Simulation of Wave Propagation along the Northern Coast of...

Simulation of Wave Propagation along the Northern Coast of Santa Catarina,Brazil

INTRODUCTION

It is well known that the wave characteristics along thecoastline result from initial conditions of deep water and fromtheir transformation in shallow water under bottom influence.The changes in wave direction imposed by refractive effects canproduce energy convergence or divergence along the coast,with respective increase or decrease in wave break height.Diffractive effects around an obstacle to wave propagation, likecoastal islands and seaward basement protrusion, equallycontribute to the wave energy longshore distribution. Thepotential energy and incident angle at break point representdeterminer factors for the generation of nearshore fieldcurrents, responsible for sediment transport on coastal zone.

Several beaches along the central-north coast of SantaCatarina State, southern Brazil, present accentuated erosionprocesses ( , F. G. 1998; ., 1999; , M.C. and , R. J., 2000). Effects of urban development andengineering structures are observed. These human interferencesoften reveal natural susceptibility to beach erosion, related togeological coast context, and the characteristics of wave energyon the coastline. One of the hypothesis to explain theserecurrent erosive processes in the study area would be theoccurrence of convergence energy zones along the coast,resulting from wave pattern transformations of incident wavesover the adjacent continental shelf.

This paper presents the results of an application of waverefraction and diffraction model on the northern portion ofSanta Catarina coast. The aim of the study is to identify thelongshore wave energy distribution and to better understand itscontribution to erosive processes observed on this coastlinearea.

The northern part of Santa Catarina coast, southern Brazil, isa wave dominated coastline with northeast-southwest general

orientation characterized by predominantly linear exposedsandy beaches (Figure 1). With 60km long, this coastline is onlyinterrupted by the Babitonga's estuary, a few river canals andsome blocks of the Crystalline Basement. This coastal areaincludes, from south to north, the beaches of Barra Velha, Barrado Sul, Praia Grande, Saudade's beach and Enseada/Ubatuba atSão Francisco do Sul Island and Itapoa's beach. Composed bypredominant quartz sand, these beaches present two majordistinct sectors concerning morphodynamic characteristics.The beaches southwards Saudade's beach are generallyintermediate with predominance of medium grain size. Towardsthe north, from this point, they are considered dissipative,composed of fine grain size ( de .,1997).

The continental shelf morphology is characterized by a lowslope bathymetry. Some features like marine terraces,paleochannels and beachrock lines are also observed (Greand de , 1998). A set of small coastal islandscan also be seen near the coastline.

The local tide is semi-diurnal and microtidal type with amean range around 0.7 m ( , 1998). The wave climatein the region is represented predominantly by southeast and eastswell incidence associated with cold fronts passage in the

HOEFEL KLEIN SOUZAANGULO

ABREU CASTILHOS

ABREU CASTILHOS

TRUCOLLO

et al

et al

STUDY AREA

Journal of Coastal Research SI 39 1638 - 1642 ICS 2004 (Proceedings) Brazil ISSN 0749-0208

J.Abreu de Castilhos†; M.A. R. Romeu‡ and J.C.R. Gré†

†Departamento de GeociênciasUniversidade Federal de Santa Catarina, FlorianópolisCEP. 88040-900 SC [email protected]@cfh.ufsc.br

ABREU DE CASTILHOS, J.; ROMEU, M. A. R. , and GRE, J. C. R., 2006. Simulation of wave propagation alongthe northern coast of Santa Catarina, Brazil. Journal of Coastal Research, SI 39 (Proceedings of the 8th InternationalCoastal Symposium), 1638 - 1642. Itajaí, SC, Brazil, ISSN 0749-0208.

