Three-dimensional modeling of tidal currents and mixing quantities over the Newfoundland Shelf

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. C5, PAGES 11,407-11,422, MAY 15, 2000 Three-dimensinal mdeling f tidal currents and mixing quantities ver the Newfundland Shelf Guqi Han Fisheries and Oceans Canada, Bedfrd Institute f Oceangraphy, Dartmuth, Nva Sctia Abstract. Majr semidiurnal (M2, S2, and N2) and diurnal (K and O ) bartrpic tides ver the Newfundland Shelf are cmputed using a three-dimensinal nnlinear primitive equatin mdel, with the vertical eddy viscsity calculated frm a level 2.5 turbulence clsure scheme. Cmputed elevatin ctidal charts fr the five cnstituents are generally cnsistent with previus knwledge fr this regin. Cmparisns based n a statistical analysis f the differences between the cmputed elevatins and currents and in situ bservatins indicate gd agreement. While M 2 tidal currents (up t cm/s) are dminant, there are lcally intensified diurnal currents (up t 5-10 cm/s) in sme uter shelf lcatins. The diurnal current intensificatin is attributed t first-mde cntinental shelf waves. An examinatin is carried ut fr the vertical structure f the cmputed M 2 current and fr the tempral and spatial variability f mdel turbulent kinetic energy, mixing length scale, vertical eddy viscsity, and bttm frictin velcity. The examinatin indicates that large vertical eddy viscsity magnitudes and bttm frictin velcities are assciated with strng currents in shallw regins, where strng vertical shears prduce large turbulent kinetic energy. Slutins with bth specified and evlving vertical stratificatin indicate that the stratificatin has a significant influence n the vertical prfile f tidal mixing parameters and currents in shallw areas. Tidally induced turbulence is substantially reduced in the bttm bundary layer and cmpletely suppressed abve it. Tidal currents decrease in the lg layer, increase significantly in the rest f the bttm bundary layer, and decrease in the upper and middle water clumn. 1. Intrductin Ocean tides ver the Newfundland Shelf (Figure 1), as in ther castal waters, are mainly driven by adjacent deep-cean tidal waves which are generated by the tide-generating frces. Tidal elevatins, and currents in particular, are significantly intensified as tidal waves apprach shallw shelf areas. Tides ver the shelf areas usually prpagate as trapped Kelvin waves against the castline, with the trapping mechanism arising frm the Crilis effect. T date, significant prgress has been made in the determinatin f tidal elevatins and currents current variability (except when an inertial scillatin assciated with a winter strm ccurs [de Yung and Tang, 1990]), tidal currents prvide an imprtant mixing mechanism ver mst f the Grand Banks. Althugh there is tw-dimensinal (2-D) numerical mdeling f majr tidal cnstituents [Petrie et al., 1987], there has been n 3-D mdeling f tidal currents Cpyright 2000 by the American Gephysical Unin. Paper number 2000JC /00/2000JC with an examinatin f assciated mixing quantities fr this regin. A 2-D depth-averaged mdel prduces the depthintegrated transprt f water but is unable t prvide any infrmatin n hw the current varies with depth. In this paper we aim t determine quantitatively tidal elevatins, 3-D currents and assciated mixing quantities fr majr semidiurnal cnstituents (M2, S2, and N2), and diurnal cnstituents (K and O ) ver the Newfundland Shelf. This is f particular imprtance and interest fr shrt-term frecasts f passive drifter trajectries wing t the relative significance f tidal currents. The quantitative mdel current prfiles pr- using numerical mdels fr wrld's cntinental shelves, sme vide a crucial cmpnent f hydrdynamicnditins fr sedf which are three-dimensinal (3-D) mdels [e.g., Davies and iment transprt mdels and fr structure assessment imprtant Jnes, 1992; Lynch and Naimie, 1993]. t il drilling prgrams in this regin. The cmputed tidal Fr the Grand Banks f Newfundland, tides exhibit cnelevatin field is als imprtant t deride altimetric height siderable spatial variability especially in amplitude [Gdin, [Hah et al., 1993; Hah, 1995], and the mdel current fields are 1980; Petrie et al., 1987; Hah et al., 1996]. Tidal cmpnents useful t detide acustic Dppler current prfiler (ADCP) accunt fr -91% f the ttal variance f the sea surface data fr the study f ther shelf dynamics. Furthermre, the height. Petrie [1982] has als shwn that the tidal band acdeterminatin f 3-D tidal currents and mixing quantities is cunts fr 51% f the current variance fr perids lnger than needed t prvide imprtant backgrund knwledge fr the 12 hurs and is an imprtant part f the current spectrum ver numerical mdeling f ther shelf prcesses. the uter Grand Banks. With their dminance in the ttal The mdel dmain cvers the shelf and ceanic area with 11,407 water depths ranging frm 10 t 5000 m, abridged by the cntinental slpe with rapid tpgraphic change. We first investigate bartrpic tides in a hmgeneus fluid. A level 2.5 turbulence clsure scheme [Mellr and Yamada, 1982], in which prgnstic turbulent kinetic energy and mixing length are cmputed, is used t accunt fr the subgrid-scale diffusin f mmentum in the vertical. We then cnsider the bartrpic tides with vertical stratificatin. The effects f the vertical stratificatin n the turbulent kinetic energy, vertical eddy

