Indian Journal of Marine Sciences
Vol. 18, September 1989, pp. 184-188
Wave refraction and longshore current patterns along Calangute
beach (Goa), west coast of India
V Krishna Kumar, C S Murty & S S C Shenoi
National Institute of Oceanography, Dona Paula, Goa 403004,
and
India
AKHeblekar
Ponda Education Society's College of Arts & Science, Farmagudi, Ponda 403405,
Goa, India
Received 19 September 1988; revised 2 June 1989
Waverefraction studyfor most predominant waveswith 6, 8, 10and 12sec period and approaching from
directions WNW,W and WSWhas been carried out along the Calangute beach. The energy distribution and
probable longshore/offshore current pattern are qualitatively assessed. The degree of refraction is less and
no abnormal energy concentrations occur along this stretch. The waves after breaking giverise to many opposing flows forming circulation cells along the entire stretch. Zones of quasi-permanent rip currents are
identified at Calangute and Candolim sections for 10 sec period waves approaching from WNW and W.
The waves from deeper water when approach the
shore undergo refraction due to variations in bottom topography and break at the coast giving rise to
longshore and onshore/offshore flows. An analysis
of wave refraction thus becomes important as it determines the nearshore circulation pattern and also
the wave energy distributions along the coast. This
is the principal source of energy which controls the
erosion/accretion or overall stability of the coastline, sediment transport, etc. The present study is
made to understand wave energy and wave height
distributions and probable longshore current patterns at Calangute beach, Goa.
Calangute beach is 7.5 kIn long sandy and almost
straight and is well known for its stabilityl. The bottom contours here run almost parallel to the coast.
Medium to very fine sands cover the sea bottom up
to 8 m of water depth and beyond that silty clays
prevaiF. Antony3 has studied wave refraction, rip
currents and sediment transport along Calangute
beach using graphical method. Murty et al.4 have
carried out field observations in this area to measure
the littoral currents in the surf zone. The shoreline
dynamics, longshore currents, sediment transport,
etc. have also been studied along Calangute beach
earlierl,2,5. The present study has been carried out
using numerical method of wave refraction using
computer, which supports the location of permanent rip current zones identified in the earlier studies but has clearly demarcated more number of rip
current zones.
184
,I
II
Materials and Methods
Bathymetric chart Nos. 2022 and 215 (N H O.
corrected up to 1977 and 1984 respectively) have
been used for the present wave refraction study. In
order to satisfy the deep water conditions of aU predominant waves which have to be studied, the deep
water limit of computation has been fixed around
120 m of water depth. Care has been taken to
choose the grid boundary on the other 2 sides so as
to accomodate even the extreme wave directions.
Each grid has a size of 900m x 900m in the deep
water, but when traced towards the shore, this grid
size
has
been
considerably
reduced
to
300m x 300m to obtain maximum accuracy within
the limits of computation. The depth values, digitized at every grid point, form the primary input data
for the analysis. Nine arbitrary stations are fixed approximately 800m apart for the convenience of understanding the areas of higher and lower energy levels along this stretch.
The waves coming from MNW, W and wsw with
periods 6, 8, 10 and 12 sec are predominant6,
of
which the 10 sec period waves are more frequent
throughout the year. Wave refraction diagrams for
the above waves have been constructed following
the numerical method7 on IDC 316 and ND 520
computers. The wave refraction diagrams for 10 sec
period waves approaching from MNW, W and
WSW are prepared. The refracted orthogonals are
traced from the deep water limits towards the shore
but the part of the refracted orthogonals from 15 m
KUMAR et aL: WAVE REFRACTION
depth contour are only shown in the figures. To examine the energy concentration/angle of approach of
the waves, the direction function (O')-which is defined as the angle subtended by the wave ray to the
normal drawn to the shoreline-and
the refraction
coefficient (K1) are presented for all predominant
waves. The wave height (h) is calculated along the
ray paths using the relation h = ho Kl K2, where K2
is the shoaling coefficient and ho is the deep water
wave height, assumed to be 1 m in the present study.
These wave heights are transferred into grid points
using 2 point Lagrangian interpolation and contoured for equal wave heights at intervals 0.05 m and
only 10 sec period waves are presented. The locations of wave breaking have been found using the
relation8 hb = 0.83 db where db is the depth of wave
breaking and hb is the breaker height. The probable
longshore/offshore flow directions deduced from
the wave refraction diagrams and wave height distribution along this stretch for 10 sec period waves
for the three different directions are also presented.
