A R DE MESQUITA AND J HARARI

INTRODUCTION

During the period 1976-1981 the NOc Prof. W. Besnard, from the University of São Paulo , Brazil, under the research project named "Hidrodinâmica Costeira", (Coastal Hydrodynamics) funded by the "Financiadora de Estudos e Projetos" - FINEP, of the Brazilian Presidency of Republic,  took several time series of oceanographic and meteorological variables in the Southern Coast of the Brazilian Shelf (Figure 1). General accounts of the above cruises are presented in Mesquita (1983, 1994 and 1998).

The general circulation of the area (PST, Santos Platform, PPR, Paranaguá Platform, and  PRJ, Rio de Janeiro Platform) was object of study and estimation via the distribution of temperature, salinity and density by Emilson (1961) and Mesquita, Leite & Rizzo (1989), where a general overview of currents surface distribution on the Shelf can be found. First direct measurementof currents were made by Johannessen (1968), with Eckman current meters,in four fixed stations along the continental Shelf, for short periods (2 days time series), on board the NOc. Alte. Saldanha from the Brazilian Navy.

Hutnance (1980), who interpreted the world`s highest values of the M₃  that occur in the area caused by the extension of the shelf, as a local resonant effect gave first account on the propagation of tidal heights. Present account gives the  harmonic constants of the principal constituents  of  tides and tidal currents of the Shelf , a description of the circulation of currents, a discussion on  the propagation of the tidal constituents,and their relationship with the vertical and horizontal distributions of tidal ellipses components and with the general circulation of the area.

MATERIAL AND METHODS

The South-Eastern Coast of the Brazilian  Shelf area is shown in Fig 1, with the mapped locations of the ports, where there are permanent stations of tidal observations and the pelagic sites on the Shelf. In Tab. 2 are shown the values of Tidal Constants of the main tidal heights constituents determined for the ports of Rio de Janeiro, Ubatuba and Cananéia  and the PRJ, PST and PPR  geographical positions shown in Fig 1.

  The dates of the cruises  and the characteristics of the time seriesof the Pelagic Tides and currents obtained are shown  in Table 1. Formore about the measurements see Mesquita (1983), Mesquita, Leite & Rizzo(1989) and Mesquita & Harari (2000). The analysis of tidal data were made via  the Harmonic Method  (Franco, 1971) and for measurements of currents by the Response Method ( Munk & Cartwright, 1966). Tab. 2 gives the tidal constants of the tidal heights for the permanent stations of the main ports of the area, such as Rio de Janeiro, Ubatuba, Santos, Cananéia, Paranaguá, São Francisco do Sul  and Imbituba, which are nominated respectively as RJA, UBA, SAN, CAN, PRG, SFS and IMB.

The Pelagic non permanent stations on the Continental Shelf were nominated as PRJ (Platform of Rio de Janeiro), PST (Platform of Santos), PPR (Platform of Paranaguá)  and PSC (Platform of Santa Catarina). Results for the Pelagic tidal constants are also reported in IAPSO'S Committee Report  n^o 2, Cartwright & Zetler (1985) and  Smithson (1992).

Station Name	Plataforma de Santos	Plataforma do Rio de Janeiro	Plataforma do Paraná	Plataforma de Paranaguá
Latitude (S)	25º 1,0'	23º 23,0'	26º 7,4'	26º 18,1'
Longitude (W)	45º 42,0'	43º 17,0'	47º 39,4'	47º 30,4'
Depht (m)	92	100	60	74
Beginning and end times of the tidal record	22/07/1977 12:00  to 04/08/1977 10:15 (GMT)	21/07/1978 12:30  to 21/08/1978 18:15 (GMT)	-	18/06/1981 07:53  to 17/07/1981 07:38 (GMT)
Extension of the tidal record (days)	12,9	31		29,0
Sampling interval (min)	15	15		15
Beginning and end times of the current meter observations	21/07/1977 22:00  to 03/08/1977 02:00 (GMT)	22/07/1978 2:00  to 3/08/1978 15:00 (GMT)	29/11/1980 12:30  to 12/12/1980 09:30 (GMT)	-
Extension of the current meter observations (days)	12,3	13	12,9
Sampling interval (hours)	4	1	1
Current meter Sampling depths (m)	05, 15, 30, 40	00-10, 20-30, 40-50, 60-70, 80-90	05-10, 20-30, 40-50

