Mohammad Saud Afzal,Lalit Kumar

Department of civil engineering,Indian Institute of Technology,Kharagpur,India

Keywords:Wave propagation SWAN Bathymetry Significant wave height and Peak wave period

ABSTRACT The propagation of waves in shallow waters is affected by the bottom topography unlike deep water waves of the coastal environment.Due to the interaction of the wave with bed topography,the wave transformation processes occur.Refraction,diffraction,shoaling,and breaking are the wave transformation processes that occur in the coastal environment.The significant wave height over rugged topography is a standardized statistics to denote the characteristic height of the random waves in a sea state.Therefore,the objective of the present study is to predict the significant wave height over rugged topography.The SWAN standalone and SWAN DHH platform are used to predict significant wave height over rugged topography in Mehamn harbour,Norway.The SWAN model results are almost similar to the lab data of Vold and Lothe (2009) for all the 22 scenarios at all the output locations.Further,the four cases reported by Taehun (2011) and lab data from Vold and Lothe (2009) for that four cases are compared with the SWAN model results.It is observed that the SWAN model results are much closer to the lab data of Vold and Lothe (2009).

1.Introduction

The estimation of wave conditions near coastal region has consistently been the central issue in recent years.The introduction of breakwaters and coastal structures near the harbour results in formation of rugged topography.A rugged topography represents the uneven or rough area of land that is covered with rocks and few trees.Various studies have been performed on rugged or uneven topography in recent times [1-6].Ocean wave propagations into harbours are large scale phenomena with complex process that involves reflection,shoaling,diffraction and refraction transformations [7-10].The propagation of waves over rugged topography affects the sediment transport and boundary layer structure significantly due to flow separation and formation of lee side vortices behind the obstruction,which leads to variation in significant wave height in coastal environment.The significant wave height is very essential parameter for risk assessment and load-response calculations for coastal and marine environment.

The shallow water waves get affected by the bottom topography unlike deep water waves.Refraction,diffraction,shoaling,and breaking are the wave transformation processes which occur when the wave approaches the shoreline.The change in direction of wave as they pass from one medium to another is called refraction of wave in coastal region.The refraction of wave is accompanied by change in wavelength and speed of wave.However,the change in the direction of wave as they pass through the opening of structure or barrier is known as diffraction.The amount of diffraction is proportional to wavelength.The change in wave height due to entrance of surface wave into shallower water is called shoaling of wave.It exhibits reduction in wavelength while the frequency remains constant.This phenomenon evident for Tsunami as they approach to coastline a great wave height is found.When the wave amplitude reaches up to critical level and wave energy is transformed into turbulent kinetic energy,the process is known as breaking of wave.The frequent occurrence of wave breaking requires more attention in coastal region.

The propagation of wave over submerged obstacle or structure is key research topic discussed by several researchers[11-14].Johnson et al.[15]performed experiments on wave propagation over reef and noted that the energy of wave was transmitted as a multiple crest system over natural reef.Madsen and Mei [16]studied the transformation of solitary wave over an uneven bed topography and reported that as the solitary wave climb the slope,the rate of amplitude of wave increases depending on the slope as well as initial amplitude condition.Further,Johnson[17]extended the work of Madsen and Mei [16]and predicted their numerical and experimental result using asymptotic method and Korteweg-de Vries equation (up to a certain depth).In one of the experiment,Dattatri et al.[18]investigated the performance of submerged breakwater characteristics and pointed the transmitted waves as a complex form which indicates the presence of higher harmonics.Later,Drouin and Ouellet [19]and Kojima et al.[20]emphasizes the wave decomposition phenomenon and associated harmonic generation of wave over obstacle.Rey et al.[21]have also reported similar experimental result of wave passing over a bar.

