shelf area off the southern Brazilian coast, is poor. However .... Axis. Direction. Angle. Bajor cm/s cm/s. Degree. Degree cm/s em/s. Degree. Degree. 5. 12.21.
Some hydrographicnl observations from three -chf; Brazilinn Shelf in the rep-ion Cabo-Frio-Ss.ntos,1966
Paper presented at the Intarnational Association of Ph~sical
OC8onopraphY9General
Asse~bly
IUGG
6erne,Switzerland Sente
*
Present
Address:~arine ::Tc~(+j~ll
Sciences Centre
1967~
IN 'rHO DUCTION The knowledge of the circulation, tidal currents and variation of other oceanographical parameters during a diurnal tidal cycle on the wide However, Johannessen {1966)
shelf area off the southern Brazilian coast, is poor.
has focussed attention on the possible existence of internal waves of tidal origi.n off the coast of
~)antos
•
V:hen the Brazilian Navy, with Gommandant
Pa1110;e Castro 110reira Ua '3ilva, very kindly offered the possibility of taking part in a cruLle with R/V 1Ii\.Lvnirante,':ialdanja ff , a time series study of temp-: rature, salinity, o:x.y-gen, phosphate and current measurements
were taken
during a 40-hour observation period at four different positions on the 3helf, SEe fig. 1.
I.n this preliminary report, current measurements and temperature
observations have beendealt with from three of the stations. OBSEHV(l.TION
and sal 70,HO and 90 meters, every were only taken every four hours.
2 hours.
However
The brackets indicate that the
measurements were not taken at all the stations. and 30 meters, and
other depths.
owever, the
Two !!..kman current meters
T .. S~K. current meters at the
.K. ones were difficult to operate, and due to
techni.cal problems some of the series are not complete. hourly values of the current measurements.. are supposed to be
W{C
the Brazilian
re call ected.
Table I gives the
The other oceanographical observations
by the drazilian
taken on board the It/V "Almirante
published
o.xygen and phosphate
The current measurements were carried out
at S-15-30-tSO), (70) and (90) meters.
Here used at
were taken at 0,5,15,20,
Heteorological observations
,;aldanja", with meteorological weather maps
avy, recorded sea levels a tttio de Janeiro and
,)an tos
..
l;'igs. 2-7 show the variation of \vind, currents, sea level and depth variations of selected isotherms at the different stations. current is superimposed on rotary tidal current.
Residual
The depth variation of the iso-
therms (also isohalines and isopycnels) show internal oscillations, as much as
a 30-meter range on St. !\, wi th the same period as the tide.
at -3ts. 3 and C these oscillations were less than half that of St ..
However, A.
At 0tS.
A
and G, long period trends in the depth variation for the isotherms do not seem to exist, but at St. B the 16° climbed to about 20-25 meters during the 40hour observations time, which indicates upwelling in the area. !t'ig.
t)
shows soroo characteristic temperature and salini ty profiles
for the different stations, and fig. 9 gives the TS diagram. )ts. Band at st .
.ti.
G
The profiles from
give about the same picture, but the condi tions are different
li'or the 'l'S diagram, the definition of the water masses, quoted from
~milson,
1961, has been dravm in, and it is clearly seen that the upper layer
at ;j·t.
is the Brazilian current, which in summer tiroo (0eptember-March) has
A
its western limit along the contour line of the edge of the 3helf. layer at Sts. 13 and
lj
represents the ,shelf water.
bottom layer consisted of sub-tropical water.
The upper
However, at all stations the
HARMONIC ANALYSIS
harmonic analysis on the diurnal and semidiurnal waves has been
.t1.
done for the currents, sea level and depth variations of the selected isotherms, and the tidal ellipses have been calculated.
Before performing the harmonic
analysis, an elimination of the non-harmonic variation was carried out by applying a filter given by .1t'jelstad ,1964, p. 23).
This fil ter is based on
taking 6 hours difference twice on a 36-hour run, lunar tiroo, resul ting in 24 values which are a combination of the hourly values. rulalysis is given in tables 2 and
The result of the harmonic
3.
J:I'rom table 2, it is seen that the grea te s t internal oscillations occur at ;jt. A.
The greatest amplitudes are in the boundary layer, decreasing downwards,
and the phase angles show relatively moderate variation with depth.
and the semi diurnal waves have the same magni tude.
The diurnal
The phase difference between
the sea level at Gabo Frio and the depth variation of the isotherms are
108.50 and 215.00 respectively for the
di urnal and semidiurnal waves.