RESULTS
 

- Propagation of tidal heights- Inspection of phases of Tab. 2 shows that semidiurnals heights constituents M₂, N₂ , K ₂, and S₂ have an anti clockwise propagation from PRJ to PST and a clockwise one between PRJ and PST. Their amplitudes show a general increase from East to West, being higher near the port of Paranaguá and then decrease .Among the diurnals  the Q₁ and O₁ ,  propagate from IMB to RJA in a West to East clockwise propagation, while K₁ and P₁ propagation follow approximately the semidiurnals components M₂, S₂, N₂, K ₂ and have also higher amplitudes near Paranaguá / Cananéia propagating clockwise from IMB and PSC to PPR (not shown) and anti-clockwise from Rio to Paranaguá.

Such opposite  senses of propagation also suggest that the K₁  has two amphidromes in the South Atlantic, one propagating clockwise and the other anti clockwise. The M3 has higher amplitudes,as the semi-diurnals, along the Paranaguá Shelf compared to the otherstations. The phases of M₃ in the area do not seem to be elucidative, as do as well, any interpretation of the propagation behavior of higher order components, such as quarter diurnals M₄, MS4 and othersnot mentioned.

-The main tidal currents constituents -.

  O₁ :    At the surface (0 to 40m), the current vector rotates also anti clockwise,in all stations, as well as in the whole column of PPR, but not PRJ, where the rotation at 20m and below 40mis clockwise.In PST, Fig 3.1, values of HM are quite large and nearly constant, while the values of Hm  decrease with depth. In PRJ, HM and Hm are large at the surface, with significant variation at intermediate depths, but nearly constant below 60m. In PPR, excepting the bottom ( where they are very small), the values of  HM and Hm  are large , with small variability, showing a maximum at 20m. In PPR, the eccentricity of the ellipses is also near to 1 Assuming the eccentricity as given by the ratio of the minor and major axes.

In general, the angles of the major axes relative to the E-W axis for the O ₁ tidal currents ellipses are similar to those of Q₁  and appear to have a counter-clockwise rotation along the depth, varying from SW- NE at the surface to nearly S-N- SE-NW from 30 to 50 m depth to nearly  E -W, from 60 to 90 m depths. The inclinations of the O₁ellipses of  are similar to those of Q₁   and the comparison also can be made by the values of (M)  that, except for differences in rotation at mid depth in PPR, are all similar as expected, bearing in mind the Rayleigh´s criterion.

 K₁  : At the surface layer (5 to 40 m) the currents vector rotates also counter-clockwisein all stations and the same is observed at all deeper layers of PPR (60m) and PRJ (90m), with only two exceptions in PRJ, at 60 and 80 meters. In PSTthe ellipses (Fig 3.2),  values ofHm and HM at 5 and 15 m are the strongest among all the constituents in that station. The same occurs in PRJ, where the value of HM of K₁ at5m is the strongest among all the tidal currents constituents in all Southern Brazilian Shelf, reaching 11. 1 cm/s. In PPR the value of HM at 5 m is large, but comparatively smaller than in other stations.

For all stations PPR, PSTand PRJ the ellipse values  of HM and Hm decrease substantially towards the bottom . In all three stations, values of (alpha M)  of the inclination of the ellipses of currents in all depths indicate a rotation of the major axis, especially at the surface, from W- E to SW-NE to S -N andSE-NW approximately, similarly for the P₁ major axes, as one goes from PRJ to PPR (Fig 5b). Similar ellipse  variability of directionsis also shown by P₁ as expected.

