numerical experiments on the generation of long ocean

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0278-4343/$ - see

doi:10.1016/j.csr

�CorrespondeAtmosfera y lo

Naturales, Univ

versitaria, Pabe

Aires, Argentina

E-mail addre

Continental Shelf Research 27 (2007) 699–712

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Numerical experiments on the generation of long ocean waves incoastal waters of the Buenos Aires province, Argentina

Walter C. Dragania,b,c,�

aServicio de Hidrografıa Naval and ESCM-INUN, Av. Montes de Oca 2124 (C1270ABV) Ciudad Autonoma de Buenos Aires, ArgentinabDepartamento Ciencias de la Atmosfera y los Oceanos, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,

(1428) Ciudad Universitaria, Pabellon II, 2do. piso., Ciudad Autonoma de Buenos Aires, ArgentinacCONICET, Consejo Nacional de Investigaciones Cientıficas y Tecnicas, Av. Rivadavia 1917, Ciudad Autonoma de Buenos Aires, Argentina

Received 18 August 2005; received in revised form 26 October 2006; accepted 7 November 2006

Available online 16 January 2007

Abstract

A numerical model (two horizontal dimensions, vertically integrated) is used to investigate the generation of long ocean

waves, ranging from 20min to almost 2 h, at Buenos Aires continental shelf. The domain includes the Rıo de la Plata

estuary and the continental shelf together and extends from 33.51 to 40.51S latitude, and from 511 to 631W longitude. Sea-

level oscillations are modeled by forcing with passage of atmospheric cold fronts and atmospheric gravity waves. Both

forcing mechanisms, which have been present during high activity lapses of long ocean waves, are mathematically

implemented. After several numerical simulations, it is concluded that the pressure and wind fields associated to cold fronts

do not generate long ocean waves in the area, though they do produce disturbances with periods longer than the tidal ones.

On the other hand, it is so concluded that atmospheric gravity waves are an effective mechanism to force long ocean waves.

Results obtained show that generation of long ocean waves is highly sensitive depending on the propagation direction and

the phase speed of the atmospheric gravity waves. The long ocean wave event detected during the large-amplitude gravity-

wave event of 13 October 1985 is successfully simulated. Finally, all our results suggest that atmospheric gravity waves are

a highly effective mechanism forcing for the generation of long ocean waves in Buenos Aires coastal waters.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Shallow water waves; Numerical simulations; Wind stress forcing; Atmospheric pressure forcing; Atmospheric gravity waves;

Buenos Aires continental shelf

1. Introduction

Large-amplitude sea-level oscillations, rangingfrom a few minutes to almost 2 h, have been

front matter r 2006 Elsevier Ltd. All rights reserved

.2006.11.009

nce address. Departamento Ciencias de la

s Oceanos, Facultad de Ciencias Exactas y

ersidad de Buenos Aires, (1428) Ciudad Uni-

llon II, 2do. piso. Ciudad Autonoma de Buenos

.

ss: [email protected].

frequently observed in different tide stations in theopen sea and at some locations on the Buenos Airescoast (Fig. 1) (Dragani, 1997). Simultaneous mea-surements of sea-level oscillations from Mar de Ajo,Pinamar and Mar del Plata, during 1982, werespectrally analyzed by Dragani et al. (2002). Theyconcluded that during events of high activity sea-level oscillations, spectral peaks covered almost thewhole frequency band between 1.1 and 4.7cycles per hour (cph). Significant coherence values

.

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dx.doi.org/10.1016/j.csr.2006.11.009

mailto:[email protected]

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Fig. 1. Buenos Aires coastal region (Argentina) and its locations, in the southwestern Atlantic Ocean. The bathymetry is labeled in meters.

W.C. Dragani / Continental Shelf Research 27 (2007) 699–712700

estimated between Mar de Ajo and Mar del Plata(172 km apart) have clearly shown that this is aregional phenomenon. The available data havesuggested that there might be two forcing mechan-isms in this area: the passage of meteorologicalfronts and the existence of atmospheric gravitywaves.