2 11,408 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF (a) Labradr Sea U05 30m 54 U07 U08 100m E02 ) Newfundland Shelf Sctian.00m Grand Bank Whale Bank ' O E03 Sutheast Sh, U02 x U01 42 Nrth Atlantic 3000m Lngitude Lngitude Figure 1. (a) Map shwing the Newfundland Shelf and adjacent waters. (b) Map shwing the mdel dmain. Open circles are the lcatins f castal tide gauge and ffshre bttm pressure gauge statins. Crsses are current meter mring sites. The western and nrthern Grand Banksectins (WGB and NGB) are indicated as slid lines. -47 viscsity, bttm frictin velcity, and hence tidal current prfiles are examined. We have used climatlgical seasnal mean density prfiles based n histrical hydrgraphic data t represent mre realistic effects. The vertical density prfile is fixed quantities is examined in sectin 5. In sectin 6 the effect f the vertical stratificatin and sme mdel parameterizatins tidal currents and mixing is examined. Sectin 7 summarizes the results. in diagnstic summer and spring cases and is allwed t evlve fr a subsequent prgnstic summer case during the mdel integratin in time. The barclinic pressure gradients are 2. Hydrdynamic Mdel turned ff in the diagnstic and prgnstic runs t disallw barclinic (internal) tides being generated in the mdel slutins. In any case, the diagnstic run des nt generate barclinic tides. Barclinic tides are bartrpically frced in a stratified cean with variable bathymetry. In cntrast bar- The hydrdynamic mdel used in this study is ECOM-si. This mdel cnsists f 3-D nnlinear primitive equatins with the Businesq and hydrstatic apprximatins and a level 2.5 turbulence clsure under a crdinate system which is rthgnally curvilinear in the hrizntal and has rr (rr = (z - trpic tides, barclinic tides primarily displace internal ispy- sr)/(s r + H), where z is the cnventinal vertical crdinate cnal surfaces, with significant vertical structure in tidal currents psitive upward and zer at the still water level, H is the lcal but with relatively weak surfac elevatin signature. Numerical water depth, and sr is the tidal elevatins) levels in the vertical studies f the stratificatin effects n the dminant tidal currents [e.g., Xing and Davies, 1996a] and n the diurnal inten- [Blumberg, 1991 ]. In this study, water is assumed hmgeneus in the baseline mdel run, with stratificatin in sme sensitivity sificatin [Xing and Davies, 1998b] fr the Nrthwest Eurpean runs. The vertical eddy viscsity cmputed using the Me#r Shelf and the barclinic tides fr castal seas [e.g., Maze, 1987; and Yamada [1982] level 2.5 turbulence mdel, whereby the Hllway, 1996; Cummins and Oey, 1997; Xing and Davies, turbulence is characterized by transprt equatins fr twice the 1998a] have been reprted. We leave the examinatin f the turbulent kinetic energy and the prduct f a macr mixing barclinic tides in this regin t a later study with a higher- length scale and twice the turbulent kinetic energy. The hrireslutin prgnstic mdel. In this study we fcus n the determinatin f the bartrpic tide, the turbulent mixing, and zntal eddy viscsity calculated using the shear-dependent Smagrinsky frmulatin [Smagrinsky, 1963] t suppress the influence f stratificatin, which is ne f the effrts [e.g., small-scale features. In ffshre shallw areas the vertical fric- Hah et al., 2000] in the frmulatin f a data-assimilative tin, especially at the sea bttm, dminates the frictinal mdel t frecast castal tides fr this regin. In sectin 2 we intrduce the hydrdynamic mdel, numerdissipatin. In deep waters, such as ver the shelf break and upper cntinental slpe, hwever, the hrizntal frictin can ical discretizatin, mdel dmain, and bundary cnditins. be imprtant. Observatinal data are described in sectin 3. Sectin 4 presents and discusses mdel slutins withut vertical stratificatin. The vertical structure f the M 2 currents and turbulent Tidal elevatins are specified at the pen bundary. The bundary elevatins are cnstructed n the basis f Petrie et al.'s [1987] mdel utput and Hah et al.'s [1996] altimetric

3 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF 11,409 tides, using an ptimal linear interplatin prcedure [Brethertn et al., 1976]. A zer nrmal velcity is impsed at the lateral land bundary, while the nrmal gradient f the tangential velcity cmpnent is set t zer at the pen bundary. The depthaveraged nrmal velcity at the pen bundary is related t the sea surface elevatin using a radiatin bundary cnditin, als used by Xing and Davies [1996b]. At the sea surface a zer stress bundary cnditin is applied, with the absence f the wind stress. Crrespndingly, the flux f turbulent kinetic energy is set t zer. At the sea bttm the quadratic stress law is used, in which the nndimensinal drag cefficient is calculated n the basis f a specified bttm rughness height f m fr the baseline (hmgeneus) and stratificatin cases. In this study we impse a minimum value f fr the drag cefficient, fllwing Blumberg [1991]. Nte that this minimum value des nt vershadw