-
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.
Journal of Coastal Research Special Issue 39, 2006,
1639
-
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
Journal of Coastal Research Special Issue 39, 2006,
1640
-
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.
Journal of Coastal Research Special Issue 39, 2006,
1641
-
Proceedings of the 13th CoastalEngineering Conferenc
Coastal Engineering
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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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