexible) are placed at 4 m distance from the embankment. Hence, the most effective position for maximum wave height reduction by both emerged and submerged bio-shield of 2 m width is 4 m distance from the embankment. It is anticipated that these results will find broad application in coastal management and planning for areas with existing coastal bio-shield as well for bio-shield restoration and establishment efforts.

The effects of wave non-linearity on wave attenuation by vegetation

Wave attenuation through mangrove forests has received more and more attention, especially in the context of increasing coastal erosion and sea-level-rise. Numerous studies have focused on studying the reduction of wave height in a mangrove forest. However, the understanding of this attenuation process is still in its infancy. In order to obtain more insight, a laboratory experiment, mimicking the processes of wave attenuation by coastal mangroves in the Mekong Delta, Vietnam was conducted. The reduction of wave height for different scenarios of mangrove densities and wave conditions was investigated. A new method to quantify vegetation attenuation induced by vegetation is presented. The wave height reduction is presented over a relative length scale (viz. the number of wavelengths), instead of an absolute length scale of the forest (e.g per meter or per 100 m). The effects of wave non-linearity on the wave height attenuation over the mangrove forest were investigated using the Ursell number. It is suggested that the non-linear character of waves has a strong influence on the attenuation of the waves inside the mangrove forest. A numerical model, mimicking the experiment was constructed in SWASH and validated using the experimental data. Finally, the data set was extended through numerical modelling so that a larger ranging relationship between wave attenuation per wave length and the Ursell number could be formulated.

Wave pattern simulation around the breakwater configuration in Bantan coast, Bengkalis

Bantan Coast in Bengkalis Island that suffered worst abrasion due to wave attack. Protection of abrasion area against the wave can be done by proper lay-out of breakwater with certain configuration. To get the optimal configuration of breakwater, wave pattern around the breakwater were analyzed quantitatively. It was conducted to obtain the optimum condition of wave height reduction produced. Evaluation of breakwater lay-out effect to wave pattern can be done by numerical model approached. Wave pattern simulation that occurred due to the breakwater was done by Surface water Modelling System (SMS) - CGWAVE software module. This module is a 2-D depth average numerical model using finite element model. To get accurate simulation, a deviation of the numerical result and the measurement result at several locations was used as the indicator parameter in the calibration process. The results showed that from the result of calibration process was used 1.3 meters wave height and 5.4 seconds wave period. Three breakwaters 20 meters slit configuration produced a maximum value of wave height reduction and wave velocity reduction (in comparison wave simulation without breakwater). This configuration produces 60% height reduction and 14% velocity reduction.

The effect of arrays of wave energy converters on the nearshore wave climate

The exploitation of wave energy using arrays of wave energy converters (WEC), which contain a large number of devices, could have significant impact on the wave climate in the nearshore region. This research investigates the impact of WEC arrays at the Westwave demonstration commercial site, which is located on the West coast of Ireland. The methodology involves the determination of an appropriate transmission coefficient (Ct) from a computational fluid dynamic (CFD) model of a numerical wave tank (NWT) simulation using ANSYS CFX and the subsequent implementation of WEC arrays using SWAN (Version 41.01). Within this analysis, the Ct value from the CFD NWT model was used in SWAN to represent WEC arrays which are treated as obstacles. Hence, a nested local wave model at the Westwave site have been developed and validated for the period of December 2015 in order to accommodate the simulation of WEC arrays. Three array configurations, which contain 12 WECs (single row, two row arrays and three row arrays), have been simulated and analysed to estimate the impact to the wave conditions at the nearshore area, while also considering the effect of array configuration on power captured. The results of the analysis suggest there is minor impact on the nearshore wave climate for all the scenarios, where the reduction in wave height and wave power was below 1% at a distance of between 1 and 3 km from the shoreline (at water depths varying from 20 to 60 m). At a distance of 100–300 m from the shoreline (at a water depth of approximately 10 m and below), a decrease in wave height and wave power of 0.1% and 0.2%, respectively, was observed. In addition, the methodology can also be applied to other types of WEC and study areas depending on the purpose of the project.