the rughness height f m fr waters shallwer than 3000 m. The slight increase (<0.0003) f the drag cefficient fr waters frm 3000 t 5000 m has little effect n the slutins ver the shelf. Fur- thermre, a hmgeneus mdel run with a rughness height f 2 cm shws limited sensitivity f the slutin t the rughness height (see sectin 6.3). The turbulent kinetic energy is specified as an empirical functin f the bttm frictin velcity. Kinematic cnditins are enfrced n the vertical velcity at the sea surface and bttm. Tidal bservatins St. Jhn's (E09), Argentia (El0), and Lng Pnd (Ell) cme frm Canadian Hydrgraphic Service, with the recrd length used in tidal analyses f 365,362, and 37 days, respectively. Eight bttm pressure gauges (E01-E08) deplyed in prduced a set f tidal data, scattered all ver the Grand Banks [Petrie et al., 1987], five (E04-E08) f which were laid n the Newfundland slpe. These bttm pressure measurements were made in depths ranging frm 70 t 404 m, with a typical duratin f half a year. Mred measurements at three sites (U06, U07, and U08) acrss the Avaln Channel frm Petrie [1991] are used fr the current cmparisn. Current measurements frm three ffshre il drilling platfrms (U04, U05, and U09) n the nrthern Grand Bank are frm Petrie et al. [1987]. Tidal current amplitudes fr three deplyments (U01, U02, and U03) n the Sutheast Shal [Rss et al., 1988] were initially underestimated, and crrected results frm J. W. Lder (persnal cmmunicatin, 1998) are used in the cmparisn. Wa- ter depths at these measurement sites vary frm 54 t 175 m, and the recrd length is ---5 mnths. The tidal analyses were perfrmed typically using hurly raw data fr the entire length f recrd and did nt include an estimatin f uncertainty. Oceangraphic prcesses ther than tidal currents were nt remved frm the raw data. The bservatinal data are nly estimates f the true tides and are subject t bth randm and systematic errrs. The discrepancies between the mdel results and the bservatins can arise frm bth uncertainties in bservatins and inaccu- The gverning equatins are discretized n the Arakawa C grid using a finite difference methd. The pressure gradient in the mmentum equatins and the velcity divergence in the cntinuity equatin are treated implicitly. The resulting linear, symmetric, and psitive definite system f equatins fr the surface elevatin field is slved by a precnditined cnjugate gradient methd. racies in the mdel. In additin t measurement errrs, uncertainties in bservatins can arise frm nntidal variability such as seasnal variatins wing t nnlinear interactins between tides and wind- r buyancy-driven currents and frm statistical factrs such as the length f the time series and the number f the cnstituents included in an harmnic analysis [Freman and Henry, 1989; Freman et al., 1993]. The mdel dmain cvers frm 42 ø t 49øN and frm 55 ø t Randm errrs frm an analysis f finite length data may 47øW and is spatially discretized by 10' latitude-lngitude grids. The grid has a meridinal spacing f 18.3 km and a znal spacing f 13.6 t 12.0 km frm suth t nrth. An riginal bttm tpgraphy data set with a 5' by 5' reslutin is cme frm the presence f nntidal variability. Fr example, tidal analyses frm 11 year-lng sea level recrds at Halifax gave a standard deviatin f 0.8 and 0.3 cm in amplitude and f 0.7 ø and 1.2 ø in phase fr M 2 and K tides [de Margerie and smthed using a five-pint filter with a weighting cefficient Lank, 1986]. Fr half-year recrds the crrespnding errrs f 0.8 fr the central pint. In the vertical the dmain is divided int 21 unequally spaced levels (tr = 0 at the sea surface and -1 at the sea bttm), with high reslutin near the bttm (the fur levels nearest the bttm are at tr = -0.99, , -0.95, and -0.90) t reslve the bttm bundary layer. Nte that the bttm stress and frictin velcity in the present tr crdinate mdel are calculated using the currents and the drag cefficients at the lwest current level, which is depthdependent, while they are usually based n a reference height wuld be 1.1 and 0.4 cm in amplitude and 1.0 ø and 1.7 ø in phases. The uncertainty in the current data may be estimated by dividing time series int "mnthly" recrds, as suggested by Freman et al. [1993]. The standard errrs at U01, calculated as the standard deviatin f the estimated harmnic parameters frm the mnthly data, are estimated t be 1.0 and 0.4 cm/s in magnitude and 6 ø and 25 ø in phase fr the M 2 and K tides. The systematic errrs may result frm a clck errr. Fr example, a timing errr f 16 min at site E02, as reprted by Petrie et al. f 1 m abve the sea bttm if derived frm bservatins. [1987], wuld have induced phase errrs f ---7 ø and 3 ø fr the A time step f 190 s is used in the slutins presented in the subsequent sectins. Sensitivity cases with time steps f 50 and semidiurnals and diurnals. 315 s shw a mean phase advance f 1 ø and a mean phase lag 4. Mdel Tidal Elevatins and Currents f 3 ø in the cmputed M 2 tidal currents, as cmpared t the Withut Stratificatin baseline slutin with the time step f 190 s. Tidal elevatins, currents, and turbulent quantities are cm- 3. Observatinal Data puted by integrating frward the mdel in time frm a state f rest with the cmpsite M 2, S2, N2, K, and O tidal elevatins We cmpare ur mdel tidal elevatins and currents with bservatinal data frm a variety f surces. Elevatin data are frm castal tide gauges and pelagic bttm pressure gauges. specified at the pen bundary. We chse a 9-day spin-up perid, judged t be sufficient fr the mdel t be independent f the initial cnditin. Then, the mdel utput frm the fl- Current data are frm mred measurements. lwing 9-day integratin after the spin-up perid is analyzed t retrieve amplitudes and phases f thse cnstituents using a harmnic analysis. One cncern is whether the M 2 and N 2 can