Looking
at the cotidal line for the ~outh Atlantic (see Defant, 1961, vol. 11, fig. 207a, p. 502), it seems that there is not much difrerence in the water at 0t.
A
occurr~nce
of high
compared with Cabo Frio, and therefore the value at Gabo Frio has
been used representing 0t. A.
The phase difference, particularly for the
semidiurnal waves, seemed to fit quite well wi th the theoretical value of IdO
O
for a simple two dimensional two-layer model, and it seemed to indicate that internal waves of tidal origin exist. But the observed in ternal os to:.)e in ternal waves of tidal origin,
, which at first glance seemed also be explained if horizontal
gradients in the temperature, salini ty and density field exist, \ see Defant 1961, vol. 11, p. 537-51.+0)..
.t:,nUlson \1961) has established that such horizontal gradients
exist in a section from t;abo l:"rio towards the south-east, see fig. 10, which has been taken from .cIn.i1son (1961).
assuming that lele have a simple two-layer model,
.,.1,.,1__
DIURNAL Sea Level
Amp.
cm.
SEMIDIURNAL Phase Angle Degree
Amp. em.
Phase Angle Degree
6.94
145.6
20.18
178.4
St. A
Rio de Janeiro
13.69
0.8
17.90
277.5
St. B
Santos
l4.e1
207.1
57.04
330.5
St. C
Amp.
m.
Phase Angle Degree
Cabo Frio
Isotherms
°c
Amp.
m.
Phase Angle Degree
24
4.9
43.5
5.3
297.0
STA 22
5.9
25.9
6.4
321.e
20
3.9
20.2
4.7
337.7
18
0.7
61.7
3.2
319.6
16
2.2
34.4
1.6
340.9 )2).40
37.14
MEAN
24
2.9
244.6
0.6
t19.1
3TB 22
2.2
246.5
1.0
58.8
20
1.2
-.8
1.5
93.1
18
1.9
34.8
1.9
199.9
16
1.5
144.4
2.6
195.7 125.
192
lIlIEA:,
28
1.6
11~7 •
1.5
295.9
26
?o
185.8
0.9
248.0
STC 24
2.6
179
1.0
2
22
2.7
156.2
1
292.2
?O
MEAN
,,0
167.39
It
.5
DIURNAL
,,~
"" I
j
Ii
SEMIDIURNAL
Rotation Minor
0.38
4.62
37.2
327 .. 8
)0.1
87.0
e . G.
C.G ..
0.l39
0.56
Bajor
c.c.
0.46 12.31 11.01
Phase Direction Angle Degree Degree
347.4
c.c.
O.US
Rotation Minor Major Minor Axis Major Axis cm/s em/s
188.6 355.4
c.c.
Phase Direction Angle Degree Degree
4.61 166.4 36.2
Major Minor ! lDepth Axis Axis cm/s cm/s
12.21 ).70 165.2
0.57
2.26
2.88
8.85
-0.70
1.16
1.22
1.95
314.4
2)6 • .3
249.8
20).9
38.6
240.6
lLl.5
348.7
)58.5
109.8
C.. o.
c.
C.c.
c.c.
c.c.
0.)5
0.24
0.51
0.42
°,. ?L._
8.28
5 8.04 0.63
0.6)
2.96
1.82
0.)6
\--.--
St. A 15
10.67
0.50
5.26
c.c.
_
)0
2)7.8
303.1
-4.05 1274.6
347.1
6.41
41.60 27.10
15
5 St. B
189.3
I
0.74
209.1
0.54
)0
7.881 3.52
20.63 I1 16.13 . ,~-- . -+---------1-'-------264.6
,13.6
87.4
0.68
~---.
297.1
c.c.
0.52
c.c.
!
17.6
0.07
-,,~.-
225.6
-----1------- ...._---------
-_
9.24 I 5.96
-.~---
).96
241.7
C.C.
0.58
50
--~-
359.3 __h3.8
1.84. 286.2
-
I
0.78 11.10
320.9
250.0
c.c.
337.9 , C.C.
-
30.)7 I 22.5)
3.70
5
)0
c.c. c. c.c. c.c. c.c.
7.25
320.7
221+.0
159.5
I
-t------t~1.5 . .-
0.45 13.35
4.69
347.9
0.22
St. C 15
c.c.
