Coastal defence structures are often constructed to prevent beach erosion. However, poorly designed structures may cause serious erosion problems in the downdrift direction. Morphological models are useful tools to predict such impacts and assess the efficiency of defence structures for different scenarios. Nevertheless, morphological modelling is still a topic under intense research effort. The processes simulated by a morphological model depend on model complexity. For instance, undertow currents are neglected in coastal area models (2DH), which is a limitation for simulating the evolution of beach profiles for long periods. Model limitations are generally overcome by predefining invariant equilibrium profiles that are allowed to shift offshore or onshore. A more flexible approach is described in this paper, which can be generalised to 3-D models. The present work is based on the coupling of the MOHID modelling system and the SWAN wave model. The impacts of different designs of detached breakwaters and groynes were simulated in a schematic beach configuration following a 2DH approach. The results of bathymetry evolution are in agreement with the patterns found in the literature for several existing structures. The model was also tested in a 3-D test case to simulate the formation of sandbars by undertow currents. The findings of this work confirmed the applicability of the MOHID modelling system to study sediment transport and morphological changes in coastal zones under the combined action of waves and currents. The same modelling methodology was applied to a coastal zone (Costa da Caparica) located at the mouth of a mesotidal estuary (Tagus Estuary, Portugal) to evaluate the hydrodynamics and sediment transport both in calm water conditions and during events of highly energetic waves. The MOHID code is available in the GitHub repository.
The morphological features of the coastal zone depend on the sediment characteristics and the combined action of waves and currents. Wind waves are the main energy source for most beaches. Particularly in the surf zone, waves may induce considerable changes in mean sea level and strong currents (Longuet-Higgins, 1970a, b, 1983). The pattern of surf zone currents varies with the angle of waves approaching the shore as well as with bathymetric heterogeneities, leading to longshore and rip currents. Sediment is usually carried shoreward during low wave conditions, mainly due to the asymmetry of waves in shallow waters (Myrhaug et al., 2004). The sediment accumulated during these periods may be eroded very rapidly under high wave conditions during a major storm. Following these energetic events, the bottom profile may recover its initial shape only if the longshore transport of sediment during the storm is low. Different structures such as breakwaters and groynes can prevent the along-shore movement of sediment (e.g. Dally and Pope, 1986). Consequently, serious erosion problems in the downdrift direction may arise from the construction of these structures. Morphological models are useful tools to assess the impact of protection structures, enabling us to consider different wave conditions and structure designs. The complexity of morphological models ranges from coastal profile models to 2- or 3-D models. Actually, morphological models are usually a set of different models or modules, depending on the chosen approach. Here the focus is on the coupling of a spectral wave model with a phase-averaged hydrodynamic and sediment transport model. Spectral wave models offer a representation of the physical processes related to the generation, propagation, and dissipation of waves (e.g. Booij et al., 1999). The wave-induced forces computed by a wave model can be provided to a hydrodynamic model in order to simulate wave-related phenomena, such as wave set-up, wave-induced currents, and mixing. On the other hand, the hydrodynamic model can return water levels and currents to the wave model (e.g. Warner et al., 2008). Additional processes can be considered in the hydrodynamic model, such as wind action, tidal motion, and river discharges. The transport of suspended sediment may be simulated by an advection/diffusion model. The mechanism of erosion/deposition of sediments is controlled by the bed shear stress induced by currents and waves. The bathymetry evolution resulting from the total sediment transport (suspended load and bed load) affects the patterns of currents and waves. Due to the interdependence of the physical processes involved in sediment dynamics, all of these models must be coupled.