Vincent and Briggs [22]performed an experimental study to analyse the transformation of monochromatic and directionally spread irregular waves passing over a submerged elliptical mound.They used a directional spectral wave generator to generate waves with equal frequency and spectral energy along with monochromatic wave of equivalent height and period.Their result showed that the monochromatic waves provide poor approximation of irregular wave condition.Beji and Battjes [23]performed laboratory experiment to elucidate the high frequency energy generation phenomenon in the power spectra of waves travelling over a submerged bar.The measurements they observed are in good agreement with the numerical model for harmonics generation and generation of wave.

Propagation of wave over non-uniform depth is mainly due to refraction [24,25].The amplitude of wave is determined by the conservation of energy flux [26].Generally linear and long crested waves incident on straight depth contours [27].Bitner [28]performed a field experiment and reported the wave propagation towards the decreasing depth.The changes of depth,wavelength and amplitude induced by shoaling can modify the statistical distribution of the waves.Further,Cherneva et al.[29]performed similar field experiment on wave propagation.Both experiments were similar in a way that they observed deviation from Gaussian statistics.Similarly,several experimental studies on water waves on submerged obstacle or topography have been performed to observe the change in spectral shape,which occurs with respect to amplification of bound harmonics when waves enter the shallower water [23,30,31].In recent studies,a noticeable dynamic response occurs after the change in depth near coastline.This nonlinear dynamic behaviour was observed in experiments as reported in several studies [32-37].

Numerical techniques are very important in recent years.Accuracy,computational time,computational cost as well as practical flexibility are key parameters of a numerical model.Berkhoff et al.[38]verified numerical wave propagation models for simple harmonic linear water waves.They mainly focus parabolic and full refraction-diffraction model.Further,Ebersole [39]developed a numerical model which predicts the monochromatic waves over complex bathymetry.They considered the refractive and diffractive effect for both models.Finite difference was used to solve the governing equation.Their model shows good agreement with the experimental results.Panchang et al.[40]performed numerical simulation of irregular wave propagation over shoal.They analysed a monochromatic refraction-diffraction model,which was used to spectral computation accurately.

Booij et al.[41]proposed a third generation numerical wave model,SWAN (Simulating WAves Nearshore) to compute random,short crested waves in coastal region with shallow water and ambient current.Eulerian formulations of discrete spectral balance of action density are used to develop the swan model.Further,Ris et al.[42]presented spectral wave model for small scale coastal region with shallow water.They verified local wind,tidal flats,barrier,islands and ambient current with the measurements.Liu and Losada [43]reviewed various numerical models to calculate wave propagation from deep water to surf zone.Their main focus was on unified depth integrated model and Reynolds averaged Navier stokes equation (RANS) model.Narayanaswamy et al.[44]proposed a hybrid SPHunwave model which was developed based on the advantages of SPH model (SPHysics) and Boussinesq model(FUNWAVE).Their model counters the wave propagation phenomena from deep sea to coastal region in presence of multiple scales both in space and time.

The recent studies of Zeng and Trulsen [34],Gramstad et al.[45],Viotti et al.[46]and Majda et al.[47]signify the existence of two different regimes.First,the propagation of waves on shoal with shallower depth,a localised maximal concentration of extreme waves can occur at or near the shallow incident edge of the sloping bottom.Second,propagation of wave on a sufficiently deep shoal it appears that no localised concentration of extreme waves occurs.Wang et al.[48].performed three-dimensional numerical simulation of wave propagation over rugged topography in Mehamn harbour using REEF3D model.This study demonstrated the influence of rugged topography on wave generation.Further,Wang et al.[49]used phase-resolved wave models that represent wave transformation phenomena over rugged topography.

The breakwaters are the small structures that provide easy passage for navigation and used to protect harbours on a gently sloping beach.The rugged topography development near the harbour influences the coastal wave climate by breaking,reflecting,and diffracting wave energy.In a large harbour,the fetch may be sufficient for the local generation of waves to be important.Studying these influences in situ poses a challenge.In recent years,spectral wave models have become more widely used and are important in describing coastal wave behaviour on smooth topography.However,the performance and precision of the spectral models for wave propagation over rugged topography has not been well examined.The present work is an attempt to demonstrate the capability of these 3rd generation wave models in predicting the same.