4 11,410 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF Lngitude Lngitude Lngitude Figure 2. Cmputed elevatin camplitude (in cm) and cphase charts (in degree) fr (a) M2, (b) K, and (c) O. The 200-m isbath is displayed as a thin slid curve. be reslved with the results f the multicnstituent simulatin frm the 9-day mdel perid that is much shrter than the syndic perid f the tw cnstituents. T address this cncern, we integrate the mdel until day 37. The results frm the last 28-day mdel perid are analyzed t retrieve the five cnstituents. We find there is hardly any difference in the tidal current magnitudes between the 28-day and 9-day analyses. This suggests that the mdel time series are very "clean" cmpared with current meter time series and the 9-day mdel perid is lng enugh t get the M 2 and N 2 well separated. Freman and Henry [1989] als demnstrated that fr time series with lw nntidal cntent a recrd lng enugh t sep- arate all frequencies by ne cycle was nt required. Figure 2 presents camplitude and cphase charts f the cmputed M2, K, and O cnstituents. In general, the M 2 tide Davies et al., 1997]. The camplitude f the cmputed K 1 cnstituent (Figure 2b) decreasesuthward frm cm at (Figure 2a) prpagatesutheastward with amplitude increas- the nrthern bundary t 6 cm at 46øN. Suth f this latitude, ing tward the Newfundland cast, cnsistent with an amphidrmic pint lcated east f the Newfundland Shelf in the the amplitude is spatially unifrm. The exceptin t this is the amplitude reductin tward the western pen bundary, cndeep Nrth Atlantic [Schwiderski, 1980]. Alng the castline sistent with the amphidrmic pint west f the Newfundland the M 2 amplitude is nearly dubled frm nrth t west f Avaln Peninsula. The amplitude ranges frm 15 cm in the nrtheast crner t 70 cm in the Placentia Bay. Suth f 46.5øN, the nearshre tide travels westward, fllwing the verall castline rientatin. Overall, the camplitude and cphase distributin is characterized by a castal Kelvin wave. Shelf [Han et al., 1996]. The O (Figure 2c) tide prpagates suthward and then westward alng the shelf with amplitude decreasing away frm the cast, in a way characteristic f a Kelvin wave prpagating alng the castline. The tw diurnal cnstituents have cmparable elevatin magnitude, with a mean rati f the O4 t K amplitudes f Overall, the The S2 (nt shwn) and especially N 2 (nt shwn) cnstituents diurnal signal is significantly weaker than the semidiurnal sigexhibit similar spatial features but with much smaller amplitudes. The mean rati f S 2 amplitudes t M 2 amplitudes is This rati fr the N 2 tide is The diurnal (K and O ) tidal waves ff the Canadian Atlantic cast prpagate alng the cntinental margin equatrnal, with a mean amplitude rati f ((K] + O )/(M 2 + S 2 + N2) ). Taking the significant amplificatin f the semidiurnal tides frm the uter t inner shelf int cnsideratin, the tidal type can be categrized as mixed, mainly semidiurnal ver the uter Newfundland Shelf, and semidiurnal near the Newward, each with a mid-cean amphidrme [e.g., Le Prvst et fundland cast. al., 1994]. Lcal amphidrmes n the Canadian Atlantic Shelf are generated alng the irregular castline with varius inland seas and embayments. Fr example, amphidrmes west f the suthwestern Newfundland Shelf [Gdin, 1980; Han et al., 1996] are assciated with an estuarine interactin between the shelf diurnal regime and the diurnal respnse in the Gulf f St. Lawrence. Flather [1988] carried ut a numerical experiment that demnstrated the significant influences f diurnal tidal flw in Juan de Fuca Strait n the diurnal tide ver the nearby Vancuver Island Shelf. The mdel diurnal ctidal charts (Figure 2) shw a significantly different spatial pattern cmpared with the M 2 ctidal chart ver the Newfundland Shelf. Sme diurnal intensifica- tin ver the uter shelf and shelf break due t a shelf wave resnance can be seen frm Figure 2 (and in particular frm the crrespnding patterns f diurnal current ellipses; see later in this sectin). The diurnal intensificatin has been reprted and studied fr ther cntinental shelf areas [e.g., Huthnance et al., 1986; Freman et al., 1993; Prctr and Davies, 1996; The spatial features in Figure 2 are generally cnsistent with previus knwledge f the M2, 82, N2, K, and 01 tidal elevatins n the Newfundland Shelf [Gdin, 1980; Petrie et al., 1987; Han et al., 1996]. A detailed cmparisn between the cmputed and bserved elevatin amplitude and phase f the M2, 82, and N 2 tides at castal tide gauges and ffshre bttm