9.01
2.89
..-
5.01
3.22
I
90 -~
and that there is no change in the current over the period concerned in the lower layer, t1argules' equation can gi va some indication of the magnitude of the internal oscillation of the boundary surface cau..sed by the variation of the tidal component perpendicular to the mentioned section. l/l~tidal
lJUring a
period, a reasonable variation of the tidal component seemed to be
10 cmls which will give a change of the boundary surface of dh :: 0,6.10- 3 L Here, h is the height of the boundary surface at the distance L from its intersection with the horizontal.
15
a
reasonable value of L, see fig. 10, is
lan, which will give a change of the boundary surface of 10 meters.
The
magnitude of this value is the same as observed and it is therefore difficult to conclude if we have true internal waves or not.
However, it seems that
the requirement for the existence of internal waves should be present, namely a
tidal wave propagating from deep water towards a wide shelf area, see model Zeilon \1934) or fig. 22J, uefant, 1961, vol. 11, p.
experiment
559.
Most
probably the observed internal oscillation is caused by a combined effect of true internal \iaVeS and transversely oscillation of the water masses due to the tidal current.
Another phenomenon which also might contribute, is the
period of inertial motion, which is about 29 hours in the area.
The fact that
such creat internal oscillations exist in the area will make it extremely difficul t to olJtain a represen tative hydrographical section from the coast towards the ocean, and will furthermore cause error in the Dynamical ~ome
internal oscillations exist on sts. B and
half the ma.gnitude comparing -wi th :3t. A.
depths)nnln-~::nr"':\"~lmjQ
t must, hOl-leVer, be noted that .:Jt. B was observed when
occurred and that both stations B and Shelf.
but with less than
The amplitudes and the phase angles
sho\1T, for some of the isotherms, particularly at greater variation.
~,
l;
~alculation.
~ water
are located further from the
l'l'om the observations at 3ts. B and c, we can only put forward the
of the
hypothesis that internal waves of tidal origin may exist.
In order to study the internal
oscillation for the hydrographical parameters on the .3helf', and roughly map their amplitudes in space, many more time series data are needed both in space and time. b)
tIDAL CU1-1REN T
Before discussing the tidal currents, some of the results of Fjeldstad t s (1929), ext.ensi ve theory for shallow water tidal currents will be briefly summarized.
tl jeldstad
in his theory, takes the earth rotation and the eddy viscosity into account and
generally he obtained excellent agreement with the observations taken on the Maud expedition on the'3iberian ,Shelf.
..fi.S
the measurements in this report are taken on a wide
shelf area, it is of interest to see how the measurements agree qualitatively with ji'jeldstad':3 theory, therefore a brief summary of his theory is given 1.
be~ow:
The current velocity describes an ellipse and the rotation is
~ ~
on both hemispheres. 2.
The ratio of the minor to the major axis is variable with depth, giving
decreasing values wi th increasing depth.
3.
Haximum currents always occur earlier than high water with the greatest
differences near the bottom and decreasing upwards.
4. The direction of tile major axis shows variation with depth. Near the bottom it nearly coincides with the direction of the propagation of the wave; going upwards it is deflected to the right on N.H. and to the left on S.H.
If
the depth is great enough, the major axis ob tains a maximum deflection at an intermediate depth and it then decreases again. surface current
h:1S
At great depth the maximum
approximately the same direction as the propagation of
the tidal wave.
S.
,l.
variable eddy nscosi ty with dep th does not alter the veloei ty distribution
sisnificantly as compared with a
const~lt
eddy viscosity.
The effect of
a variable eddy viscosity gives only the difference that when the edqy viscosity is smail, the ch8Ilge in the velocity is more rapid, and vice versa.
6.
The velocity
than c
=
f gh!
It is greater is narrow.
7•
A
of propagation of the wave is generally greater
but it is dei.!endent on the form of the tidal ellipse.
wnen
the ellipse is broad, and smaller when the ellipse
It also depends on the
slOI~
of the wave crest.
simple case concerning the reflection of the wave has also
been treated.
When the tidal wave propagates perpendicular to
the coast, it is found that the orientation of the current ellipse is unchanged but that the phase difference between the maximum current and surface elevation is increased.
This phase difference
has its greatest value near the shore and decreases, given the same value as the incidental wave alone, when at great distance from shore.
However, .(i'jeldstad pointed out that when the observations are
compared wi th the theory, we must have in mind that the observations are generally subjected to great error, and in particular the direction of the axis of the ellipse is sensitive to error in the observations. Fjeldstad (1929) has also given a formula which gives the maximum depth from
\
the bottom where the friction is fel t. lJ
JI ;;
=rrr~ .r-- A
The formula is as follows:
eddy viscosity: "... = frequency:
~
Using a value of 200 for the eddy viscosity
coreolis parameter
==
•
• units), the frictional
influence from the bottom is felt approximately 200 meters upwards for the diurnal wave, which rooans for the entire layer on the Brazilian Shelf. frictional influence for the semi-diurnal wave is about
65
meters.