The hydrodynamics inside the surf zone is influenced by important 3-D effects. Due to the absence of 3-D processes (e.g. undertow), coastal area models (2DH) fail to reproduce a consistent evolution of beach profiles for long periods. This shortcoming can be overcome by predefining invariant equilibrium profiles. In this case, the equilibrium profile only shifts offshore or onshore depending on the overall sediment balance along the profile, similarly to a coastal profile model (e.g. Kriebel and Dean, 1985; Kristensen et al., 2013). As the sediment transport in the swash zone is usually neglected in large-scale 2DH models, this approach also has the advantage of updating the shoreline position. However, limitations arise when a structure is present in the surf zone. Moreover, the processes responsible for sandbar evolution are not considered. Attempts to simulate sandbar dynamics have been performed generally with cross-shore 2-D (2DV) and quasi-3-D models (e.g. Drønen and Deigaard, 2007; Ruessink et al., 2007). Nevertheless, the proper reproduction of sandbar migration is still an active topic of research (e.g. Dubarbier et al., 2015). Inaccuracies in the cross-shore sediment transport may degrade the coastal profile, which is a restriction for the simulation of long-term morphological evolution.
In this work, we test a more flexible approach to overcoming the 2DH model limitations in order to simulate morphological evolution for long periods. Instead of fixing an equilibrium profile to update the bathymetry and shoreline position, we defined a maximum slope that when surpassed generates sediment transport in the downslope direction. Thus, rather than extrapolating erosion or deposition fluxes over the entire profile, only individual grid cells are affected. This approach may be more appropriate in order to consider the effect of non-uniform grain-size distributions on the overall sediment transport, through morphological models that account for multiple sediment fractions. Grain-size sorting is generally observed along the cross-shore beach profile, as well as in the longshore beach direction (Komar, 1998). Furthermore, the method can be generalised to 3-D models for a better representation of sandbar slopes and to update the shoreline position.
This paper is divided into five sections. A brief description of the effect of waves in the nearshore hydrodynamics and sediment transport is given in Sect. 2. The numerical modelling approach is presented in Sect. 3. The methodology was verified for different test cases (Sect. 4). Firstly, the morphological evolution of a schematic beach was evaluated for different designs of coastal defence structures (detached breakwaters and groynes) following a 2DH model configuration. The model was applied later in a 3-D configuration for the same schematic beach to verify the development of sandbars. Finally, the numerical modelling methodology was applied to assess the hydrodynamics and sediment transport under extreme wave conditions in a coastal zone (Costa da Caparica) located at the mouth of a mesotidal estuary (Tagus Estuary, Portugal). The main conclusions found from these test cases are discussed in Sect. 5.
The effect of breaking waves on the mean sea level (wave set-up) has been known since the laboratory measurements performed by Saville (1961), confirmed further by Bowen et al. (1968). This tilt of the mean sea level is explained by the horizontal flux of momentum carried by waves or, equivalently, by the radiation stress, a vertically integrated momentum flux whose gradient balances the wave set-up (Longuet-Higgins and Stewart 1962, 1964). In the surf zone, wave heights and orbital velocities decrease towards the shore due to wave breaking. As a consequence, the radiation stress also decreases, resulting in a force directed towards the shore. This force is balanced by a hydrostatic pressure gradient that increases the mean sea level onshore.
Breaking waves can also drive strong currents in the surf zone, which are important for sediment transport and morphological evolution in the coastal zone. The horizontal mass transport associated with waves, or Stokes drift, is oriented shoreward and vertically sheared, being more intense at the surface (e.g. Ardhuin et al., 2008). As a result, mass conservation in the nearshore is satisfied by a seaward transport in the lower part of the water column, called undertow, which has an important role in sandbar formation. The undertow is strongest in steep beaches and may be insignificant for moderate beach slopes, where circulation tends to break up into rip currents (Longuet-Higgins, 1983). Also, obliquely breaking waves generate longshore currents (Longuet-Higgins, 1970a, b) and, consequently, longshore sediment transport. Although nearshore sediment dynamics are dominated by wave action, tidal motion can also play an important role, alternately moving the breaker zone and shoreline position shoreward and seaward, which may prevent the development of longshore bars in the surf zone (e.g. Levoy et al., 2000).