5 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF 11,411 Table 1. Summary f Observed and Cmputed Semidiurnal Tidal Elevatins at Tide and Pressure Gauge Sites Site AO PO AMO PMO E E E E E E E E E El Ell E E E E E E E E E El Ell E E E E E E E E E El Ell AO, amplitude (cm) bserved; PO, phase (degree) bserved; AMO, difference f mdel amplitudes frm bservatins; PMO, mdelbservatin phase difference. pressure gauges is given in Table 1. At mst f the sites, amplitude difference is <1 cm, and the phase difference is within 5 ø (Figure 3). The cmparisn shws that the mdel has hardly any mean biases in reprducing elevatin amplitude and phases f the semidiurnals. The rt mean square (RMS) difference is 1.8 cm fr amplitude and 3.6 ø fr phase. Anther indicatr f the mdel-bservatin mismatch is Hs, the RMS value which accunts fr bth amplitude and phase discrepancies [Davies et al., 1997]. In terms f the small phase discrepancies, except fr diurnal cnstituents at a few sites (see Tables 1 and 2), the RMS values separately fr amplitudes and phases are adequate t represent the differences. Table 2 cmpares the bserved and cmputed elevatin parameters fr the K and O tides. The cmputed amplitudes and phases shw negligible biases, similar t thse fr the semidiurnals. At mst f the sites, amplitude difference is <1 cm, and the phase difference is within 15 ø (Figure 3). The RMS amplitude and phase differences are 1.0 cm and 11 ø. Cmpared with the semidiurnals, the diurnals have smaller abslute amplitude differences but larger relative differences. The RMS phase difference f 3.6 ø fr M 2 crrespnds t ---7 min nly, whereas the difference f 11 ø fr K represents up t 40 min. A cmparisn f Petrie et al.'s [1987] 2-D mdel utput with bservatins indicated that the 2-D mdel is nearly as accurate as the present 3-D mdel in reprducing the tidal elevatins ver the Newfundland Shelf. It is nt surprising that the mdels prduce accurate interir elevatins since the mdel dmains are small cmpared with the hrizntal scale f tidal elevatin amplitudes and phases, which are specified n mst f the mdel's lateral bundary based n available data and mdel results. Hwever, the gd agreement f the present mdel with tide gauge data alng the cast f Avaln Peninsula des demnstrate the mdel's ability in reprducing ac- curate tidal elevatins. The cmputed M 2 tidal current ellipses at the sea surface (r = 0) and the third level (r = -0.95) abve the bttm are shwn in Figure 4. At the surface (Figure 4a) a nearly rectilinear flw is fund alng the cast f Avaln Peninsula. The current in the Avaln Channel is weaker and nearly rectilinear with the majr axis aligned alng the channel. Over the Grand Bank f Newfundland the flw patterns are mre circular. Strng tidal currents ccur in the uter shelf and shelf break regin, especially ver the shallw banks and shals. The maximum current magnitude reaches cm/s near the Sutheast Shal. The spatial pattern f the bttm tidal current ellipses (Figure 4b) is similar t that f the surface current, but the magnitude f the bttm current is significantly reduced by bttm frictin. The S2 and N 2 currents (nt shwn) have similar spatial patterns t the M 2 currents but with much smaller magnitudes (abut ne third). The cmputed K tidal current at the sea surface (Figure 4c) is weak in general, cmpared with the M 2 current. Hwever, relatively strnger currents (>5 cm/s) exist in sme uter shelf and shelf break areas. There are strngestidal currents (---10 cm/s) n the suthwestern uter shelf near 55.5øW. The K current based n the Kelvin wave thery is estimated t have magnitudes f 1-2 cm/s frm the cmputed K elevatin amplitude (Figure 2b). Therefre Kelvin waves, which pssess relatively large surface displacements and weak currents [LeBlnd and Mysak, 1978], are unable t generate the lcalized diurnal current intensificatin. On the ther hand, the intensificatin f these tidal currents can be explained in terms f cntinental shelf waves which feature relatively large currents and small elevatins [Crawfrd and Thmsn, 1982; als see Huthnance et al., 1986; Freman et al., 1993; Prctr and Davies, 1996; Davies et al., 1997]. Frm the dispersin relatinships fr western and nrthern Grand Banks sectins crssing the intensificatin areas (Figure 5b) we can see that first-mde shelf waves are permitted at the K frequency. The largest currents assciated with the shelf waves are fund ver the segment where the K current intensificatin ccurs (Figures 4c and 5c). Therefre this uter shelf current intensificatin is prbably caused by a resnance between a first-mde cntinental shelf wave and the K tide. The perid f the first-mde shelf waves depends critically n the crss-shelf bttm slpe, s the intensificatin is highly selective. Thmsn and Crawfrd [1982] argue that the shelf wave currents are indirectly frced thrugh an ffshre mass flux within a time-dependent bttm turbulent bundary layer prduced by tidal currents. Similarly, the O tidal current (Figure 4d) is generally small in this regin but significantly intensified n the suthwestern and nrtheastern uter shelves. The intensificatin can als be explained by the first-mde cntinental shelf wave. Bth K and O bttm current magnitudes (nt shwn) are als reduced by bttm frictin.