Cartwright and Young (1974) stated that ameteorological front is more obviously associatedto a discontinuity in wind speed and direction thanto one in pressure. They considered obvious that itseffects on sea-level should be, at least qualitatively,similar to those of a fast-moving step in pressure.Several studies on atmospheric gravity wavesforcing sea-level oscillations have been performedin many coastal zones around the world. Forexample, Wilson (1954) studied the generation oflong-period seiches in Table Bay, Cape Town, bybarometric oscillation. Munk et al. (1956) analyzedrecords of sea-level oscillations in Oceanside andScripps, which were associated to internal waves onthe atmospheric inversion layer. Others, Tintoreet al. (1988), Monserrat et al. (1991a, b), Gomiset al. (1993), Garcies et al. (1996) and Rabinovichand Monserrat (1996) studied large sea-level oscilla-tions in several bays and harbors of the westernMediterranean, which were also associated withatmospheric pressure fluctuations.

Dragani (1997) and Dragani et al. (2002) con-cluded that due to the simultaneous occurrence of

atmospheric gravity waves and sea-level oscillations,and considering the similarities in spectral structuresof both phenomena, atmospheric gravity waves maybe the main forcing mechanisms of sea-leveloscillations in Buenos Aires coastal waters. Thefollowing results suggest that sea-level oscillationscould be forced by atmospheric gravity wavesassociated to frontal passages. (i) Frontal passages(with predominant northeastward propagation) andassociated atmospheric gravity waves were detectedduring high energetic sea-level oscillation events. (ii)Sea-level oscillations were generally observed first atMar del Plata and, subsequently, further north atPinamar and Mar de Ajo, and it could be associatedto the predominant propagation direction of atmo-spheric perturbation. (iii) Long ocean wave activityhas been generally detected at all three stations andsignificant coherence values were found betweensea-level at Mar de Ajo and Pinamar stations. (iv)Sea-level (Mar del Plata) and atmospheric pressure(Punta Medanos) spectra, 150 km apart, haveshown the most energetic spectral contents at lowfrequencies (approximately around 1 cph).

The aim of this paper is to study the generation oflong ocean waves in the Buenos Aires continentalshelf. A mathematical model that includes passagesof fronts and atmospheric gravity waves as forcingmechanisms is used. First, the finite differencenumerical model is presented in Section 2, givingdetails of the relevant equations, the size, resolution

ARTICLE IN PRESSW.C. Dragani / Continental Shelf Research 27 (2007) 699–712 701

and integration times of the model. Weather patternduring sea-level oscillation events is briefly de-scribed in Section 3. The implemented methodolo-gies to obtain the analytical representation of bothforcing mechanisms are described in Section 4.Results of a series of numerical experiments todetermine the effect of both forcing mechanismsover the continental shelf waters are reported inSection 5. A summary and discussion of theconclusions obtained from investigations with thenumerical model is presented in Section 6. Only aselection of the numerical model results has beenincluded in this paper.

2. The model

The basic form of the numerical model used inthis study was developed by Caviglia and Dragani(1996). The two-dimensional model uses the verti-cally integrated shallow fluid equations for massand momentum conservation:

qZqtþ

qqxðhþ ZÞU þ

qqyðhþ ZÞV ¼ 0, (1)

qU

qtþU

qU

qxþ V

qU

qy� fV

¼ �gqZqx�

1

rqPa

qxþðtsx � tbxÞ

rðhþ ZÞþ AHr

2U , ð2Þ

qV

qtþU

qV

qxþ V

qV

qyþ fU

¼ �gqZqy�

1

rqPa

qyþðtsy � tbyÞ

rðhþ ZÞþ AHr

2V , ð3Þ

where t is the time, U and V are mean verticallyaveraged velocities in the x (west-east) and y (south-north) directions, respectively, g (9.8m s�2) theacceleration due to gravity, Z the free surfaceelevation above mean water level, h the depth belowmean water level, f( ¼ 2(7.292 10�5 s�1) sin(�371) ¼�8.77710�5 s�1) the Coriolis parameter, r the waterdensity, Pa the atmospheric pressure, tsx and tsy the x

and y components of surface wind stress, tbx and tby

the x and y components of bottom shear stress, AH

the horizontal eddy viscosity coefficient and r2 thehorizontal Laplacian operator. We have neglected thehorizontal variations in the vertically integrateddensity field due to variations in temperature andsalinity, and assumed a constant density of1025Kgm�3.