The present work is based on the coupling of the MOHID modelling system (Leitão, 2003; Leitão et al., 2008) and the SWAN wave model (Booij et al., 1999). The MOHID code organisation follows an object oriented strategy that permits the integration of different scales and processes. Herein, the focus is given to the hydrodynamics and sediment transport in the nearshore area. Thus, we considered the processes related to the hydrodynamics, turbulence, advection/diffusion of suspended sediment, erosion/deposition of sediments, bed load sediment transport, and morphological evolution. A brief description of the most important aspects of the hydrodynamic model for this work is presented in this section, followed by the main novelties implemented in the MOHID code: a new method to calculate the bed load transport under the combined effect of currents and waves; and a bed slope correction considered to overcome the 2DH model limitations and to update the shoreline. This work represents an extension of the development of the morphological model previously described in Franz et al. (2017).
The SWAN wave model represents the processes of wave generation, propagation,
refraction, shoaling, non-linear (quadruplet and triad) wave–wave
interactions, and dissipation (whitecapping, bottom friction, and
depth-induced breaking). More information can be found in the documentation
of the SWAN wave model (
The MOHID hydrodynamic module solves the Navier–Stokes equations,
considering the incompressibility, hydrostatic,
Boussinesq, and Reynolds
approximations (Martins, 2000; Leitão, 2003):
The spatial discretisation is performed by following the finite-volume method. The water level and vertical velocity are computed through the continuity equation integrated over the entire water column or applied to each control volume, respectively. The equations are solved through the alternating direction implicit (ADI) method in an Arakawa C-grid structure. A generic vertical discretisation allows implementation of different types of vertical coordinates (e.g. Sigma or Cartesian) (Martins, 2001). The turbulent viscosity is computed differently for the horizontal and vertical directions. The horizontal turbulent viscosity is defined as a constant value, based on the grid resolution and a reference velocity, or as a function of horizontal velocity gradients, based on Smagorinsky (1963). The vertical turbulent viscosity is computed by the Global Ocean Turbulence Model (GOTM), which is coupled to MOHID and consists of a set of turbulence-closure models (Buchard et al., 1999; Villarreal et al., 2005). Effects of wave breaking on vertical turbulence can be taken into account through surface boundary conditions (Delpey et al., 2014).
To solve the Navier–Stokes and continuity equation, appropriate boundary conditions are required for the lateral (e.g. land and open sea), surface, and bottom boundaries. MOHID has the option of a great variety of open boundary conditions of several types: Dirichlet, Neumann, radiation, cyclic, relaxation (or nudging), etc. Some boundary conditions can be combinations of the types enumerated, e.g. a combination of radiation with nudging (Blumberg and Kantha, 1985). Open boundary conditions (OBCs) can be imposed by prescribing the values of a specific variable (Dirichlet boundary condition). This condition is commonly applied in coastal models to impose tidal levels when the correspondent barotropic velocities are not available. On the other hand, following a Neumann boundary condition, the gradient of a specific variable is imposed instead of a prescribed value. Assuming a null gradient condition, the value of a variable at a boundary point is equal to the value at an adjacent interior point. When the shoreline location and bathymetry are uniform, e.g. in schematic cases, cyclic boundary conditions can be applied.
A relaxation scheme can be applied as an OBC by assuming a decay time that
increases gradually from the boundary to infinite after a defined number of
cells (see Martinsen and Engedahl, 1987; Engedahl, 1995):
Radiation methods can also be used to impose the OBCs, which allow the
propagation of internal disturbances on water levels through the open
boundaries. These disturbances can be caused, for example, by the wave
forces. MOHID has two types of radiation conditions (Leitão, 2003), based
on Blumberg and Kantha (1985), Eq. (3), and Flather (1976), Eq. (4):
In the case of land points, the closed boundary condition is imposed as null fluxes of mass and momentum in the perpendicular direction. However, for the parallel direction two boundary conditions can be used in MOHID: no-slip and free-slip (Leitão, 2003). In the no-slip condition, the normal and parallel velocities in the land boundary are assumed to be equal to zero. This generates a persistent gradient in the velocity components parallel to the land boundary and, consequently, a persistent sink associated with the horizontal turbulent diffusion of momentum. The covering and uncovering of boundary cells can be represented in MOHID by a wetting/drying scheme (Martins et al., 2001).