6 11,412 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF Semidiurnals (M2, S2 and N2) I Amplitude Difference (cm) Diurnals (K1 and O1) Phase Difference (degree) Amplitude Difference (cm) Phase Difference (degree) Figure 3. Histgrams fr the amplitude and phase differences between the mdel and in situ bserved elevatins fr the semidiurnals and the diurnals. It fllws that the mdel tidal currents ver the Newfund- land Shelf can be classified as weak t mderate cmpared with ther Atlantic shelf areas such as the Nrthwest Eurpean Shelf [e.g., Davies et al., 1997; Davies and Jnes, 1992]. In general, the semidiurnal cnstituents dminate the current variability n the Newfundland Shelf. Hwever, the diurnal currents are imprtant in sme uter shelf and shelf break areas prbably because f the presence f the diurnalfrequency cntinental shelf waves. The surface current features in the present mdel are generally cnsistent with previus 2-D mdel results [de Margetie and Lank, 1986]. The cmputed magnitudes and phases f the znal (u, eastward psitive) and meridinal (, nrthward psitive) cmpnents fr the five cnstituents are cmpared with mred current meter measurements (Figure 6). The scatter diagrams fr the M 2 cnstituent shw verall gd agreement between the mdeled and bserved currents. Altgether, there are 46 available intercmparisns. The RMS differences f the M 2 cnstituent (46 cmparisns) between the mdeled and bserved are 2.3 cm/s in amplitude and 28 ø in phase. If we exclude the psitins where the bserved current magnitude is <1 cm/s, the RMS differences (41 cmparisns) are 2.2 cm/s and 30 ø. We can als see frm Figure 6 that the mdel prduces the currents f the tw ther semidiurnal cnstituents better than Table 2. Same as Table 1 but fr the Diurnal Tidal Elevatins Site AO PO AMO PMO g 1 E E E E E E E E E El Ell O1 E E E E E E E E E El Ell

7 ., HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF 11, (a) M 2 at =O (b) M 2 at = L)::: 48 Lngitude (c) K at I s i, ', % ','. './ 44., ' '-.'00 t ',, :: ''. :-..;-.: 43. '.,., 42 ''' Lngitude Lngitude Figure 4. Subsampled M 2 current ellipses (a) at the surface and (b) at a near-bttm level (r = -0.95), and (c) K and (d) O current ellipses at the surface. The radial lines in ellipses indicate a cmmn time. The WGB and NGB sectins are shwn as dashed lines in Figures 4c and 4d. The 200-m isbath is displayed as a thin slid curve. thse f the tw diurnal currents. If we exclude the psitins where the bserved current magnitude is <1 cm/s, the RMS amplitude differences between the mdeled and bserved currents are 0.6, 0.9, 1.3, and 0.7 cm/s fr the S2 (27 cmparisns), N 2 (31 cmparisns), K (21 cmparisns), and O (22 cmparisns) tides, respectively. The crrespnding phase differences are 35 ø, 46 ø, 58 ø, and 75 ø. 5. Vertical Structure f Mdel Tidal Currents and Mixing Quantities In this sectin we make a clse examinatin f vertical struc- ture f cmputed tidal currents and mixing quantities at selected individual sites t give a dynamic insight int the mdel results. We cnsider nly the M 2 current prfiles since the M 2 currents dminate the tidal current variability. The vertical prfiles f cmputed M 2 tidal currents (Figure 7) are shwn at selected sites U01, U04, and U09. At the shallw (54 m) site U01, M 2 tidal currents are relatively large, f the rder f 20 cm/s, and the turbulent viscus effects are strng, with a sheared bundary layer extending frm the bttm t abve the middepth. The znal cmpnent f current at depth is a little underestimated, while the meridinal cmpnent is in gd agreement with bservatins. The phase values in bth cmpnents are well prduced. At the deeper (90 m) shelf lcatin U09, tidal currents are weaker, and vertical current shear exists in the lwer water clumn and near the sea bttm. The mdel verestimates the current magnitude at this site. At the much deeper (196 m) shelf break site U04, viscus effects are smaller, and the frictinally retarded bundary layer is even thinner and kept within the 5-10% f the water clumn (---10 m) frm bttm. The upper water clumn is nt influenced by bttm frictin and remains shear free. The u cmpnent is apprximately reprduced in the mdel, and the v cmpnent is extremely weak. Farther ffshre ver

8 11,414 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF I I I I ' ' _102 ß 0 3 r -I _ b) i i i Offshre Distance (km) i i i i i i i i _ K1 5OO i i 0 5 -,'0 -, 5 ;0 3'0 3; 4'0 4; (c) Wavenumber (10-6 m -1) i i i i i i i i i Offshre Distance (km) Figure 5. (a) Bttm prfiles f the western (slid line) and nrthern (dashed line) Grand Bank sectins (see Figure 1 fr lcatins), (b) dispersin relatins fr first-mde cntinental shelf waves, and (c) current speed (in an arbitrary unit) as a functin f ffshre distance alng the sectins at the K frequency. the cntinental slpe (say at a depth f 1000 m), tidal currents by the M 2 tidal variability and is large at the shallw lcatins are extremely small (1-2 cm/s) and, in essence, are inviscid free stream flws abve a very thin bttm bundary layer. At the shallw lcatin U01, twice the mdel turbulent kinetic energy q2 (Figure 8) near the bttm is f the rder f 10-4 m2/s 2. A significant amunt f the turbulent energy is where the tidal current is strng. The mdulatin by the ther cnstituents varies spatially. At U04 the evlutin f the frictin velcity deviates significantly frm a single M 2 harmnic, attributable t the increased imprtance f the diurnal cntributin. transferred upward, even t the upper water clumn. The The hrizntal distributin f the abslute bttm frictin turbulent energy shws