The expressions for the x and y components ofsurface wind are given by

tsx ¼ raCdajV 10jV 10x;

tsy ¼ raCdajV 10jV10y;

(4)

where |V10| is the wind velocity at 10m above waterlevel while V10x and V10y are the x and y

components of wind velocity, ra (1.25Kgm�3) thedensity of air, and Cda the wind drag coefficient thatin accordance with the WAMDI Group (1988) canbe calculated as follows:

Cda ¼ 0:0012875 V10j jo7:5ms�1;

Cda ¼ 0:0008þ 0:000065 V 10j j V10j jX7:5ms�1:

(5)

The bottom stress is determined using a quadraticform of the depth mean current:

tbx ¼ rkUffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2 þ V2

p;

tby ¼ rkVffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2 þ V2

p;

(6)

where k is a dimensionless coefficient of bottomfriction. Several numerical experiments were carriedout using seabed drag coefficient values rangingfrom 0.001 to 0.003 and horizontal eddy viscosityvalues from 30 to 60m2 s�1. Numerical simulationsrevealed that the obtained results were insensitive tochanges in such parameters. Consequently, thelowest values tested for both of them were adoptedin this paper. The system of equations is solved bythe finite differencing method by means of thealternating-direction implicit (ADI) algorithm(Douglas and Gunn, 1964).

The model domain (Fig. 1) extends in latitudefrom 33.5 to 40.51S, and in longitude from 51 to631W. The original bathymetry was obtained fromnautical charts published by the Servicio deHidrografıa Naval de Argentina (SHN, 1986a, b,1993). A square inverse distance method was used tocreate a regularly spaced grid from irregularlyspaced bathymetry data. The resulting bathymetryis taken at 5� 5 km intervals, thus there are 215 gridpoints in the east-west and 158 grid points in thenorth-south directions. This grid represents arectangular domain with a distance of 780 km inthe north-south and 1065 km in the east-westdirections. The resulting grid has the shallowestdepths (0.8m) in the upper estuary and the greatestdepths (5444m) at the southeastern corner of thedomain. Some numerical experiments were carriedout in order to determine the most convenient value

ARTICLE IN PRESSW.C. Dragani / Continental Shelf Research 27 (2007) 699–712702

for the time step. The obtained value, whichsatisfied the CFL criteria, was lower than 10 sbecause the depth in the south-eastern corner of thecomputational domain (Fig. 1) is deeper than5000m. In order to improve the model performance(increasing the value of Dt) any ocean depths greaterthan 1000m were set to this value, so that a timestep of Dt ¼ 60 s could be used. After running somenumerical experiments no significant differenceswere observed between simulations obtained fromthe original and the modified bathymetries and,consequently, the last one was adopted in this work(Dragani, 1997).

The initial conditions were taken as still-watervalues, that is U, V and Z are zero everywhere.Along closed boundaries the normal component ofcurrent was set to zero. The staggered grid of thismodel requires sea surface elevation and velocitytangent to the open boundary to be specified orcomputed at each open boundary at each time step.Along the eastern boundary seaward of the shelfbreak, depths are greater than 200m, and sea-leveland velocity may be set to zero. It is the cross-shelfopen boundary conditions that have the great effecton the interior solution. Then variables at northernand southern open boundaries were calculated usingan explicit Orlanski radiation condition (Orlanski,1976).

A preliminary experiment (with no rotation, nobottom-friction, no horizontal eddy viscosity, andwithout atmospheric forcing) was designed toinvestigate the propagation characteristics of freeedge waves. The fluid was initially at rest with thesea surface elevated in a symmetrical moundcentered at the middle of the computational domainwith maximum elevation at the coast (0.8m) andlinearly decreasing offshore. Numerical experimentspresented by Dragani (1997) revealed that speed ofpropagation of free waves matches the theoreticaldispersion-curve (assuming the cross-shelf bottomslope equal to 0.001 for the inner continental shelf).

3. Weather patterns during sea-level oscillation

events

Dragani (1997), Nunez et al. (1998) and Draganiet al. (2002) described the typical synoptic situationduring sea-level oscillation events. Low-level atmo-spheric cyclonic circulation and the passage ofatmospheric fronts were always present duringthose lapses. It was shown that energetic events ofsea-level oscillations and atmospheric pressure

disturbances were simultaneously detected and theyshowed intense energetic contributions in the samefrequency band. Significant coherence values werefound between water levels at Mar del Plata andsurface atmospheric pressure at Punta Medanos(150 km north-northeast of Mar del Plata). Duringthose events, synoptic upper analysis showed jetstreams at 250 h Pa level, located approximatelysouth of Bahıa Blanca, and behind—and parallelto—the surface front. Hourly meteorological datashowed large pressure fluctuations and intense gustsat Mar del Plata. Upper-air soundings obtained atComandante Espora Navy Base (6 km east of BahıaBlanca) showed a lower pronounced troposphericinversion which depicts an example of the state ofthe atmosphere when a frontal surface lies over-head. The propagation medium for atmosphericgravity waves appears to be a low-level inversion(Bosart and Cussen, 1973; Gedzelman and Rilling,1978; Stobie et al., 1983) represented, in this case, bywarm air flowing from the north over cold airflowing from the south.