Several oceanic beaches along the northern coast of Santa Catarina State, southern Brazil present accentuatederosion processes. The wave climate in the study area consists of southeast and east swell incidence associated withcold fronts passage in the region, and northeast wave direction. The potential energy and incident angle at breakpoint represent decisive factors for the generation of nearshore field currents, responsible for sediment transport oncoastal zone. This paper presents the results of an application of wave refraction and diffraction model in the studyarea.Aseries of simulations was performed including the three main oceanographic scenarios for the region. Resultsof simulations showed the development of convergence energy zones, mainly associated with lower wave frequencyfrom SE and east wave direction. Under less energetic wave conditions, linked to east and northeast wave incidence,a more homogeneous distribution of break wave height along the coast was observed. The incident angles at thebreak point result in a longshore current towards the south and the north under southeast and northeast waveconditions, respectively. Predictions for wave incoming from east showed the absence of longshore current or theoccurrence of oscillating vectors towards both directions. Convergence zones of energy along the coastlineassociated with incidence of energetic oblique waves could be in the origin of intense erosion processes that takeplace in the region.

ADDITIONAL INDEX WORDS: Wave refraction-diffraction, REF/DIF model, southern Brazilian coastline

ABSTRACT

‡ LHAIMAR -Departamento Eng. Sanitária eAmbientalUniversidade Federal de Santa Catarina, FlorianópolisCEP. 88040-900 SC [email protected]

Journal of Coastal Research Special Issue 39, 2006,

Figure 1. Study area.

region, and northeast direction for sea conditions ( ,1996). According to this last author, annual significant waveheight in the region is 1.0 m, but under storms conditions thewave height can reach maximum values of 3.00 m.

The REF/DIF 1 model and , 1986) wasused to simulate wave transformation on the continental shelfadjacent to the study area, including physical process of waverefraction and diffraction The applied model here is based onthe parabolic approximation of the mild slope equation of

(1972), and describes the transmitted wave field of amonochromatic wave in a predominant direction. This modelcharacteristic presents limitations to simulate the wave climatein nature, represented by a wide range of frequencies anddirections Some studies also showed that, due to its highsensitivity to seafloor perturbations, monocrhomaticapproaches tend to both underestimate and overestimate locallythe wave heights ( and , 1989;

., 1990; and , 1991).In order to surpass this model difficulty and provide a more

realistic wave modeling, the monochromatic results can becombined in order to simulate the directional wave spectrum toa given region ( and , 1993). To different waveconditions a specific directional spreading function wasapplied, according to (1985). In the simulations ofdirectional spectrum, to each frequency used, a principal andfourotherdirections around this last wereconsideredwitha= 5°.

The bathymetric grid to study area was obtained fromnautical chart number 1800, 1830 and 1804 (Brazilian Navy)and covered an area of 70 x 120 km with a total of 1022051points with spacing to and of 140m (Figure 2).

Aseries of model simulations was performed including threemain oceanographic for the region, presented by (1996):southeast, east and Northeast wave conditions. A total of 30simulations were performed in order to analyze the field wavevariations on studied sector and mainly to determine the wavecharacteristics in the breaking point under different wave

conditions. High and mean range of energy for each typicalscenario modeled was considered. For incoming wave fromsoutheast, east and northeast, the wave periods used were 10 sand 15 s, 8 s and10 s and 6 s and 8 s, respectively.

Due to the important contribution of southeast swell to thenearshore field currents, in the study area, a third condition ofminimum energy was also considered, with a period of 6.0s.

The results of the simulation on wave propagation in thestudy area are presented in refraction-diffraction diagrams. Theanalysis of the variation concerning the spatial wave energy(Hs) shows that the refraction effects are weak in the presence ofhigh-frequency swells, represented by periods of peaks of 6s.For southeast and east-northeast simulations, the refractiveeffects occur only above 10m of depth near the coastline,resulting in a more homogeneous alongshore energydistribution. With the progressive decrease in peak frequency,the refractive effects increase considerably. In the simulationswith periods of 8s and 10s, under southeast and east swellconditions, the influence of the bottom occurs as from 20 and 40m deeps, respectively. The most important refraction processesare observed in the simulations of low-frequency wave forsoutheast swell with a peak period of 15s (see Figure 3a).

The increase of refractive effects produce convergence anddivergence zones of energy along the coastline, especially at thenorth and south of São Francisco do Sul Island. In these sectors,zones of concentration of energy are visible, mainly in Itapoa'sbeaches in the north. Such zones may be related to the presenceof irregularity in the local bathymetry.