It is well-known facts that most of the 3rd generation wave(SWAN) models are assumed to be valid in an area where the bottom topography is smooth or not uneven.Therefore,the principal goal of this paper is to predict the significant wave height over rugged topography and the test case has been chosen in Mehamn harbour,Norway using the third generation SWAN model.In recent years,unstructured grid SWAN models have become more popular for modelling complex geometries and are effective alternatives to the grid nesting approach [50,51].Therefore,the unstructured SWAN model is also used to simulate the wave propagation over rugged topography.

2.Materials and methods

2.1.Study area

Mehamn harbour port lies in Finnmark county which is in the northern part of Norway.The Mehamn is located on the small Vedvik peninsula (part of Nordkinn Peninsula) at southern end of a bay of the Barents Sea (Fig.1).

The latitude and longitude of Mehamn harbour Norway are 71.034 N and 27.851 E respectively.In Mehamn harbour,the introduction of breakwaters causes formation of bottom rugged topography that was discussed by several researchers [52,53].Moreover,amongst the rugged topography areas,Mehamn harbour area was chosen due to the availability of datasets like wave parameters,water levels,wind data,information about the obstacles,which are essential input parameters for the numerical wave model.The present study uses intermediate to shallow water depth dataset of Mehamn harbour from Vold and Lothe [52]and Taehun [53].

A set of intermediate to shallow water wave data was obtained by Vold and Lothe [52](2009) near Mehamn harbour,Norway.The wave gauges were installed at 10 (ten) different locations which record waves for 22 (twenty-two) different conditions.The wave condition at location 4 has been imposed on the northern boundary for carrying out the modelling using SWAN model.The main reason to select the location 4 is its mere proximity to the northern boundary of SWAN model.The Location 3 as depicted in Taehun [53]report has not been used since it lies outside the boundary domain of the computation.The locations at Mehamn seaport were plotted and represented by Taehun [53]in Fig.2.The coordinates for all the wave gauge locations of Mehamn harbour (Norway) are shown below in Table 1.

Table 1 Wave gauge locations’ coordinates of Mehamn sea port (Norway).

Fig.1.Location of Mehamn seaport (Norway).

Fig.2.The location map of Mehamn (Norway) by Taehun[53].

2.2.Experimental setup

The bathymetry near the Mehamn site has been obtained by Vold and Lothe [52].They performed experiments on waves by using a spectral wave generator in the SINTEF Coastal and Hydraulics Laboratory’s wave basin.A lab test model has been prepared based on the actual bathymetric settings of the area.The resolution of the bathymetric data is 3× 3 m.It starts from-44,600 m to-43,400 m UTM in X coordinate and 1,453,300 m to 1,454,800 m UTM in Y coordinate.The bathymetric plot by SWAN model is presented in Fig.3.

Fig.3.Water depths near the Mehamn harbour site (Norway).

The bathymetry is measured with respect to chart datum at the Mehamn harbour.The mean water level as obtained from the lab data is+2 m.The wave data available for the study area is presented in Table 2,where Hs (m) are the significant wave heights and Tp (s) is the peak wave period.The data is as obtained from wave data analysis at wave gauge location 4 (four).Further,the wave spectrum information is necessary to set the boundary condition of numerical wave models such as SWAN [54].The maritime Industries use the Joint North Sea Wave Observation Project (JONSWAP) spectrum to the numerical model for the vessel and structure design.However,JONSWAP spectra are also used by coastal engineers to regulate wave generation in laboratory flumes.The JONSWAP spectra are used worldwide due to their idealized fetchlimited conditions and applicability for variable wind regimes during storms and hurricanes [55,56].

Table 2 Summary of lab wave data (prototype values).