4. Atmospheric forcings

4.1. Passage of an atmospheric cold front

In this paper, an analytical model (Dragani, 1999)is used to simulate the surface wind and pressurefields associated to the passage of a typical sub-tropical atmospheric cold front. In this analyticalmodel, a surface low-pressure center moving east-ward along the southern boundary of the computa-tional domain is considered. The associated coldfront can cyclonically rotate around the low-pressurecenter.

Surface wind and pressure fields are obtained byadding three elemental fields: a basic, a pure rotationand a pure convergent field. Surface pressure andwind fields are displaced eastward with constantspeed and the front can rotate cyclonically around thelow center. Resulting pressure and wind fields containthe most important features associated to the atmo-spheric front (Fig. 2).

4.2. Atmospheric gravity waves

In order to represent the surface pressure fieldPa(x, y, t) associated to atmospheric gravity waveswe have considered a sum of monochromatic wavespropagating along a direction which forms an anglea (counterclockwise positive) with the southern

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Fig. 2. Simulated passage of atmospheric cold front (pressure in h Pa and wind intensity in m s�1), after 24 h of simulation.

Fig. 3. Sketch of the of atmospheric gravity wave activity area.

The front (at the surface) and the jet streak, inflexion axis and

ridge axis (at 300 hPa height) are pointed out.

W.C. Dragani / Continental Shelf Research 27 (2007) 699–712 703

boundary:

Paðx; y; tÞ ¼ Sn

i¼1pi cosðkxi

xþ kyiy� oitÞ, (7)

where n is the amount of waves to be considered, pi

the wave amplitudes, kxi ykyi the wavenumberskxi ¼ ki cos(a) and kyi ¼ ki sin(a), where ki ¼ 2p/Li

and Li is the wavelength) and oi the radianfrequency ( ¼ 2p/Ti, where Ti is the period of eachwave). Wavelength Li is estimated using c ¼ Li/Ti,where c is the wave speed.

In order to quantify the parameters in Eq. (7)surface pressure records gathered with microbaro-graphers from Punta Medanos and El Rincon wereused (Dragani et al., 2002). These data reveal thatthe most energetic spectral band covers periodsranging from 30 to 80min. The maximum trough-to-crest pressure amplitude recorded was 4 hPa.The shortest atmospheric pressure disturbanceslapse lasted 5 h and the longest one 43 h. Due tothe fact that only two meteorological stations on thecoast of Buenos Aires were provided with micro-barographers, it was very difficult to determine thearea where atmospheric gravity waves were mani-fested.

In several studies on mesoscale wave disturbancesevents Uccellini and Koch (1987) observed that thejet axis, a surface front, an inflexion axis (between

the trough and ridges axis) and the ridge axis boundthe area of wave activity (Fig. 3). Regarding thepropagation direction of atmospheric gravity wavesit tends to match best with wind direction ofupper tropospheric westerlies (Gedzelman andRilling, 1978). Moreover, they showed that atmo-spherical gravity waves could be considered as notdispersive waves. They observed that although thesewaves have a broad spectrum of wave periods, theentire wave packet moves with the same velocity.

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Fig. 4. Instantaneous free-surface elevation (in cm) at Buenos

Aires continental shelf (Argentina), after 24 h of simulation.

Fig. 5. Sea-level histories at Mar del Plata (MP), continental

shelf (CS) and deep ocean (DO).


In several observational experiments of mesoscalewave disturbances, it was observed that phasespeeds of atmospheric gravity waves were rangedfrom 20 to 40m s�1 (Stobie et al., 1983; Demariaet al., 1989; Powers and Reed, 1993).

Thus, in order to implement a realistic forcingmechanism for the atmospheric gravity wavesperiods, amplitudes and duration of events wereobtained from the available measurements (Nunezet al., 1998). Nevertheless, the area of wave activity,the phase speed and the direction of propagationwere indirectly estimated from synoptic upperanalysis, upper-air soundings and using somegeneral and well-known features of the atmosphericgravity wave studies previously mentioned.