M₂   :   At the surface (5 to 40m) of PST, (Fig3.3), the currents vector rotates anti clockwise, while in PRJ rotation is in both directions along the depth and in PPR rotation is also anti clockwise. From  40m to the bottom, in PRJ and PPR, M₂   also rotates anticlockwise, with the only exception at the depth of 40m of PPR. The values of HM and Hm indicate strong M2 currents in PST and PPR, being the strongest in PPR (maximum of 7.5 cm/s, at20m). These currents are fairly weak in PRJ,which showed in the column, however,higher values of currents at the bottom layer, 80 to 90 m.

A general feature is the small HM variability of the maximum and minimum values along the vertical, being almost constant along the depth in all sites. Directions of the ellipses, given by the (alphaM) are nearly the same in PPR, along the vertical profile, being nearly NW-SE in all the depths of observation of currents. The same is  seen in the PRJ, only approximately, as the ellipses have a nearly W-E orientation of (alphaM). Orientation of ellipses in PST is nearly NW-SE from surface to 20m and exactly E-W at 30 m, turning to almost NW-SE direction at 40 m.

It is remarkable the small variation of the M2 ellipses inclination ( alpha ) in PPR along the vertical, all being in the NW-SE direction (approximately);  also noticeable is the  inclination of the N₂  ellipses that shows similar directions as those of the M₂ at all depths of PPR,PST and PRJ. It is also remarkable that the  bottom HM valuesof currentsat PPR (60m) andPRJ (90m) are higher than in all layers above.

M₃ :  In PST, at the surface, the currents vector rotates clockwise 5m, (Fig. 3.4),and anti clockwise between 10 and 40m; in PRJ, there is a great deal of variabilityin the direction of rotation along the depth; and, in PPR, the rotation is mostly anti clockwise, except at 20 and 40m. The values of HM and Hm  along the vertical, however, present relatively small variations, in all the three stations, but the directions of the currents ellipses as given by ( alpha M)  vary along the depth.

Ellipses of the three sites seem to have retained the same general ( alphaM)  values from surface to 30 m, they were almost similar between 40 to 60 m with different values ( alphaM)  from the previous ones and from 70 to 90 m only in PRJ, where they showed inclination varying from NE to N in the bottom layer. It is also noticeable that the larger M₃ values of the  area occur at depths of 60 to 80 meters of PRJ. The ter-diurnal ellipses of currents, as the semi-diurnals, have each one similar amplitudes along the depth in each site and, except for the 5m layer, have also similar characteristics of amplitude HM and (alphaM)  vertical  distributions in all layers of each station

DISCUSSION AND CONCLUSIONS

- Tidal heights and induced tidal currents - The greatest values of the surface tidal currents of PST , O₁ (8.67 cm/s) and K₁   (7.4 cm/s) are induced by the diurnal heights constituents O ₁   (10.1 cm) and K₁, (5.9 cm), while the M₂ tidal height with 21.3 cm and S₂ with 14.7 cm are the dominant height components of tides,but produce smaller current components.

M₂   : 6.05 cm/ sec and S:2.65 cm/sec.  Similarly, in PPR the S ₂  (17.4 cm), and M₂  (24.4 cm) tidal heights  produce currents components S₂ (4.32 cm/s) and M₂ (7.32 cm/s)nearly as energetic as O₁ (6.25 cm/s) and K₁ (4.23 cm/s) that are induced by the tidal heights O₁ (10.8 cm) and K ₁ (6.4 cm), that are smaller than  the semidiurnals heights of M₂ and S2.

Also   tidal current components of PRJ  (5 to 40m) are generally smaller but behave similarly as those of  PST. Currents components O1  (7.4 cm/s) and K1 (11.1 cm/s) of PRJ are greater than the ones of M₂   (1.3 cm/s) and S2 (2.9 cm/s),  although the corresponding diurnal heights,  O₁ (9.7 cm) and K ₁ (5.6 cm), are smaller than the semidiurnals heights  M₂   (24.1 cm) and S2 (15.4 cm) .

Other relation, mostly true for the surface layersof PRJ, is that  the semi-diurnals heights M₂ and S2 are greater than O₁ and K₁ , but the induced current components M2 and S₂  are smaller than the currents induced by O₁ and K₁;  that is, smaller diurnal heights O1 and K ₁,  induce greater diurnal amplitudes of currents, mostly at the surface, than the much higher heights of semidiurnal components, M₂  and S₂, induce semidiurnals currents.