The JONSWAP spectra can be formulated using shape parameters through the alpha and gamma coefficients,known as scale pa-rameter and peak enhancement factors respectively.The alpha and gamma parameters can also be calculated through the dimensionless relations of the peak frequency.However,the scatter in the values of alpha and gamma shape parameters are wide,and as a result an accurate correlation with the dimensionless fetch cannot be produced [57].The JONSWAP spectrum with a default gamma value of 3.3 (in SWAN) has been used in all the scenarios of the present study.

Fig.4.2D Frequency vs Energy spectrum Scenario 1,location 1.

2.3.Description of model

SWAN (Simulating WAves Nearshore) model was first introduced by Booji [58].SWAN (Simulating WAves Nearshore) is an open source,freely available,computer model that is used widely by scientists and engineers for research and consultancy practice to obtain the realistic estimates of wave parameters.Using the linear wave theory and the conservation of wave crests,the wave propagation velocities in spatial within Cartesian framework and spectral space are described by the kinematics of a wave train.The processes of generation,dissipation and nonlinear wave-wave interactions are represented explicitly with state-of-art formulations.This also makes the SWAN model a so called third-generation model.In contrast to the other third-generation wave models,the SWAN model is based on implicit propagation schemes.An advantage of this implicit scheme is that the model is very robust in practical coastal applications.Also,the model has the potential to represent wind induced wave growth,dissipation of wave by white capping and bottom friction,three and four wave non-linear interactions,refraction,and wave breaking [59].The governing formulation of SWAN in Cartesian co-ordinates is shown in Eq.1.

Here,σ=radian frequency (as observed in a frame of reference moving with current velocity),N=wave action density which is equal to energy density divided by relative frequency (N=E/σ),θ=direction of wave propagation,C=velocity of wave propagation in (x,y,σ,θ) space,and Stot=non-conservative term expressed as wave energy density.

Wave energy density is used to represent all physical processes,which generate,dissipate,or redistribute wave energy.The implicit upwind scheme was used in SWAN model to wave action density propagation,which has the great advantage that the propagation time step is not limited by any numerical condition since the scheme is unconditionally stable in the geographic and spectral spaces [59].In SWAN DHH GUI interface the values of wave parameters,water levels,wind data,information about obstacles were provided.In the present study,water level of+2 m,wave parameters are considered whereas there is no wind,current and no obstacles were considered.Obstacles in SWAN are narrow artificial objects such as breakwaters that partly or wholly block wave propagation.The model is often used to optimize breakwater design(location,cross-section).The location has to be given by means of coordinates of points along the axis of the structure.The computational grid covers the entire input grid region with the same origin and the waves have been imposed on the northern boundary,as it was on the northern boundary the wave maker was located in the laboratory test.

In present study,location 4 was used to input the parameters and remaining 9 (nine) individual locations were used to provide output.These output locations are same as in Taehun [53]except location 3.The location no 3 of Taehun [53]lies outside the domain of the computational grid.Hence,no comparison will be done for location (No 3).Apart from location 3,all other locations are same in Vold and Lothe [52],where wave gauge data were recorded for the Mehamn Harbour studies.After the simulation,a wave spectrum is obtained at all the locations of output.For convenience the spectrum for scenario 1 at location 1 is shown in Fig.4.

In the output,a plot of entire study area showing the significant wave height with the wave direction and mean wave period at each location of the computational grid for scenario 1 are shown in Figs.5 and 6 respectively.

3.Result and discussion

The wave heights obtained from the lab data and SWAN model were considered as input at location 4 (four).The MATLAB was used to analyse spectrum parameters.The analysis resulted in a zero down crossing and a zero up crossing plot for each wave scenario.There are 22 (twenty-two) such plots are used as inputs at location 4.A representative plot of the zero down crossing analysis for scenario 1 is presented in Fig.7.The plots for all other different locations and scenarios of both zero up crossing and zero down crossing analysis are determined similarly.

Fig.5.Significant wave height plot with direction of the study area.

Fig.6.Mean wave period plot of the study area.

The input parameter used at location 4 (four) in SWAN model and lab data wave heights were plotted in Fig.8.