5. Numerical experiments: results

5.1. Passage of an atmospheric cold front

Several numerical experiments (more than onehundred) with different pressure and wind fieldsgenerated as it was explained in Section 4.1 werecarried out, and sea-level oscillations (with periodsranging from 20min to almost 2 h) were notgenerated. The results for a typical experiment arepresented. The model was spun up by increasinglinearly the wind and pressure fields from 0 over12 h. During this lapse the front kept stationary atthe southwestern corner of the domain. After that,the front and the associate pressure and wind fieldsmoved eastward with constant velocity (30 kmh�1)and the frontal line rotated cyclonwise (0.51 h�1)around the low-pressure center moving along thesouthern boundary. Consequently, the surfacefrontal line moves combining both movements arotational and a translating one. Pressure andwind fields, after 24 h of simulation, are presentedin Fig. 2. Northwesterlies on the warm side andSouthwesterlies on the cold side can be appreciated.A snapshot of sea-level response is presented inFig. 4. Set down reaches the highest value along thecoast, decreases towards the slope and is practicallynegligible (lower than 0.1m) in the deep ocean.

Sea-level evolution for three selected points(MP—Mar del Plata—on the coast, CS in thecontinental shelf and DO in the deep ocean, seeFig. 1) is presented in Fig. 5. The highest sea-leveldisturbances are observed on the coast (MP) whereset down exceeds 0.4m. In the continental shelf(CS), sea-level disturbances are lower than on thecoast (MP) but it is higher than in the deep ocean

(DO). According to our results, we have concludedthat the pressure and the wind fields coupled withthe passage of atmospheric fronts do not generatelong ocean waves in the area, even though they canproduce disturbances with periods greater than thetidal ones.

5.2. Atmospheric gravity waves

Several numerical experiments were carried outwith trains of non-dispersive waves with 60, 75 and120min periods and 0.75 hPa amplitude. Thesetrains of waves propagate approximately south-eastward behind and parallel to a front that moveseastward. It was considered that the jet stream (alsoparallel to the front) was stationary at the south-western corner of the domain and that atmosphericgravity wave activity was confined between thefrontal line and the jet stream. Results correspond-ing to a selection of 12 numerical experiments are

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Fig. 6. Continental shelf profile from A (latitude: 381 020S,

longitude: 571 350W) to A0 (latitude: 391 030S, longitude: 551

330W), AA0 transect is shown in Fig. 1 (dashed line). Bathymetric

data were taken from SHN (1993).


presented in this work. Results obtained with trainsof waves with 20, 30 and 40m s�1 phase speeds and300, 310, 320 and 3301 propagation directions (a)were selected and compared. In each experiment theatmospheric gravity wave activity lasted 30 h.

Spectra obtained from simulated sea-levels at MPpoint were estimated. They were obtained by meansof the fast Fourier’s transform procedure, from a setof 512 data (1.42 days). The data were convolutedby means of a 511-point Kaiser–Bessel bandpassfilter, with a passing-wave response function ofapproximately 0.166–3 h periods (Hamming, 1977;Harris, 1978). Table 1 shows spectral contents atMP point computed from each sea-level spectrumby adding up all the spectral contributions placed atthe range of periods from 9.4 to 113.3min. Thehighest spectral content (81 cm2) was obtained using30m s�1 and 3301 and, the lowest one (16.8 cm2)with 40m s�1 and 3101. Since relatively high levelsof spectral contents were found in all of theexperiments it is suggested that atmospheric gravitywaves constitute a highly effective forcing mechan-ism for the generation of long ocean waves. Eventhough, noticeable differences between two casesnearly close (30m s�1 and 3301 vs. 40m s�1 and3101) showed that long ocean wave generation ishighly sensitive to direction of propagation andphase speed of the atmospheric gravity waves. Inthis paper we have only analyzed the capability ofthe atmospheric gravity waves to generate sea-leveldisturbances.

Dragani et al. (2002) studied the coherence andphase difference between pairs of sea-level oscilla-tions data series measured in coastal stations andpresented some results corresponding to a highenergetic event occurred at Mar de Ajo andPinamar, during 8–10 September, 1982. It wasnoted that the phase difference was approximatelya linear function of frequency, which implies thatthe wave motion is essentially non-dispersive. A lagof 0.8 h between Pinamar and Mar de Ajo north-

Table 1

Spectral contents (cm2) at MP obtained from numerical experi-

ments forcing by atmospheric gravity waves

Celerity (m s�1) Direction (deg.)