At the bottom,the currentsof PPR and PRJ seem to be following accordingly, i.e., higher values of current components are associated with higher values of the corresponding components of tidal heights, as the diurnal amplitudes decrease towards the bottom and the semi-diurnals and the terdiurnal tend to preserve their surface values along the depth to 40m layer and tend to be come smaller with depth.

- The general characteristic - of the structure of the tidal currents  is that the diurnal components of currents have greater amplitudes at the surface layers down to 40 meeters layer and then become smaller whit deeph. The semidiurnals currents, otherwise, have approximately constant amplitudes along  the vertical profile,  feature also followed by M ₃ . The highest values of tidal heights constituents do not necessarily  induce the highest values of currents components and the ellipses axes of diurnal tidal components tend to rotate counter-clockwise, from surface to the bottom, apparently following the hydrographic and meteorological forcing along the surface layer , the mid layer and the bottom layer.

At the bottom,the currents of PPR and PRJ seem to be following accordingly, i.e.,highest values of currents components are associated with highest values of the corresponding components of tidal heights, as the diurnal amplitudes of currents decrease towards the bottom and the semi-diurnals and the ter-diurnals tend to preserve their surfaces values along the depth. The height constituentsP1, K₁, N₂ , S₂, K₂ and M₂  propagate counter-clockwise from PRJ to PSTand clockwisefromPPR to PST, suggesting two amphidromic systems for each of these constituents in the South Atlantic;  on the other hand, constituents Q1 and O₁ propagate clockwise,  from PPR to PRJ.

For the principal diurnal constituents (Q₁ , O₁ , P₁ and K₁ ), the rotation of the currents vector at the surface, in the Southern Brazilian shelf,  is counter-clockwise; however, in the Northern station (PRJ), below the surface layer, some clockwise rotation is observed, for all these tidal current constituents,  probably due to increasing shear between the coastal currents and the Brazil Current, which may induce vortices with clockwise polarization in all tidal bands. This is also the case of the semidiurnal and ter-diurnal current constituents. The principal semi-diurnal current constituents (N ₂, M₂, S₂, K2) and M₃ have rotation which is counter-clockwise at the surface layer in PST,and vary along the vertical in PRJ, where these currents are normally very weak and mainly counter-clockwise, with a few exceptions, along the column.

At PPR and PRJ mid water, intrusion of the Tropical Water seems to have  influenced the clockwise  rotation of the semidiurnal constituents, (M₂ and S2). The principal ter-diurnal current constituent (M₃) presents a counter-clockwise rotation at the surface layer in PST(except at 5M), a variable rotation along the vertical in PRJ and is predominantly counter-clockwise in PPR (except 20 and 40m). The M₃ ellipses do not exhibit large spatial variation of the intensity, both horizontally and vertically, as shown by the diurnal and semidiurnals tidal components.The important feature is relative to the surface currents, where they are predominantly diurnal, in PRJ,  and have significant semidiurnals components in PST and PPR.

Diurnal currents are strong at the surface, but tend to decrease along the depth,while semidiurnal and the M ₃ currents, have approximately the same values along the vertical. It appears also that the double sense of propagation of the tidal heights, as indicated by the phases of the tidal constituents,  are related to the South Atlantic amphidromes of the M₂ constituents, which induce intermixed clockwise and counterclockwise tidal currents in the water columns. Further aspects of the tidal forcing exhibited by different responses of water masses of the region (Coastal Water,Shelf Water Tropical Water and Subtropical Water)  are shown in Mesquita & Harari (2000), that can be found at UNESCO e-library http://ioc.unesco.org/iocweb/iocpub/iocpdf/w171.pdf
 

ACKNOWLEDGMENTS

We are grateful to  FINEP ( Financiadora de Estudos e Projetos) of the  Presidency of the  Republic  of Brazil,  to FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo ) and to the British Council , UK.

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