At the surface, fluxes of momentum from wind action and wave breaking can be considered (Delpey et al., 2014). At the bottom, the method proposed by Soulsby and Clarke (2005) to compute the bed shear stress was implemented in this work, consisting of a steady component due to currents together with an oscillatory component due to waves. In a laminar flow, the combined bed shear stress is a simple linear addition of the laminar current-alone and wave-alone shear stresses. However, in turbulent flows this addition is non-linear and the mean and oscillatory components of the stress are enhanced beyond the values of the laminar case. The mean bed shear stress is used for determining the friction acting on the current, whereas the maximum shear stress is used to determine the threshold of sediment motion. The turbulence generated by the skin friction acts directly on bottom sediment grains (Einstein, 1950), contrarily to that related to bed forms. Thus, the threshold of sediment motion depends on the grain-related bed shear stress.
The transport of sand is divided into suspended and bed load, in which the sand particles are in frequent contact with the bed. The suspended sediment transport is computed by resolving the advection/diffusion equation. This approach is more realistic than considering empirical equations based on the instantaneous bed shear stresses, as the suspended load is not in equilibrium with the instantaneous bed shear stresses in unsteady flows. The net upward flux of suspended sand depends on the equilibrium concentration near the bottom, estimated by empirical equations available in the literature, extrapolated following the Rouse profile to the middle of the near-bed layer, which in 2DH mode means the middle of the water column. The adopted methodology was described previously in Franz et al. (2017), converging for different numbers of vertical layers.
The bed load transport under the combined effect of currents and waves is
computed following the semi-empirical formulation of Soulsby and
Damgaard (2005). The formulation was derived for current plus sinusoidal and
asymmetrical waves, as well as asymmetrical waves alone. Amoudry and
Liu (2010) obtained a generally good agreement comparing the results of
Soulsby and Damgaard (2005) formulations with a sheet flow model, concluding
that it can be implemented in both intrawave and wave-averaged models in
order to study sediment transport. The parallel
To compute the sediment fluxes between grid cells, the components of the
non-dimensional bed load transport vector are rotated to the grid
referential (
Wave action induces a shoreward sediment transport that has no counterpart in
2DH models, leading to sand accumulation in the nearshore and increasing the
steepness of the beach profile. Actually, undertow currents are responsible
for a seaward sediment transport, which may generate sandbars. Diverse
opposing forces are responsible for creating an equilibrium profile, which
depends on sediment characteristics and wave heights (Dean, 1991). To account
for the neglected forces in 2DH models, we defined a maximum slope
(
Initial bathymetry
The wave-induced force (radiation stress) computed by the SWAN wave model is provided to the MOHID hydrodynamic model in order to simulate the wave-induced currents and wave set-up. Fields of significant wave height, wave period, wavelength, wave direction, and maximal orbital velocity near the bottom are also provided by SWAN to MOHID in order to compute the bed shear stress and sediment transport. On the other hand, the MOHID hydrodynamic model returns fields of water level and current to SWAN. The water level variation caused by the tidal motion changes the breaker zone and shoreline position, affecting waves and sediment transport. The morphological evolution modifies the currents and waves. Thus, the bathymetry changes computed by MOHID are also updated in SWAN. The different fields computed by SWAN must be updated in MOHID, and the different fields computed by MOHID must be updated in SWAN, with an adequate frequency for each application depending on the variability of forcing conditions and the speed of morphological changes.
The coupling between the MOHID modelling system and the SWAN wave model was performed by files transferring through tools developed in the Fortran language to convert the results to the appropriate format and another tool developed in the Python language to automatically manage the runs of the tools and models. At this time, we have focused on model results instead of numerical efficiency. However, considering the domain decomposition parallelisation approach implemented using MPI directives and the morphological acceleration factor, the computational time required to simulate the presented test cases was feasible through the use of a regular computer with six cores.