330 320 310 300

20 50.2 43.3 21.9 34.5

30 81.0 53.3 37.9 36.6

40 41.0 28.7 16.8 17.5

ward propagation was also obtained, which is inagreement with the observations. Considering thedistance between Pinamar and Mar de Ajo and theestimated lag between both stations a wave phasespeed of 17.4m s�1 was obtained.

The 50- and 100-m depth contours graduallydiverge from northeast to southwest on the BuenosAires continental shelf (Fig. 1). The region boundedbetween both contours appears as a very flat zonecharacterized by almost constant depth (70–80m).A representative bottom profile for the continentalshelf is shown in Fig. 6. This continental shelfprofile can be represented by a horizontal, finite-width shelf model and thus, the simplest shallowwater gravity wave approximation can be used as afirst approximation to assess the edge wave speed.Using h ¼ 44m as a realistic value for the con-tinental shelf mean depth between Mar de Ajo andMar del Plata, the wave speed c for the edge-wavescan be calculated as (gh)1/2, where g is theacceleration due to gravity (Leblond and Mysak,1978). Using the aforementioned values, a wavespeed of 20.9m s�1 and a lag of 0.7 h betweenPinamar and Mar de Ajo were obtained. Takingthese values into account, the waves in this region ofthe continental shelf appear to travel a little moreslowly than predicted by the theory.

5.3. Numerical simulation of long ocean waves during

the large-amplitude gravity-wave event of 13 October

1985

The analysis of the gravity wave event occurredalong the Buenos Aires coast on 13 October 1985was given by Nunez et al. (1998). The surfaceweather pattern (taken from NCEP/NCARdatabase: www.cdc.noaa.gov) corresponding toOctober, 12, 18Z, is shown in Fig. 7. It can be seena low-pressure center at 401S, 651W and isobars

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Fig. 7. Surface weather pattern (source: NCEP/NCAR database: www.cdc.noaa.gov) corresponding to 12 October 1985, 18Z. Contours

in h Pa.

Fig. 8. (a) Filtered atmospheric pressure records (Pa) at Punta

Medanos. (b) Pressure atmospheric spectra (in solid line) and the

corresponding to the implemented forcing (in dashed line) at

Punta Medanos. Spectral contents (Pa2) are pointed out.


significantly curved (located at 62–631W) whichindicate the position of a surface cold front comingfrom the west. Wind is blowing from the southwest(north) behind (ahead) the surface cold front. Thisatmospheric situation agrees very well with thetypical synoptic one observed during sea-leveloscillation events, described in Section 3. A non-dispersive wave train propagating parallel to the jetstream direction (3301) with constant phase speedequal to 30m s�1 was considered for the simulation.The filtered atmospheric pressure data from PuntaMedanos and its spectrum are shown in Fig. 8. Thespectrum reveals a broad concentration of spectralenergy at low frequencies (lower than 1.5 cph). Alow peak is located at 2.13 cph. Nevertheless, it mustbe pointed out that due to the microbarographicrecord scale (seven days a page) high-frequencyatmospheric disturbances were not well resolved.Spectral content was 30.0 Pa2. Sea-level filtered datafrom Mar del Plata and its spectrum are presentedin Fig. 9. The highest energetic peak is placed at0.85 cph (70.7min) and a lower peak is located at1.82 (33.0min). Spectral content was 46.1 cm2.

Atmospheric pressure disturbances obtained withthe forcing mechanism described in Section 4.2, at agrid point corresponding to Punta Medanos, ispresented in Fig. 10. This forcing was implementedby adding up six waves with 0.95, 0.40, 0.40, 0.70,0.2 and 0.2 hPa amplitudes and 137, 89, 79, 60, 48and 39min periods, respectively, which representsthe spectral contents located at the most intense

frequency band (frequencies lower than 1.5 cph) ofthe observed spectrum (Fig. 8b). Fig. 8b shows thatthe most energetic band of the the Punta Medanosatmospheric pressure spectrum (between 0.5 and1.5 cph) matched well with the forcing spectrum.The forcing activity is extended between the frontal

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Fig. 9. Filtered sea-level records (a) and its spectrum (b) at Mar

del Plata. Spectral peaks periods (minutes) and spectral content

(cm2) are pointed out.