Results and Discussion
The rays traced from deep water for 10 sec period
waves for all 3 directions, WNW, W and WSW (Fig.
1, a-c), show no abnormal wave energy concentrations along this stretch. The orthogonals show refraction of no significance beyond 10 m contour
(but slightly refract towards the shore). This is because of the nature of the bottom topography which
runs almost parallel to the coast. At st 3, close to the
coast, bottom contours bulge slightly offshore. Irrespective of the wave directions, orthogonals converge near st 3 giving rise to higher wave energy levels, while at the sides of this (near sts 2 and 4 ), there
are zones of divergences giving rise to areas of low
wave energies. The waves approaching from west
experience least refraction as they are near normal
to the shore. One can notice that the areas of convergence shift considerably when a change in the direction of wave occurs ..
The refraction coefficient (K1) is distributed
around 1 along the study area irrespective of the period and direction (Fig. 2) which indicates the absence of abnormal energy concentrations. There is a
slight tendency for WNW waves to refract towards
south (maximum 0' = 20°) while the waves from W
refract irregularly showing no tendencies in particular. But the WSW waves show a northward tendency
(maximum (J = 30°). Aclose look at the wave orthogonals reveals that in general, the waves approaching this coastline, irrespective of their deep
water directions, after the refraction over the shal-
& WNGSHORE
CURRENT PAlTERNS
.
Ill,
54
N
.~
..•.
,
'\ ,
,
.
"
t
~
~
~
.•.
CUM
,
\
T
i'
...-;.
~,
•
~-----
-
Fig. i-Wave refraction diagrams for waveS approaching from
(a)WNW.(b)Wand(c)WSW[Pw
= (Osee)
185
INDIAN J MAR SCI, VOL. 18, SEPTEMBER
DIR ECTION
D.=WNW
F UNCTlON
C
o 11'0
0'5
10 S0-5
1.51
o
10
20 1.5!
0
CK,'
30
'
~
...
,J
,
"!.s ••. ""
• .r..••..
N 1'0
_--, --",
....•.
, -,: t: 10'5
.....
.......•.
--~;..........,
',,' '\
~
.•
\~,
,'II'
• ' •••••
o
20
10 N
o
t
10 S
•......••
10 S 1.51
0
0." WSW
WNW
p.=8Sec.
~
COEFFICIENT
20
1-0
:x:
REFRACTION
D.'WSW
p. = 6 Sec.
D••
e', - ----
1989
i
10 N
o
1'0
10 0'5
20 1'5[
0
1'0
Q 0-5
-~
~ 1.51
0
j=
,'';',
'
Pw"lISec.
...
10()
to'1I
t30I.51
10 S 0
L--lo
I'
"
' ,.\\
"
\" '
,,'~'
~ ----.....
.•
l \ "'"'-'\ I,
"
oU
l.I.I
t 1'0
10 N
10 S 0
U 0'5
o
f:=
20
« II":~
~
to'5
10 N
t;
j30
10
.
.~
P .12 I' Sec .
•
,,,,
l.I.I
a:
1'0
S 1'0
O'll
10 S 0'11
1.5!
o
Z
0
ot~
S0
j:10 S 1.51
0
N I'~0
~ 0
/0()
20
•........•
I 2
•
I
34587
•••
STATIONS
Fig. 2-Refraction
I
••
I
~o
20N
0
l'lI~
I'
I'
•........
.,•........•
./'
L--lo
I
2
.....
3411878.
STATIONS
,
\,.,.1
10 N 1-0
o to-II
10 S l.lIl
0
j=
~.."
\
D.'WSW
"
,,-.
I' I1
~
~~~587.'
20
\
ION
v,
••••
0
130
10 S
t
STATIONS
coefficient (Kt) and direction function (9') for waves approaching fromWNM, W and WSW (Pw= 6,8,10 and 12
see)
low shelf have a tendency to refract towards north
or appear to be coming from southerly quadrant.