The
.after the
theory it can be assumed that maximum deflection of the major aris of the tidal current might occur at some intermediate depth for the semi-diurnal wave, but not for the diurnal. Table 3 ruld figs. 11-12 show that the rotation of the current is genuinely
~ ~
apart from
t~
depths at 3t. B.
The ratio of the minor to
the major axis has the greatest value at greater depth.
IS
meters and at st.
~t.
it increases with
The deflection of the major axis has the right direction for
the semi diurnal wave, but not for the diurnal wave. on
t.;
This is particularly clear
v where the measurement has been performed down to the bottom.
However,
it must be mentioned that the deflection of the ma.jor axis can also be due to internal waves, and as seen from the time series data of the temperature, such internal waVes might exist. currents in
5
and
15
~ters
The relatively greater amplitude of the tidal for Qi£. 13 and C might to soroo extent be explained
by the greater gradient of the
3t.
1-\..
~
in the boundary layer when compared with
0ince the axis of the ellipses shows variation with depth caused by
influence of friction and possibly internal waves, the direction of propagation of the tidal wave does not coincide with the direction of the axis. gives that for a depth of
50
If'jeldstad
meters to the bottom, the difference is about
2CP for the surface current if the friction is felt for the whole layer.
However,
as a general result it is seen that the tidal wave propagates towards the shore. d
qualitative agreement with rjeldstad's theory is obtained for part of the
observation
but a general conclusion canno't be drawn
area of the::wuthe
Braziliar coast
out ;;tore
bo
Table
h
However, the wide shelf
to be an
to carry
fricti
and fig. 14 gives the average values of the wind and the current
for a diurnal period.
The means have been calculated for 1-24, 7-)0 and 13-36 in orde:
to see if great variation exists over the 36-hour period.
The T3 diagram gave
that the upper layer at st. A was representing' the Brazilian current, and from the current rneasure:ments, particularly for
15 and 30 meters, is it seen that
the direction is apprOximately parallel with the contour line of the shelf. characteris tic speed is half a knot.
.t1.
The lesser speed in the 5-meter depth
aught be explained b,:/ the wind towards the south east during the two previous days,
T~Y MEAN 1-24 hr. (Lunar Time)
MEAN 7-.30
MEAN 13-36
hr.
hr. (Lunar Time)
(Lunar Time)
Speed Direction Spe,d Direction Speed Direction Toward Toward Toward Wind m/s Wind m/s Wind m/s curro cm/s Degree curr. em/s Degree curro em/s Degree
1.28
201.0
1.04
165.4
1.07
207.2
5.67
255.7
3.47
265.5
4.72
299.0
15 m
24.87
230.6
19.55
236.3
18.47
253.5
30
m
26.81
217.4
18.64
230.9
17.41
251.1
Wind
2.09
241.1
1.78
244.8
1.57
242.2
5m
24.55
244.4
26.01
246.3
22.88
226.1
IS
m
20.23
244.6
20.61
234.4
19.47
226.6
130 I
m
23.41
253.3
23.82
238.4
21.51
230.4
I Wind
0.85
80.6
0.85
68.2
0.78
84.2
m
8.37
341.6
8.13
329.2
5.44
357.7
15 m
11.81
15.2
11.85
1.5
9.41
10.4
30 m
5.73
308.0
7.01
320.3
6.74
350.2
m
1.04
5.2
1.19
10.2
2.07
12.5
m
3.37
357.3
5.17
I.,
6.63
353.7
Wind \
! Curr.
5.
Station A
Station
'I
B !
I
i
!
I
I i
IS I i
Station C
j
150 !
!
, 90
(
I
referring to the weather maps published by the Hrazilian Navey. The velocity at
st.
B gave about the same values as compared with 3t. A,
but according to the TS diagram this was not the Brazilian current, but must be a coastal current.
1
wi.nd factor of O. Ol27/lin t/J' = 0.02, or 2% for too low to cause the observed surface current. changed about
and the wind direction
but the wind
was again
tha t the wind
on board
direction
'current to
st.
~t
~,
the direction of the current
opposite when compared wi th St. B, we assume
representative of the
the curr{:tnt at St.