3.1.Comparison of the results: lab data and SWAN model

The results obtained from SWAN DHH model are compared against the lab results of Mehamn at 8 (eight) different locations.The wave condition at location 4 (four) is used as input conditions for all the 22 (twenty-two) different scenarios.The results obtained from SWAN were compared against those obtained from the Mehamn lab data at 8 (eight) different locations.The location 3 lies outside the domain so it has not been compared,and location 4 has been fed as an input to the model hence not shown in the plot.The comparison of significant wave heights’ results obtained at different wave gauge locations using SWAN with the Lab data for all the 22 scenarios are shown in Figs.9-16.

Fig.7.Zero down crossing analysis for test 1,Location 4.

Fig.8.Plot of SWAN model input and lab data at location 4 (input location).

3.2.Comparison of the results: lab data,SWAN,MIKE 21 BW and STWAVE

Taehun [53]performed the numerical analysis by MIKE 21 BW and STWAVE conditions with four scenarios as shown in Table 3.

Fig.9.Comparison of results at wave gauge location 1.

Fig.10.Comparison of results at wave gauge location 2.

Fig.11.Comparison of results at wave gauge location 5.

These simulation scenarios are different from the lab results obtained by Vold and Lothe [52].It is also observed that the Taehun [53]input to these scenarios was different from that has been taken in the study of Vold and Lothe [52].However,the outputs of MIKE 21 BW and STWAVE in conditions 1 and 4 at location 4 are very closed to present study scenarios 18 and 4 respectively.The cases 2 and 3 from Taehun [53]are not compared with the results of SWAN and lab data because the results themselves differ a lot and no suitable simulation scenarios from Vold and Lothe[52]are found.Therefore,significant wave height at all the eight locations is obtained for scenario 18 and 4 for comparing the performance of the models in predicting the significant wave heights over a rugged topography.Table 4 and 5 summarize the results for scenarios 18 and 4 respectively.

Figs.17 and 18 show the comparison of results obtained by SWAN,MIKE 21 BW and STWAVE with the lab data for scenario 29 and scenario 16 respectively.

For the test Cases 2 and 3 of Taehun [53],the analysis is performed again,and their results have been compared against MIKE 21 BW and STWAVE results.The input parameter of SWAN model is kept same as output obtained at location 4 of Taehun [53].Table 6 and 7 summarize the results for these two scenarios i.e.,Test Cases 2 and 3.

Fig.12.Comparison of results at wave gauge location 6.

Fig.13.Comparison of results at wave gauge location 7.

Fig.14.Comparison of results at wave gauge location 8.

Figs.19 and 20 show the comparison of results obtained by SWAN,MIKE 21 BW and STWAVE for Case 2 and Case 3 of Taehun [53]respectively.

3.3.Sensitivity analysis

Sensitivity analysis for SWAN model has been tested for three different cases.First one is introduction of bed friction;second is having more than one boundary condition on the north boundary and the third one is the use of triangular mesh instead of regular rectangular grids.

3.3.1.Introducingbedfriction

Fig.15.Comparison of results at wave gauge location 9.

Fig.16.Comparison of results at wave gauge location 10.

Fig.17.Comparison of results using SWAN,MIKE 21 BW,and STWAVE with Lab data for scenario 29.

Generally,the Hasselmann et al.[55],Collins [1],and Madsen et al.[60]formulation are used for bed friction in SWAN model sensitivity analysis.However,the JONSWAP formulation is used with a constant friction coefficient or with a varying friction coeffi-cient that depends on the frequency-dependant directional spreading in present study.In the other formulation the friction coeffi-cient is set to 0.038 m2s-3for frequencies with directional spreading lower than or equal to 100 and it is set to 0.067 m2s-3for frequencies with a directional spreading higher than or equal to 300.For intermediate values of the directional spreading the friction coefficient varies linearly between these two values.The JONSWAP friction formulation is used in the present study.The analysis is performed using SWAN standalone model and their results are computed at all the output locations for scenario 18 with and without friction in Table 8.