prminent tempral variability. The vertical structure f the mixing length scale I is nearly parablic and shws insignificantempral change. The maximum mixvelcity averaged ver 16 M 2 tidal cycles (cycles 17-33) indicates that the mdel bttm frictin velcity varies frm 0.1 t 0.6 cm/s ver the Newfundland Shelf (Figure 10a), with a ing length scale is - 4 m at middepth. The vertical eddy vis- maximum arund the Sutheast Shal. Given the bttm friccsity 't prfile is smewhat parablic, with a maximum value tin velcity, we can estimate the thickness f the bttm f m2/s belw middepth. The eddy viscsity als subject bundary layer by using c u,/f, in which c = and f t prminent change with tidal phases. In the shelf break regin U04, cmputed tidal currents are smaller, and the turbulence is weaker. The turbulent energy is an rder smaller than that at U01, with smaller tempral variability. The mixing length prfile has a similar structure t that at U01. An exceptin is the increased maximum mixing length scale f - 8 m, reflecting the increased water depth. The resuiting maximum eddy viscsity m2/s, nly a 40% reductin cmpared with the value at U01. The tempral and spatial variability f the turbulent kinetic energy, mixing length scale, and vertical eddy viscsity in the present mdel is cnsistent with that fund in ther tidal mdels [e.g., Xing and Davies, 1996a, b]. Large vertical shear in is the lcal Crilis parameter [Lder and Greenberg, 1986]. There have been many studies f the tidal bttm bundary layer and the shelf frnt, sme f which [e.g., Lder and Greenberg, 1986; Stigebrandt, 1988; Kitaigrdskii, 1992; Zilitinkevich and Mirnv, 1996] use c l = 0.2 and thers which use c [Garrett et al., 1978] r 0.3 [Davies and/imridge, 1993]. In this study we find the use f c fr the hmgeneus case and 0.2 fr the stratificatin case (see sectin 6) gives an verall cnsistency with what the cmputed tidal current prfiles wuld imply. With c = 0.4 the estimated maximum thickness f the tidally averaged bundary layer is - 25 m, lcated ver Sutheast Shal. Therefre tidal mixing alne seems insufficient get the water well mixed ver the depth. hrizntal tidal currents near the bttm and in shallw areas The lg layer thickness can be estimated using O.04u,/f generates large turbulent kinetic energy. The vertical eddy viscsities depend n bth turbulent kinetic energy and mixing length scale, with maxima a little belw the middepth. Tempral changes f the cmputed bttm frictin velcities u, at U01, U04, and a much deeper lcatin (1000 m) are shwn in Figure 9a. Overall, the frictin velcity is dminated [Sulsby, 1983]. Frm Figure 10a the maximum thickness f the tidally averaged lg layer is m, lcated ver Sutheast Shal. Fr the Newfundland Shelf the mdel frictin velcity is averaged at 0.25 cm/s, s the mean lg layer thickness is m. The mdel results in this sectin clearly indicate the signif-

9 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF 11,415 Amplitude 'G' ' O O O -ul ß 'O 0 ß Observatin (cm/s) 5 ' O 4 O E3 : 1 OO O,O Observatin (cm/s) 5. '--4 t 3 O -u2 O O : 1 t (b O Observatin (cm/s) 5... E _ O (5::) -u2 : 1 0,c),,, Observatin (cm/s) 5, E ( 'u (5) O O M2 4OO 3OO loo -loo S2 Phase Observatin (degree) 4OO loo -loo f,, N2 Observatin (degree) loo -100 f ;0 3; Observatin (degree) 4OO loo -loo Ol loo, -100 j p Observatin (degree) 0 I ' '00 3' Observatin (cm/s) Observatin (degree) Figure 6. Scatter diagrams fr the amplitude and phase between the mdel and in situ bserved currents fr M2, S2, N2, K, and O (frm tp t bttm). icant hrizntal variatin f magnitudes f the turbulent kinetic energy, vertical eddy viscsity, and bttm frictin velcity. Large vertical viscsity magnitudes are assciated with strng currents in shallw regins, where strng vertical shears prduce large turbulent kinetic energy. The bundary layer is thickest in lcatins where the turbulent energy is largest. Similar findings were reprted by Xing and Davies [1996a] frm the Hebrides Shelf tide mdel, which has a slip bttm bundary cnditin similar t that in the present study. An alternative t the slip cnditin is the nnslip cnditin [e.g., Davies, 1993; Xing and Davies, 1995]. The use f the slip bundary cnditin can lead t a very rapid increase f the turbulent kinetic energy in the very thin near-bed layer as cmpared with that f the nnslip cnditin [Xing and Davies, 1995, 1996c]. evlve seasnally. We will examine the effects f vertical stratificatin n tidal currents and turbulent quantities in this sectin. The density prfiles in Figure 11a are climatlgical seasnal means fr spring and summer, averaged hrizntally ver the cmputatinal dmain at selected standard depths (0, 10, 20, 30, 40, 200, 1000, and 5000 m). The climatlgical seasnal mean density fields at the standard depths are estimated frm the Bedfrd Institute's histrical hydrgraphic database using an ptimal interplatin prcedure. The Brunt- Vaisala frequency N prfiles crrespnding t the density prfiles are presented in Figure 11b. It is evident that stratificatin ver the shelf is much strnger in summer than in spring and is strngest at water depth frm 10 t 30 m in summer. Althugh it is mre realistic t specify the hrizntally and 6. Sensitivity Studies vertically variable density fields, a cmparisn has indicated that the cmputed currents and mixing quantities with the 6.1. Diagnstic Run With Fixed Vertical Stratificatin hrizntally unifrm summer density prfile have nly minr Water is assumed t be hmgeneus in the vertical in sectins differences frm thse with the 3-D summer density field. 4 and 5. Hwever, stratificatin des exist in this regin and Therefre the hrizntally unifrm density prfiles are speci-