The variations of refractive effects reflect the differentconditions of the regional wave climate. While the long periodsare related to swell conditions, associated with synopticconditions in South Atlantic, the shorter periods reflect localmeteorological conditions, with reduced fetch, generatingsmaller waves denominated as “sea” conditions.

The diffractive effects occur mainly next to the islands nearthe coastline, around São Francisco do Sul Island as well as theMorro da Esperança promontory between Saudade's andEnseada beaches (Figures 3a and 5a). A decrease in the waveheight is observed in these places, with a shadow zonegeneration, protected from incident swells.

Concerning the islands, a displacement of the shadow zonenorthwards or southwards is also observed under obliqueincidence from south-southeast or northeast waves.

The longshore distribution of the wave energy at thebreaking point is associated with the importance of therefractive effects on the continental shelf, resulting indivergence or convergence of energy along the wavepropagation, as well as diffractive processes near the coast. Theresults for the wave energy along the study area is presentedbelow, according to the three simulate scenarios of waveincidence.

In the simulation of SE swell of maximum energy (3.00m15s) the model predict wave heights at the break point (Hb)around 3,5 to 4,5m along all the study area, due to its highdegree of exposure in relation to this wave direction (Figure 3a).However, a relatively homogeneous distribution of greaterenergy along the São Francisco do Sul island is observed, whilein the Barra do Sul, Barra Velha, and Itapoa's beaches greaterwave heights occur locally, generating lateral gradients ofenergy distribution. Zones of low energy only occur locally,associated with more protected sectors of the coast, aroundislands and promontories in north part of São Francisco do SulIsland.

With the increase of the peak frequency and initial wave

ALVES

(KIRBY DALRYMPLE

BERKOFF

VINCENT BRIGGS PANTCHANGO'REILLY GUZA

O'REILLY GUZA

GODA

ALVES

METHODOLOGY

RESULTS AND DISCUSSION

etal

x y

2

Wave Refration

Wave Breaking Height (Hb)

Scenario I

.

.

Modeling of Wave Propagation and Southern Brazilian Coast

Figure 2. Detail map of bathymetry used to simulate the wavepropagation in the study area.


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height (1.5m - 10s), a more homogeneous field energy along thecoast is observed in response to refractive effects decrease. Thebreak height predicted by the model to this wave conditionpresented an average of 2.0 m along the study area (Figure 3b).Besides the greater homogeneity of the wave field on the coast,zones of energy concentration are also observed in thissimulation, with a similar pattern to the previous case

In the simulation of minimum energy event to southeastswell (0.5m - 6.0s) the refractive effects are practically absent.The model predicts breaking heights of about 0.75m along thecoastline, except the shadow zones between the islands and thecoastline, where the break heights are inferior to 0.3m (Figure

sector of Itapoa's beach is observed. This probably results fromboth sea bottom irregularities and the development of adivergence zone in Enseada beach, north sector of SãoFrancisco do Sul Island, associated with the predominance ofdiffractive over refractive processes in this scenario.

The simulation of east swell of maximum wave energy (1.5mand 10s), presented a similar result to the event of samemagnitude to southeast swells, with mean values of waveheights of about 2.0m at the break point. The spatial pattern ofenergy concentration zones is equally similar to the observed atthe southeast swell (Barra Velha, Barra do Sul, south andcentral-north part of Praia Grande, central sector of Enseada,and along of Itapoá's beach). However, in this case, a littledisplacement southwards of this concentration zones occurs, inresponse to the changes in the wave incidence direction. In theBarra Velha and Barra do Sul sectors, a spatial decrease in theenergy concentration zones is showed in this wave simulation,

as well as the appearance of another zone convergence towardsthe south. A reduction of the shadow zones close to the islandscan be seen in this simulation, followed by a decrease in thewave breaking heights in these places

With decrease of wave energy (1.0m and 8.0s), the results ofsimulation showed a wave breaking height distribution around1.3m along the study area, with peaks of 1.5m, and followingthe same spatial pattern of convergence and divergence ofenergy along the coast, as seen in the previous condition.