The morphological evolution of a schematic beach was simulated to assess
model results, considering the beach response for different designs of
detached breakwaters and groynes. Constant wave conditions were defined along
the offshore boundary (1.5 m of wave height, 8 s of peak wave period, and
15
The open boundary condition was defined as a null gradient for the sediment
concentrations in the water column, as well as for the sediment mass
evolution at the bed (or, equivalently, for bathymetry). A null gradient
condition was also imposed at the open boundaries for the normal and
tangential current velocities. The radiation condition of Blumberg and
Kantha (1985) was imposed for water level, Eq. (3), assuming a passive
condition at the cross-shore boundaries (
The initial bathymetry was defined by considering an equilibrium profile of
the form
Detached breakwaters considered for test case scenarios.
* Beach response according to Dally and Pope (1986).
Model results for the breakwater's length-to-distance ratio of 0.2.
Bathymetry
Model results for the breakwater's length-to-distance ratio of 0.5.
Bathymetry
Model results for the breakwater's length-to-distance ratio of 1.0.
Bathymetry
Model results for the breakwater's length-to-distance ratio of 2.0.
Bathymetry
Detached breakwaters generate sediment transport from the adjacent coast to
the lee side of the structure, leading to the formation of a bulge or salient
in the beach planform. Depending on geometrical features of the breakwater,
wave climate, and sediment availability, the salient may become attached to
the breakwater, forming a tombolo. Based on the analysis of several existing
breakwater projects, Dally and Pope (1986) found that a ratio (
Groyne with a length of 100 m from the shoreline. Bathymetry
Groyne with a length of 200 m from the shoreline. Bathymetry
Simulated sandbars for different wave heights. The horizontal plane
of the bathymetry
Model results for a near-equilibrium planform of the shoreline agree with the
analysis of Dally and Pope (1986), demonstrating the development of a salient
for
Bathymetries of the Tagus Estuary hydrodynamic model
Residual velocity in the Tagus Estuary mouth at the surface
Wave conditions for the winter of 2013/2014 obtained from the Portuguese coast wave model in the location of the port of Lisbon wave buoy.
Velocity results of the Costa da Caparica model during flood
Wave results of the Costa da Caparica model.
Velocity results of the Costa da Caparica model during flood
Results of bed load sediment transport for the scenarios
without waves
Groynes are applied to reduce the littoral drift in the surf zone, trapping sediment on the updrift side of the structure, which may cause erosion problems on the downdrift side. Moreover, the longshore currents are forced to deviate into deeper water around groynes, causing sediment losses from nearshore to offshore. The morphological impacts of the groynes are a function of their length from the shoreline. Model results were assessed for two designs of groynes, with lengths of 100 and 200 m (Figs. 6 and 7). As expected, greater erosion occurs on the downdrift side for a longer groyne, as more sediment from the littoral drift gets trapped on the updrift side. Furthermore, offshore sediment transport becomes intensified in the 200 m length groyne design, as the deviation of longshore currents is more important. In this case, the retrogradation of the shoreline is similar to the case of a detached breakwater in which a tombolo was formed.
In this test case, we verified the model capacity to generate sandbars in a
3-D approach. The same domain and sand granulometry (0.2 mm) as in the
previous 2DH test cases were considered, but without protection structures.
Two wave heights (1.5 and 1.0 m) were defined in sequence along the offshore
boundary during periods of 45 days of morphological evolution (3 h of
simulation time with a morphological acceleration factor of 365). The peak
wave period and peak wave direction were maintained constant (8 s and
15
The water column was divided into five layers of a sigma vertical coordinate
and a simple exponential approach was followed to consider the vertical
variation of the wave-induced forces: an exponential decrease in the
radiation stress is imposed from the surface to the bottom, following the
same shape as the profile of the orbital velocities, provided by the linear
wave theory. The vertical radiation stress profile is designed to conserve
the vertically integrated flux of momentum, which remains equal to the flux
given by SWAN. The effects of wave breaking on vertical turbulence were
disregarded in this work. The idea here is only to provide an approximate
representation of the vertical distribution of wave momentum, in order to
generate a general undertow pattern. Thus, the corresponding results should
be considered as a first qualitative evaluation of the effect of such an
undertow in our morphological module, the latter being our focus here. It is
left for further work to use a more advanced formulation of 3-D wave–current
interactions for more quantitative investigations. The
The open boundary conditions for sediment concentrations in the water column and sediment mass evolution at the bed column were defined as a null gradient, as well as the boundary conditions for normal and tangential velocities, as in the previous 2DH test cases. Considering that no structures were included in this test case, the bathymetry evolution was expected to be nearly uniform along the beach. Thus, a cyclic boundary condition was imposed at the cross-shore boundaries together with a Flather radiation condition at the offshore boundary (Eq. 4).