Fig.18.Comparison of results using SWAN,MIKE 21 BW,and STWAVE with Lab data for scenario 16.

Fig.19.Comparison of SWAN result with MIKE 21 BW and STWAVE Case 2.

Table 3 Shows the four scenarios reported by Taehun [53].

Table 4 Comparison of lab data,SWAN,MIKE 21 BW,and STWAVE model results for case 1.

Fig.20.Comparison of SWAN results with MIKE 21 BW and STWAVE Case 3.

Table 5 Comparison of lab data,SWAN,MIKE 21 BW,and STWAVE model results for Case 4.

Table 6 Comparison of SWAN,MIKE 21 BW,STWAVE model results for Case 2.

Table 7 Comparison of SWAN,MIKE 21 BW,STWAVE model results for case 3.

Table 8 SWAN model sensitivity analysis with friction.

The difference between two cases is very less almost negligible,which indicates that current SWAN model setup is not sensitive on introduction of bottom friction.

3.3.2.Morethanonewaveconditionontheboundary

The SWAN model performance is tested with different boundary conditions rather than one constant boundary condition.For the present test,Scenario 18 was chosen and compared with default value of only one boundary condition.The north side of the domain was considered as boundary with wave conditions of wave gauge number 4 of scenario 18 in Vold and Lothe [52](Hs=3.38 m Tp=15.09 s).In new case,two boundaries were chosen,one going from (-44,600,1,454,800) to (-44,321,1,454,800) m on the northern boundary having wave conditions of wave gauge number 4 of scenario 18 in Vold and Lothe [52](Hs=3.38 m Tp=15.09 s).The other boundary was given from (-44,321,1,454,800) to (-43,400,1,454,800) having wave conditions of wave gauge number 3 of scenario 18 in Vold and Lothe [52](Hs=3.29 m Tp=15.09 s).The SWAN standalone model performance results were computed at all the output locations for scenario 18 and shown in Table 9.

Table 9 SWAN model sensitivity analysis with boundary conditions.

Table 10 Comparison table of significant wave height obtained using regular and unstructured mesh with lab data.

The difference between two cases is not negligible which indicates that current SWAN model setup is sensitive on introduction of more than one boundary condition.This means having real boundary condition (line boundary) in SWAN setup rather than having a representative point being used as line boundary will give better results.

Fig.21.Plot of Significant wave height using unstructured triangular mesh.

3.3.3.Useoftriangularmesh

The regular rectangular computational grid has been used in last several decades.However,triangular computational meshes in place of regular rectangular grids are used in this study.The computations have been performed in SWAN standalone version.The triangular (unstructured) meshes provide much better representa-tion of complex boundaries such as coastlines and areas around islands than do conventional regular grids and also provide the opportunity to concentrate mesh resolution in areas of interest like regions of strong bathymetry variations in estuaries and fjords,to a degree not possible on a curvilinear grid.Hence,there is no need for nesting.The triangular mesh is generated throughout the study area.The unstructured (triangular) meshes were implemented in the model for the sensitivity analysis.The scenario 18 of Vold and Lothe [52]was selected and compared against the results obtained using regular and unstructured meshes.The SWAN unstructured mesh was used as shown in Fig.21.

The resolution of the triangle side was of the order of 10 m.Hence,SWAN model with regular grid resolution was analysed again with resolution of 10mx10m.The result obtained from the analysis was compared against the regular computational grid.The comparison between the triangular and rectangular mesh against the lab data was shown in Fig.22.

Further,the significant wave height obtained using regular and unstructured mesh with lab data is presented in Table 10.

There was very less or negligible difference in the result of regular structured grid and unstructured grid of significant wave height.Also,the results of regular and unstructured grid were compared against the lab data of Vold and Lothe [52]and very less difference in the significant wave height was obtained.

Fig.22.Comparison plot of significant wave height obtained using regular and unstructured mesh with lab data.