In situ observations and simulations of coastal wave field transformation by wave energy converters

Wave energy is a potential emerging contributor to future global low-emission energy needs. If wave energy is to become a significant part of renewable energy portfolios, then wave energy converters (WECs) will need to be installed in large numbers in array configurations. The environmental effects of wave energy extraction to date has relied on physical (i.e., tank) and numerical modelling studies.In this study, a network of in situ wave measurement devices were deployed around an array of three submerged point absorber WECs, operating intermittently, each with a nominal 240 kW peak capacity. The study site was 3 km offshore (in approximately 24 m water depth) and the field campaign was conducted over approximately one year, with a primary goal of studying ‘down-wave’ effects of the WECs. The observations were used to calibrate and validate a numerical spectral wave model which can represent frequency-dependent absorption by WECs within the model. For the purpose of a straightforward analysis, we focus on a period when only one WEC was operating. Measurements show a decrease in wave height between locations up-wave and down-wave of the WEC, for the period with only one operating WEC. The numerical model demonstrates that the observed wave height attenuation is due to WEC absorption and exceeds the natural variability of wave height at the site. Impacts on the wave field are particularly strong directly down-wave (40 m) of the WEC with reduction of the wind-sea wave height up to 20%.

Experiments on Surface Waves Interacting with Flexible Aquatic Vegetation

Surface wave interaction with aquatic vegetation appears to play a key role in coastal hydro-morpho-dynamics. As an example, the presence of a dense meadow at intermediate water depth is usually associated with a stable and resilient shore. Wave-meadow interactions are investigated here by means of physical modelling, with a focus on wave height distribution and hydrodynamics. The central part of a wave flume is covered by flexible artificial seagrass, composed of polyethylene leaves. This vegetation is tested in both near emergent and submerged conditions. The wave height reduction is evaluated by means of a drag coefficient defined from linear wave theory, which contains all the unknowns of the adopted methodology. The behaviour of such a coefficient is investigated as a function of a wave related Reynolds number. The influence of the flexibility of the leaves is also considered, together with a wave frequency parameter. The results show a complex behaviour with three different trends for near rigid, intermediate or highly flexible leaves. Amplitudes of the orbital velocities are investigated and show a fairly good match with the linear wave theory. On the contrary, the mean velocity along the water column appears to be modified by the seagrass for submerged leaves.

Co-located wave-wind farms for improved O&M efficiency

Co-located wave-wind farms enhance the competitiveness of marine energy in a number of ways, and in particular through their benefits in terms of Operation and Maintenance (O&M) – the subject of this work. The objective is to investigate how the reduction in significant wave height within a co-located farm caused by the extraction of wave power by the wave energy converters (WECs), also known as the shadow effect, results in enlarged weather windows for O&M tasks. This investigation is carried out through a case study of four wind farms in the North Sea, including a sensitivity analysis in terms of: (i) location (depth and distance from the coast), (ii) sea climate, and (iii) wind farm layout. Real (observed) sea conditions are considered, and a third-generation wave model (SWAN) is implemented on a high-resolution grid. It is found that the combination of wave and offshore wind energy increases the accessibility for O&M tasks over 13% in all the cases considered, leading to accessibility values of up to 82%. The best results are obtained for wind farms with square-like geometries, where the co-located WECs intercept both the prevailing and secondary wave directions, and with small spacings between converters. Besides, proximity to land is found to not be a favourable factor for exploiting this synergy between wave and offshore wind power.

Modelling impacts of tidal stream turbines on surface waves

Abstract A high resolution Computational Flow Dynamics (CFD) numerical model is built based on a laboratory experiment in this research to study impacts of tidal turbines on surface wave dynamics. A reduction of ∼ 3 % in wave height is observed under the influence of a standalone turbine located 0.4 m from the free surface. The artificial wave energy dissipation routine ‘OBSTACLE’ within FVCOM is shown to effectively capture the correct level of wave height reduction, reproducing the CFD results with significantly less computational effort. The turbine simulation system is then applied to a series of test cases to investigate impact of a standalone turbine on bed shear stress. Results suggest an apparent increase in bed stress ( ∼ 7 % ) upstream of the turbine due to the inclusion of surface waves. However, in the immediate wake of the turbine, bed stress is dominated by the presence of the turbine itself, accounting for a ∼ 50 % increase, with waves having a seemingly negligible effect up to 9D (D is the turbine diameter) downstream of the turbine. Beyond this point, the effect of waves on bed shear stress become apparent again. The influence of OBSTACLE on bed stress is also noticeable in the far wake, showing a reduction of ∼ 2 % in wave height.