The model was capable of representing an undertow pattern and associated sediment transport that induce the formation of longshore sandbars (Fig. 8). A longitudinal current is presented in the surf zone, similarly to that observed in 2DH. However, a cross-shore velocity component is now represented by the 3-D model. Inside the surf zone, this component is shoreward near the surface and seaward near the bottom. As expected, the cross-shore component has opposite directions before and after the breaking zone. The sandbar migrated seaward, changing the location of the breaking zone until wave heights decreased to 1.0 m after 45 days. At this time, waves were able to propagate further without breaking, creating a new sandbar nearer the coast. Finally, the results demonstrate the model's potential to represent the formation of multiple sandbars, which are observed in many places (e.g. Dolan and Dean, 1985; Ruessink et al., 2009).
The hydrodynamics and sediment transport on the southern coast of the Tagus Estuary mouth (Costa da Caparica) are evaluated under extreme wave conditions by coupling the MOHID modelling system and the SWAN wave model. A significant coastline retreat was observed in the Costa da Caparica in the last century. Defence structures (groynes) were built around the 1960s to reduce coastal erosion, resulting in some stability until the 2000/2001 winter, when this issue started to receive more attention from the local authorities (Veloso-Gomes et al., 2009). The importance of the problem has augmented due to urbanisation and tourism development. The location near to the Tagus Estuary inlet increases the complexity of sediment dynamics in this zone.
A downscaling approach was followed to provide appropriate boundary
conditions for the Costa da Caparica model, considering previous results of
the wave and hydrodynamic modelling system for the Portuguese coast developed
by the MARETEC research group (
The Tagus Estuary is classified as mesotidal, with an average tidal height of
2.0 m in the mouth (Lemos, 1972). The tide is the main mechanism forcing the
flow in the estuary, determining current directions and water level
variations (Franz et al., 2014d). The maximum velocities reach 2 m s
The effects of the waves on the currents and sediment transport were
investigated during a high-energy event in the winter of 2013/2014 caused by
the Hercules storm. The wave conditions for the period of study in the
location of the port of Lisbon wave buoy reached wave heights higher than
7 m and wave periods of up to 20 s (Fig. 11). A variable grid resolution
was defined for the Costa da Caparica domain, ranging from 50 to 10 m near
the coast. The water column was divided into 10 layers, including five layers
in the first metre above the bottom with fixed thicknesses ranging from 0.1
to 0.3 m, and five sigma layers on top. The exponential approach described
in the last section was followed to represent the vertical variation of the
wave-induced forces. The vertical viscosity was computed by the
In a first scenario, the effects of the waves on the currents and sediment
transport were neglected. Therefore, just the influence of hydrodynamic
boundary conditions from the Tagus Estuary model was taken into account. The
results of the Costa da Caparica model without the wave action demonstrate
strong velocities of up to 2 m s
During the period of study, the waves propagated from offshore, mainly with a west-northwesterly (WNW) direction (Fig. 11). The bathymetric features (Fig. 9) cause the modification of the wave propagation direction through refraction to a west-southwesterly (WSW) or southwesterly (SW) direction in the nearshore (Fig. 13). The effect of the currents and water level variations on wave propagation was also considered, with an update frequency of 1 h, the same frequency at which the wave forcing was updated in MOHID. The oblique angle of the waves' incidence generates a nearshore longitudinal current oriented to the estuary inlet (Fig. 14), reinforcing the velocities observed in the scenario in which the wave action was neglected. The velocity vectors have a shoreward component at the surface, whereas near the bottom a seaward component is observed, caused by the vertical variation of the wave-induced forces. Although the currents were intensified along the coast of the Costa da Caparica, a small reduction of velocities can be observed in the northern part of the model domain.