3.4.Discussion of results

For case 1 and 4 of Taehun [53],the results obtained from SWAN model are very close to lab results (physical model).Their results are compared against the results of MIKE21 BW and STWAVE model.The results from MIKE 21 BW and STWAVE model are also close but at some locations,there is a clear mismatch from lab results.This may occur due to different physics used behind the models.Also,there is a difference of bottom friction in MIKE 21 BW and STWAVE,white capping could be the probable reasons.For cases 2 and 3 of Taehun [53]result of SWAN model are compared to MIKE 21 BW and STWAVE model.There is no any other scenario discussed in Vold and Lothe [52]to match these cases.The results of SWAN and STWAVE model are close at some points and different at others.No specific reason could be given for this finding as results of MIKE 21 BW and STWAVE did not follow a pattern.Difference in model settings could be one of the reasons.It is also noticed that SWAN results give a higher value near the north boundary and starts getting very close to the lab results when we move away from the boundary.The reason of a little higher value of Hs cannot be attributed to dissipation due to friction as tested out in model sensitivity analysis.Other model parameters settings could also be attributed to slight mismatch in the results obtained from SWAN and lab test.

Sensitivity analysis on more than one boundary conditions indicate that better results are obtained if we give a more realistic boundary condition rather than a representative boundary condition of one point to the entire boundary line.The sensitivity analysis with use of unstructured mesh indicates that better results are obtained at some locations compared to the regular grids.The difference between the results is less but a better pattern is obtained with unstructured mesh than a regular rectangular grid.The advantage of unstructured meshes over conventional regular grid is to provide much better representation of complex boundaries such as coastlines and areas around islands.They also provide the opportunity to concentrate mesh resolution in areas of interest like regions of strong bathymetry variations in estuaries and fjords.

4.Conclusions and recommendations

The problems involving the diffraction of surface waves by vertical barriers have been drawing a great attention of many researchers because of their engineering applications such as wave makers and breakwaters which protect a harbour from the rough sea [61,62].The implementation of phase decoupled refractiondiffraction approximation in SWAN model enables their application to simulate wave transformation over irregular or uneven bottom topography and provides better results [63].In addition,SWAN seems to produce the most smoothed distribution of wave height along the direction perpendicular to wave propagation.The obtained results indicate that the SWAN model results are in close match with the actual lab data results as compared to MIKE 21 BW and STWAVE model.However,the SWAN model can even be fine-tuned to get much better results.Instead of using single point wave data as the boundary condition a line boundary could be used in SWAN model to get better results.

As demonstrated in sensitivity analysis,for a real simulation,an attempt should be made to refine the mesh with triangles rather than rectangular grids.Use of unstructured grid could be one of the methods which latest version of SWAN model is capable to support.The use of unstructured grids facilitates to resolve the model area with a relative high accuracy but with much fewer grid points than with regular grids.Although,the CPU cost per iteration is relative higher than cases with structured grids (as is often the case),this effect is more than offset by the reduction in the number of grid points.Also,bottom friction could be included in the setup for a more realistic estimate of wave transformation.The results from SWAN model suggest that it is able to model phenomena of refraction,shoaling,diffraction and reflection to some extent.However,the model needs to be developed properly for reflection phenomenon.To have a proper understanding of reflection phenomenon a wave data investigation just near the land boundary or an obstacle needs to be carried out,which can be compared against the SWAN model results.

In the present study,only a serial computation is carried out for SWAN unstructured meshes.This means that parallel simulations on both shared and distributed memory platforms are not possible for unstructured grids.Parallelization of SWAN model using unstructured grids is under way.Therefore,attention should be paid to the optimization of mesh size to avoid errors due to lack of computational capacity of the computer.

5.Funding

Sponsored Research and Industrial Consultancy (SRIC),Indian Institute of Technology Kharagpur.

Declaration of competing interest

The authors declare no conflict of interest.

Acknowledgments

This work was carried out as part of the Institute Scheme for Innovative Research and Development (ISIRD) program from IIT Kharagpur.