Fig. 10. Filtered atmospheric pressure of the forcing at a grid

point corresponding to Punta Medanos, time in hours after the

initial time of the numerical simulation.


line (which moves 30 kmh�1 eastward from thewestern boundary) and the jet stream (which wassupposed stationary at the southwestern corner ofthe domain). Atmospheric gravity waves propagatesoutheastwards at 30m s�1. When the front leavesthe computational domain, through the easternboundary, atmospheric gravity wave activityvanishes and sea-level begins to fluctuate freely.

Figs. 11a–c show the surface pressure field andthe frontal line position, and Figs. 11d–f theinstantaneous surface elevation after 12, 24 and36 h of simulation. The atmospheric gravity wavetrain propagates south-southeastwards, behindthe frontal line, in an approximately perpendiculardirection with respect to the coastal line (Fig. 11a).

After 12 h of simulation (Fig. 11d), sea surfaceelevation, forced by the atmospheric perturbation,presents an irregular pattern behind the frontal lineposition. Ahead of the frontal line (ocean area notdirectly forced by the atmospheric gravity wave fieldyet), sea surface elevation presents a more organizedpattern where weak ocean waves propagate pre-dominantly northeastwards, approximately normalto the atmospheric gravity wave propagation direc-tion. After 24 h of simulation (Fig. 11b), the frontalline position is located approximately at the middleof the computational domain, between the Rıo de laPlata estuary and Mar del Plata. Behind the frontalline, sea-level presents a more organized pattern(Fig. 11e), where long ocean waves have crest andtroughs normally oriented with respect to thecoastal line near the southwestern corner of thedomain. Ahead of the frontal line long ocean wavesare refracted and a wave train can be seen enteringthe outer Rıo de la Plata estuary.

After 36 h of simulation (Fig. 11c), atmosphericgravity waves cover the whole inner Buenos Airescontinental shelf and the Rıo de la Plata estuary.Behind the frontal line, between the southwesterncorner of the domain and Mar del Plata (Fig. 11f),long ocean waves present a well defined patterncharacterized by crest and troughs normally or-iented with respect to the coastal line. Inside the Rıode la Plata estuary, long ocean waves are signifi-cantly attenuated probably due to bottom frictiondissipation effects (in the middle Rıo de la Platamean depth is less than 5m and, in the inner part,mean depth is less than 3m). In general, the greateroscillations occurred in the continental shelf nearthe coast. Sea-level disturbances decreased off-shoreand vanished in the DO. Some spurious boundaryeffects seem evident in Fig. 11f, very close to thesouthern border beyond the continental shelf, in thedeep ocean region. A preliminary numerical experi-ment, using a larger model domain where thesouthern boundary was located further south, wascarried out in order to determine whether or not thespurious effects could affect the simulation espe-cially in coastal areas between Mar del Plata andMar de Ajo. The simulation carried out using thelarger domain and the one corresponding to Fig. 11did not show significant differences and, conse-quently, the last one was adopted in all numericalexperiments presented in this paper

Modeled sea-level oscillations at MP (Mar delPlata), PIN (Pinamar), AJO (Mar de Ajo), CS andDO (see Fig. 1) are shown in Fig. 12. The highest

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Fig. 11. Instantaneous atmospheric surface pressure (in Pa) corresponding to the forcing (a, b and c), the frontal line is pointed out.

Propagation direction of the atmospheric gravity wave (black arrow) and advance direction of the cold front (white arrow) are indicated.

Instantaneous view of the sea-level response (in cm) (d, e and f). a–d, b–e and c–f corresponding to12, 24 and 36 h after the initial time of

the simulation, respectively.


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Fig. 11. (Continued)


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Fig. 13. Sea-level spectra at Mar del Plata (MP), continental

shelf (CS) and deep ocean (DO) resulting of the simulation. Total

energy values (cm2) are pointed out.