Based on a few existing data in the literature, a uniform granulometry was assumed for the Costa da Caparica model with a diameter of 0.3 mm (Freire et al., 2006). A more representative set of granulometry data is necessary to better characterise the sediment distribution in the model domain, considering that grain-size sorting is expected to occur due to the complex hydrodynamics, wave variability and bathymetric heterogeneities. Thus, the results of sediment transport should be seen as a first qualitative assessment. Moreover, the morphological evolution was ignored at this stage.
The patterns of the bed load sediment transport for the scenarios without waves and under extreme wave conditions are presented in Fig. 15. Along the coast of the Costa da Caparica, the results of the bed load sediment transport are practically null when the wave action was disregarded, suggesting that the tidal currents are irrelevant for the sediment transport in this area. By contrast, simulations including wave forcing show a very strong bed load sediment transport due to waves. However, the importance of the tidal currents for the sediment transport in the inlet of the Tagus Estuary is noticeable. The littoral drift caused by the waves is deflected seaward by the tidal currents during the ebb tide and by the longer groynes present near the estuary inlet.
The potential of a new modelling approach to simulate the impact of
different designs of coastal defence structures was demonstrated in this
paper. The coupling between the MOHID modelling system and the SWAN wave
model can be useful for engineering studies in order to evaluate the best
solution to protect the coast against erosion. The speed-up of morphological
changes, along with the multiprocessing architecture, allows for the
modelling of bed evolution for long periods and for the study of several
scenarios. The acceleration factor of 365 allowed us to simulate many years
of morphological evolution of a schematic beach with constant wave
conditions in a feasible computational time. The bathymetry results reached
an equilibrium condition, demonstrating the model stability. The
acceleration factor is user-defined, depending on the variability of forcing
conditions and speed of morphological changes. The morphological changes
should not be speeded up (acceleration factor
The potential for modelling the evolution of sandbars was also demonstrated in this paper. In the future, an up-to-date methodology can be applied to resolve the vertical variation of wave-induced forces, as well as wave-induced vertical mixing, based on e.g. the generalised Lagrangian mean (GLM) theory implemented in the MOHID code (see Delpey et al., 2014). The test cases shown in this paper are only a preliminary demonstration of model potential, which is thought to be encouraging. The findings of this work confirmed the applicability of the MOHID modelling system in studying sediment transport and morphological changes in coastal systems under the combined action of waves and currents.
The application of the described modelling methodology to a coastal zone located near the inlet of a mesotidal estuary with strong tidal currents allowed for an assessment of the hydrodynamics and sediment transport in situations of calm water conditions (no waves) and under extreme wave conditions. Although these initial results are just a qualitative assessment of sediment transport, the applicability of the modelling methodology to complex cases was demonstrated. In the future, with a more representative set of data, quantitative studies could be performed, taking into account the morphological evolution. Furthermore, the methodology can be used to evaluate different designs of defence structures in order to propose a more efficient solution for the coastline retreat and intense erosion observed in recent years on the coast of the Costa da Caparica.
No data sets were used in this article.
The MOHID code updated with the developments performed in this work is available in the repository:
The authors declare that they have no conflict of interest.
The authors are grateful to the Portuguese Environment Agency (APA) for providing the bathymetry data for the coast of the Costa da Caparica. The first author was financed by the Brazilian National Council for Scientific and Technological Development (CNPq) under the Ciências Sem Fronteiras programme (research grant no. 237448/2012-2). MARETEC acknowledges the ERDF funds of the Competitiveness Factors Operational Programme (COMPETE), and national funds from the Foundation for Science and Technology (FCT) (project UID/EEA/50009/2013).Edited by: John M. Huthnance Reviewed by: André B. Fortunato and one anonymous referee