Protection of gravel-dominated coasts through wave farms: Layout and shoreline evolution

The impacts of wave farms (arrays of wave energy converters, or WECs) on the nearshore must be fully understood for wave technology to develop and thus contribute to a sustainable, carbon-free energy mix in the near future. The objective of this work is to investigate the role played by the farm layout on the wave propagation patterns leewards and the implications for longshore sediment transport (LST) and shoreline evolution on a gravel-dominated deltaic coast. Changes in wave propagation in four scenarios, corresponding to as many wave farm layouts, are computed by means of a spectral numerical model (Delft3D-WAVE) under (i) low-energy and storm conditions, and (ii) westerly and easterly waves - the two prevailing wave directions. On this basis, sediment transport rates are computed and changes in the shoreline position assessed using a one-line model. To quantify the impact of the wave farm on the nearshore wave conditions, sediment transport and shoreline, we define three ad hoc indicators: the non-dimensional wave height reduction, the non-dimensional LST rate reduction and the non-dimensional shoreline advance. Significant wave heights decrease in the lee of the wave farm, with the consequent reduction in LST rates. As a result, the dry beach area increases in every scenario under both westerly and easterly waves. We find that case studies with the WECs arranged on fewer rows but covering a greater stretch of coastline provide better coastal protection. These results confirm that wave farms can be used not only to generate carbon-free energy but also to protect gravel-dominated coasts.

Experimental Study on the Hydrodynamic Performance of Floating Pontoon Type Breakwater With Skirt Walls

Floating breakwaters (FBWs) are widely used in moderate wave climatic conditions for coastal protection against erosion and for wave reduction around offshore loading terminals and open ocean construction sites. Literature shows that the width of a pontoon-type FBW is about 50% of the incident wavelength in order to achieve 50% wave height reduction at the lee side of the FBW. Hence, for a typical wavelength of 40 m, the width needed for pontoon FBW is about 20 m. Such an FBW may not be cost competitive. Is it possible to reduce the width of the pontoon FBW significantly by adding skirt walls (single, twin, triple, or five) at its keel. What will be the effect on mooring forces? In order to find solutions for these problems, experimental investigations were carried out on a typical pontoon-type FBW as well as pontoon with skirt walls. Both opaque and porous skirt walls were used. Wave transmission, reflection, and mooring forces, both on the sea side and lee side, were measured. It was found from this study that it is possible to reduce the width by 20 to 40% by introducing three or five skirt walls. However, introducing skirt walls increased the mooring forces by 10 to 30%. The results of this study are expected to be useful for cost-effective design of FBWs.

An energy-controlling boundary condition for partial wave reflections in the mild slope equation

An energy-controlling technique to actively manage the reflective property of waves from solid boundary is presented. As linear waves propagate through an energy-controlling area, a reduction in wave heights occurs due to energy dissipation, which can be placed under direct control through the imaginary part of the wavenumber and phase velocity. Based on this relationship, the present study investigates a new method to control reflected waves with desired heights in the mild slope equation model. The method is validated through numerical tests for various reflection coefficients and the results confirm the promising use of energy-controlling boundary condition for partial wave reflections.

Morphological hysteresis in the evolution of beach profiles under sequences of wave climates - Part 1; observations

Novel series of experiments are presented that demonstrate morphological hysteresis in the evolution to equilibrium of beach profiles under sequences of different wave climates. The experiments were conducted in a wave flume at medium scale using both monochromatic and random waves, representing 2D conditions. Beach profiles were obtained with high spatial resolution at frequent intervals with a laser profiler, from which shoreline location, bar position and sediment transport rates were derived. Experiments were conducted for sequences of wave climates, where a sequence comprised of 6–13 sequential tests, each commencing with the beach profile from the preceding test. Each test was run until equilibrium conditions were obtained and had a constant wave height, increased or decreased relative to the preceding test. Cyclical conditions were also included, with erosive and accretive wave conditions of short durations alternating through multiple cycles, so that equilibrium conditions were not reached during a test. With a sequence of increasing wave heights, the relationship between the shoreline position and the bulk cross-shore sediment transport, at equilibrium, was non-monotonic, indicating a maximum in the landward sediment transport rate. For test series comprised of a sequence of increasing wave heights followed by a sequence of decreasing wave heights, morphological hysteresis was observed in the equilibrium shoreline position and bulk cross-shore sediment transport, such that shoreline recession, or offshore transport, continued in some instances after reductions in wave height. This is inconsistent with classical equilibrium type shoreline evolution models. However, when equilibrium conditions were not reached, in the cyclic sequences, no such morphological hysteresis was observed and a dynamic equilibrium is reached. The morphological hysteresis occurs because of the decay, stranding, or increased relative depth, of the breaker bar following a reduction in wave height, often in conjunction with a new breaker bar generated by further offshore transport in the inner surf zone. Similar sequences of morphological response are evident in field data and larger scale tests in the literature. Finally, it is shown that the morphological hysteresis can be explained using the classical equilibrium beach state model of Wright et al. (1985) by introducing the concept of a subsequent alternate active beach state, which may occur following a change in wave conditions.