The wave heights are distributed from 0.9 to 0.95
m at around 15 m of water depth and show a gradual
increase towards the shore in all the cases of wave
approach (Fig. 3a-c). There is no abnormal increase
in the wave height as the maximum wave height occurred is only 1.3 m. The zones of higher and lower
wave heights occur almost alternately but with an
uneven spacing along this coast. This assymetric distribution of wave heights give rise to flows along and
across the shore9• From the regions of high wave energy, water may flow to the areas of low wave energy
to maintain equilibrium, thus generating longshore
currents. These currents may even flow against the
waves when they turn seaward in the areas of divergences as rip currents. The probable longshore/offshore currents generated by refraction of waves/
wave height distribution are presented in Fig. 4 for
10 see period waves for 3 different directions. This
qualitative presentation of the alongshore currents
clearly shows that the flow sytem existing along this
coast is not a simple one and there must be a number of circulation cells existing alongwith meandering flows depending on the direction of wave approach. Near sts 4 (Calangute) and 6 (Candolim)
186
''
,~''''- '. " ,
/\"
/'/"
there are quasi-permanent zones of rip currents for
the waves approaching from WNW and W.
Eventhough these rip current sites are more or
less permanent for both the wave directions, the intensity of these rip cells might be different along and
normal to the shore. From Fig. 4 it is evident that the
rip current zone near st 6 (be) has a wider spread
compared to the one near st 4 (a).
Antony3 in his wave refraction studies through
graphical method along this beach reported that
there are certain zones of wave energy concentrations and the longshore currents during a particular season depend mainly on the direction of the
predominant waves. He has identified zones of rip
currents near Candolim and Baga during monsoon
season and also reported that the rip currents near
Candolim are active during fair weather season also.
Murty et al.4 through their field observations made
in different months using dyes, located several rip
zones along this beach. They also have observed
that the part of the beach between Calangute and
Candolim is more vulnerable to rip currents. Murty
and Veerayya5 while studying the longshore currents and associated sediment transport in the nearshore areas of Kerala and Goa, mainly through
wave refraction diagrams, reported a number of cel-
(
"
KUMAR et aL: WAVE REFRACIlON
& WNGSHORE
CURRENT PAlTERNS
P,,- 1I5ec
II" - WIllI
"'7\
A?~\
•. t~
,.,
\,
,
,,
10:
fl.
==.
,
•• SIIllIlEM'l
~I~~~
,
,,
uS
-
Rip
arnnt
Z •••
Fig. 4-Probable longshore current directions for 10 sec period
waves approaching from WNW, W and WSW [Areas near st. 4
(a) and st. 6 (be) show zones of quasi-permanent rip currents]
.
--&rukerlk'lt:
10,
29
N '
~~f~·m
©
')
,
,,
,,
US~
lular patterns of flows for waves of near normal incidence while meandering flows-either in an up
coast or down coast direction-for waves approaching the shore from a direction different from the
normal to the shore. In general, these studies reveal
the fact that the longshore current directions are
highly variable along this coast supporting the present study. The zones of rip currents identified earlier are almost the same as found in this study. But it
is· noticeable that more number of rips have been
observed in this study cOII}pared to the earlier studies. The numerical method of wave refraction using
computer, followed in this study, is much more precise and reliable compared to the graphical method
followed in the earlier studies.
Acknowledgement
The authors wish to thank Dr J S Sastry for his
keen interest and encouragement.
References
1 Murty C S, Studies on physical aspects of shoreline dynamics
at some selected places along west coast of Indio, Ph D thesis,
University of Kerala, 1977.
187
INDIAN J MAR Sel, VOL. 18, SEPTEMBER
2 Veerayya M, Studies on the geological aspects of the beaches
of Goo in relation to some meteorological and physical oceanographic factors, Ph D thesis, Andhra University, 1978.
3 AntonyMK, IndianJ MarSci, 5 (1976) 1.
4 Murty e S, Veerayya M & Varadachari V V R, Indian J Mar
Sci,4(1975) 1.
5 Murty e S & Veerayya M, Mahasagar - Bull Natn Inst Oceanogr, 18 (1975) 163.
6 Varkey M J, Kesavadas V. Narayana Swarny G. Joseoh P S &
Sastry J S, Wave (sweln Atlas for Arabian Sea and BayofBengal (National Institute of Oceanography, Panaji, Goa, India)
1982.
188
I'
1989
7 Mahadevan R, Numerical calculation of wave refraction, Tech
Rep No 2/83 (National Institute of Oceanography, Panaji,
Goa,India) 1983.
8 Galvin e J, in Waves on beaches and resulting sediment transport, edited by R E Meyer (Academic Press, London) 1972,
413.
9 Longuet-Higgins M S, in Waves on beaches and resulting sediment transport, edited by R E Meyer (Academic Press, London) 1972, 203.