Fig. 12. Sea-level response (cm) at Mar del Plata (MP), Pinamar

(PIN), Mar de Ajo (AJO), continental shelf (CS) and the deep

ocean (DO) resulting from numerical simulation forcing by

atmospheric gravity wave.


sea-level oscillations (trough-to-crest amplitudes)occur on the coast (0.35m at MP, 0.25m at PINand 0.28m at AJO), decrease off-shore (0.10m atCS) and vanish in DO (lower than 0.05m at DO).Simulated sea-level oscillations are observed first atMP and, subsequently, further north at PI and AJOwhich is in agreement with the observations(Dragani et al., 2002). Observed sea-level oscilla-tions gathered at Mar del Plata (Fig. 9a) have beendetected approximately 2 h before the recordedatmospheric pressure disturbances at Punta Medanos(Fig. 8a). This lapse is in accordance with thetemporal difference obtained between the modeledsea-level oscillations at MP (Fig. 12a) and thesimulated atmospheric pressure activity at PuntaMedanos (Fig. 10). The higher simulated sea-levelamplitudes (Fig. 12a) result to be slightly smaller thanthe observed ones (Fig. 9a) by a factor approximatelyequal to 0.7.

The cross-shelf decay of the wave amplitudeobtained from simulations (Fig. 12) is consistentwith the theoretical solution for trapped edge waveson a horizontal, finite width continental shelf(Leblond and Mysak, 1978). The ratio betweensimulated amplitudes at CS (Fig. 12d) and at thecoast is 0.38 and the corresponding ratio betweenthe ones at DO (Fig. 12e) and at the coast is 0.10,which compare very well with the ratios predictedby the theory (0.42 and less than 0.10, respectively).

The MP, CS and DO sea-level spectra (frequen-cies lower than 2.5 cph) are presented in Fig. 13. Themost energetic band is placed at frequencies rangingfrom 0.5 to 1.5 cph. This is in consistence with theforcing spectrum (Fig. 8b) that has the majorenergetic contribution at 0.8 cph. In the MDspectra, the peak is placed at 0.84 cph and the totalspectral energy is 55.7 cm2. MD sea-level spectrumpresents great similarity with Mar del Plataspectrum. They show the highest spectral peak atthe same frequency and Mar del Plata spectrumpresents a spectral content (46.1 cm2) slightlysmaller than the value obtained for MP (55.7 cm2).In CS, the spectral peak is also placed at 0.848 cphand the total spectral energy (2.8 cm2) is much lessthan the value obtained for MP. Finally, DO sea-level spectrum shows the peak at 1.172 cph and thetotal spectral energy is negligible (0.7 cm2). Resultsclearly show that total spectral energy decreasesprogressively from the shore to the DO.

6. Summary

After several numerical simulations, we con-cluded that the pressure and the wind fields, coupled

ARTICLE IN PRESSW.C. Dragani / Continental Shelf Research 27 (2007) 699–712 711

with the passage of cold fronts, do not generate longocean waves (ranging from 20min to almost 2 h)over the Buenos Aires continental shelf, though theyproduce disturbances with periods longer than thetidal ones. On the other hand, results obtained fromthe atmospheric gravity waves show that theyconstitute a highly effective forcing mechanism forthe generation of long ocean waves. Twelvenumerical experiments were carried out with trainsof non-dispersive waves with 60, 75 and 120minperiods and 0.75 h Pa amplitude and 20, 30 and40m s�1 phase speeds and 3001, 3101, 3201 and 3301propagation directions. Relatively high spectralcontents are obtained in all the experiments. Never-theless, noticeable differences between two casesnearly close (30m s�1 and 3301 vs. 40m s�1 and3101) show that long ocean wave generation ishighly sensitive to the direction of propagation andthe phase speed of atmospheric gravity waves.

The large-amplitude gravity wave and long oceanwave events of 13 October 1985 were successfullysimulated. A non-dispersive atmospheric gravitywave train propagating parallel to the jet streamdirection (3301) and a constant phase speed equal to30m s�1 was implemented and its atmosphericpressure spectrum was in consistence with the PuntaMedanos atmospheric pressure spectrum (Fig. 8b).The results show that the peak at the MD simulatedspectrum is placed at 0.85 cph and the total spectralenergy is 55.7 cm2, thus achieving great similaritywith the Mar del Plata observed spectrum. More-over, it was found that simulated total spectralenergy decreases progressively from the shore to thedeep ocean.

Finally, based on to the occurrence of simulta-neous atmospheric gravity waves and long oceanwave events, the similarities of the spectral structuresof both waving phenomena (Dragani et al., 2002),and the high effectiveness in the atmospheric–oceanenergetic transference (proved through the numer-ical simulations), it is possible to conclude thatatmospheric gravity waves are the most probableforcing mechanism able to generate long oceanwaves in the Buenos Aires continental shelf.

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