G
indicated
under possible
current.
are present at ')t. G
~kmanls
area, the spa ed was much
Great internal ()scillations of the isothe
and
B, but when using
small to have caused the current,
~urement
consideration.
~t.
The wind speed was greater at
101.1
tidal origin or caused
st.
Residual value is
These oscillaticrn
A.
mainly
rnight be internal waves of
lt,
transverse oscillation
Rotary tidal. currents seem to be
the magnitude at ::>li.
reduced to less than hal
A,
when comparing
, isohalins and isopycnels
the water masses.
counter-clf)t~
uenced by bottom friction
possibly internal waves.
of half a knot are pre th is at St.
lj.
current runs seem to be much inn uenced by the
se exist and the tidal
at :::its.
and B, but
The measurement shows that the of the 1helf at 3t. wind
current to the Brazilian current in the area of
meters
it.
of a counter
•
set
•
Defant, 1~.
.t'hysical
1'.Jnilson, I.
l) cea1 ography,
vol. 11 - Pergamon Press, 1961.
The Shelf and coastal wa ters off 30uthern Brazil.
-Lnstituto Uceanografico, Torno XI. ~Ijeldstad,
J .~.
Part 1.
Ueofysiske Publikasjoner.
akademi i Oslo vol. 1"je1dstad, J .l!;.
Universidade de Sao t'aul0, 1961.
l.nternal waves of tidal origin.
of observation
m.
No.
S,
Boleyime do
Theory and analysis
iJet Norske Videnskaps-
Nov. 196h.
Gontribution to the ijynamics of free progressive tidal waves.
The Norwegian North
alar .t;xpedition wi th l!Maud" 1918-1925,
results, vol. lv, No.3.
~cientific
Published by (Jeofysisk Institutt, Bergen.
In coo.eration wi th other institutions. Johannessen, O.M. Brazil.
Note on diurnal temperature observation of the coast of Santos, ljontribuicoes :\.vulsas Do Insti tuto Gceanografico, Universidade
lJe3ao Paulo, 1966. Zeilon, N..
I!.xperiments on boundary tides. Hedd .. Uoteborgs Hogsko1ad, oceanograf. Inst. no.
8, 1934.
....
_.......... _ _.-..._- --_ .__ .--_. . _....
1\'
..
'.
_~
PROJETO
.._ ----_. __ .. - .. ..... _._-_. .... __:__ _...:.._.::. .:____.:....__. ___ ....:....:._._ ..., ....... ..~....'-. ::......_ ........~. :.~: :.. : .. c.·.: .. .::. ...:.. .•..
I
B RASI L
A "../ ~,,'
I I
~
/
I
c o
/
/
I I I
I
I
j.--OOl._.d
I _ I_ ... -.-----'-'--45 J
0
STAT/ON
A
1966
0r.~~,~.~'~.r.~.t~ "W" ll· . . . •.'~~121,~-r~-r~~~.Jg~~~I-rI~'~'I~['~,~~L7~i~~-,~I~;~~~~~,~~~~ r iii iii i del/'ee 8
knols
WIND
1
36(,
poo
~200
4
~ iOe
_
v.'ocoIV
-- - d"ectlon em/s
40
CURRENT
-5 ......m, (DEPTH) "'-
30
20
'---
dtllree _ 360 ~ 300
i
";200 1'00
10
Jo
o 50 r
C~
dell,ee 1 360 1 300
40~
20~
-1
10,00
~
10
oL
j
r em/s
60
CURRENT
30m
;~~
del/r ••
30~
l~60
------_ ---- ---
20~ 10
200
l500 ~
.......
i r
200
I -i100
oL
I JO
aeO'"
:>so
\
CURRENT
\
70m \
~ "-.._-----...." CURRENT
1
300
11
200
100
J0
90 m
0'-
.. em
2ZOr
SEA LEVEL.CABO FRIO and
2cx.:..~
~ If;O~
RIO
na~
~! ~
" " q " q
....
~
STATION A 19>66 nav ._ ~f i1 Y «, fI " lip. \1 .., • t; '" q 1 ': ti 'J
't"
, , q If SEA LEVEL- RIO DE JANEIRO ClAd CAOO FRI'O
'" ~
:~ 2 1&
10
t~I------------~~------~-------------------------------------------------------------~
~
t
ISOTHERM
STATION
8
1966
-VELOCITy ~--
OlfltICTIO/lllf
CURRENT
5 m (DEPTH)
cia gr ••
----
40
---- ----
......
rem"
CURRENT
1 360 -