To the east-northeast simulation (1.0m - 6s), the predictedwave Heights at the break point reached about 1.2m to 1.3m,decreasing to 0.5m close to the island related to shadow areas.The change in the incident wave angles caused an expressivedisplacement of the convergence zones in Itapoá, Barra Velha,Barra do Sul, as well as in the central and south sectors of SãoFrancisco do Sul island. A spatial increase and a migrationsouthwards to the shadow zone of islands in front of PraiaGrande and in the north of Barra do Sul is also shown. In thisoceanographic condition one observes the persistence of thedivergence energy zone in the central and north sectors ofEnseada shown in the previous scenario, under low waveenergy.

Considering the general orientation of the coastline in thestudy area and the mean wave energy conditions to the threemain directions of incidence simulated, the higher the energyconditions, the higher the wave angle at breaking line. Thesevariations were equally identified inside each main direction,indicating the occurrence of variations in longshore currents

Scenario II

Scenario III

Alongshore WaveAngle Incidence (°)

.

.

3c). However, the persistence of the focusing effect in the south

Figure 3a. SE wave simulation: high level of energy (15s 3.0m).

Figure 3b. SE wave simulation: mean level of energy (10s 1.5 m). Figure 4a. East wave incidence: simulation of 10 s and 1.5 m.

Figure 3c. SE wave simulation: low level of energy (6s 0.5m).

Abreu de Castilhos .et al


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and sediment transport.The Figure 6 shows the obtained results concerning angle at

breaking wave along the study area. To southeast swells, theincidence angles present a mean value of 40 , indicating anorthwards littoral drift vector under this oceanographiccondition. With east-northeast wave incidence, the angles alongthe coastline presented values between 10 and 35 , and a meanvalue of 22 , which results in a southwards longshore transport.

To the east swell simulations, the angles at breaking pointoscillate between 0 and 10 along the coast, resulting in absenceof littoral drift and in the occurrence of vectors towards bothNorth and south direction.

Wave data obtained indicated a predominance of east andeast-southeast swells in the region - approximately 60% of theoccurrences-, followed by southeast swells, corresponding to27% of the observed oceanographic conditions ( , 1996).In this context, due to the low incidence of waves from the northquadrant, the resulting vectors of longitudinal currents indicatea northwards net littoral drift in the study area.

The northern coast of Santa Catarina presents a high degreeof exposure to the waves coming from southeast and eastdirections. In addition to these wave exposure conditions, the

characteristics of local bathymetry combined with refractiveeffects over the continental shelf produce convergence zones ofenergy along the coastline, as observed in the beaches of BarraVelha, Barra do Sul and Itapoá, and also in the northern part ofSão Francisco island. This wave energy behaviour in the regioncould explain the strong beach erosion observed in thesecoastline sectors. At Barra Velha, the convergence of waveenergy could be equally responsible for the overwash process

2001) that occurs in this place. On the other hand, theincidence of energetic oblique waves from southern quadrant isresponsible for the net sediment transport towards the north,which can promote local disturbance on sediment budget andcontribute to the erosive process in the study area.

The authors thank the Petroleo Brasileiro PETROBRAS forfinancial support to the development of thiwork and theDepartamento de Geociências/UFSC, as well as theLAHIMAR/UFSC for assistance and technical support.

o

o o

o

o o

ALVES

(CARUSO,

CONCLUSIONS

ACKNOWLEDGEMENTS

Figure 5b. Northeast wave simulation: 6s of period and 1.0 m.

Modeling of Wave Propagation and Southern Brazilian Coast

Figure 4b. East wave incidence: simulation of 8s and 1.0 m.

Figure 5a. Northeast wave incidence of 8s period and 1.0 m.Figure 6. Computed breaking wave angle in the wave climatesimulation.


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Proceedings of the 13th CoastalEngineering Conferenc

Coastal Engineering

JournalWaterway, Port, Coastal and Ocean Eng.

Journal Waterway, Port, Coastal and OceanEng.

In et al. Anais doSimpósio Bras i le i ro sobre Praias Arenosas:morfodinâmica, ecologia,usos, riscos e gestão

Maré meteorológica e forçantesatmosféricas locais em São Francisco do Sul SC.

Journal ofWaterway Port, Coastal and Ocean Eng

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