10 11,416 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF U01 0 I! -0.4 I U04 ß I t> U09 ß i x i i i -.8-1, lo 20 1 O u-amplitude (cm/s) u-phase (degree) v-amplitude (cm/s) 1 O v-phase (degree) Figure 7. Cmputed vertical prfiles f M 2 currents at U01, U04, and U09 fr the baseline case (thick slid lines), the stratificatin case (thin dashed lines), the case with the bttm rughness height f 2 cm (thick dashed lines), and the single M 2 cmputatin (thin slid lines). Crsses are the in situ bservatins. u ' I _ U _ q2 (10-4 m2/s 2) I(m) v t (m 2/s) Figure 8. Cmputed vertical prfiles f twice turbulent kinetic energy q2, mixing length l, and vertical eddy viscsity v t at U01 and U04. The prfiles are presented at a time interval f-3 hurs frm M 2 cycles

11 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF 11,417 I I I I I I I I 0.5 (al M 2 Cycle I I I I I I I I (b),, ' I i I I M 2 Cycle Figure 9. Time series f the bttm frictin velcity. (a) Spatial change at U01 (thick slid line), U04 (dtted line), and at a lcatin with a depth f 1000 m (thin slid line) and (b) sensitivity at U01 t the vertical stratificatin (pen circles) and the bttm rughness height (dashed line). fled and kept fixed during the mdel integratin in time. As a result, there are n internal tides generated. The barclinic pressure terms in the mmentum equatins are turned ff. The nly effect f the stratificatin n the turbulence and currents is thrugh the buyancy terms in the twice turbulent kinetic energy equatin and in the equatin fr the prduct f the twice turbulent kinetic energy and the mixing length scale and thrugh the stability functins. In the rest f this sectin the results presented are fr the summer case with the hrizntally unifrm stratificatin (Figure 11, dashed lines) unless it is stated therwise. The cmputed M 2 tidal elevatins with the vertical stratificatin are nt significantly different frm thse fr the hmgeneus water. A cmparisn at all the grid pints shws RMS (a) u. (cm/s) fr the baseline case (b) u. (cm/s) fr the summer case (c) u. (cm/s) fr the spring case 49 i, _ ', Lngitude Lngitude Lngitude Figure 10. Bttm frictin velcity (in cm/s) averaged frm M 2 cycles fr (a) the baseline, (b) the summer, and (c) spring stratificatin cases. The 200-m isbath is displayed as a thin slid curve.

12 _ 11,418 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF! i! 0 lo -,, (a) lo (b) Summer Spring / / r OO I i i ' ' t (kg/m) ( N (radian s-1) Figure 11. (a) Seasnal mean density prfiles and (b) crrespnding Brunt-Vaisala frequency prfiles in spring (slid line) and summer (dashed line). differences f 0.1 cm fr amplitude and 0.3 ø fr phase. Hwever, the mdel M 2 tidal current ellipses with and withut the stratificatin have distinguishable changes in shallw areas, with little r n changes in waters deeper than 200 m. The RMS differences at the nine mring sites (nine sites by 20 levels by tw cmpnents) are 1 cm/s fr amplitude and 21 ø fr phase. The phase difference ccurs primarily n the lwer water clumn, especially near the bttm. Suppressin f turbulence ccurs in the water clumn where the density increases with depth. At the shallw lcatin U01 the stratificatin cmpletely suppresses the turbulence in the upper and middle water clumn (Figure 12), resulting in a shear-free (Figure 7) and inviscid layer. The vertical eddy viscsity is essentially the specified backgrund value f 10-5 m2/s. The turbulent kinetic energy near the bed is als weakened by nearly 50%. The vertical eddy viscsity cefficient there is reduced by up t ne rder. The maximum viscsity cefficient ccurs very clse t the bttm. The bttm frictin velcity is significantly reduced (Figures 9b and 10b). At the deep shelf break U04, turbulence is cnfined t the near-bed layer. The stratificatin in spring can als substantially reduce tidally generated turbulence in the bttm bundary layer and cmpletely shut ff the turbulence abve the layer at U01 (Figure 12). This is because the stratificatin strength in the bttm bundary layer is cmparable in spring t that in summer (Figure 11). The present mdel effects f vertical stratificatin n the turbulent quantities are generally cnsistent with findings by Xing and Davies [1996a, c] but withut the spuriusly large eddy viscsity in the upper water clumn seen in their mdel results. Cmparing current prfiles at U01 with and withut the stratificatin, we can see that the stratificatin at this lcatin des affect the current structure, leading t a shear-free and weaker (Figure 7) and inviscid (Figure 12) flw in the upper and middle water clumn. Similar change has been reprted by Xing and Davies [1996a]. The current in the lg layer (within -2.5, 0.8, and 1.2 m abve bttm r rr < -0.95, , and at U01, U04, and U09, respectively) is reduced and s is the bttm frictin velcity (Figure 9b). The frictin velcity is calculated at the lwest hrizntal current level (rr = ), the height f which abve the sea bttm varies with water depth (e.g.,-0.3, 1, and 0.5 m at U01, U04, and U09). There is significant current intensificatin in the bttm bundary layer (which is -10 m thick frm the turbulence and current prfiles) excluding the lg layer. Nte that the thickness f the bttm bundary layer in the stratificatin case can be estimated n the basis f the bttm frictinal velcity using c = 0.2 (half f the value fr the hmgeneus case), cnsistent with sme earlier studies [e.g., Lder and Greenberg, 1986]. The current phases are als subject changes with the stratificatin, significant in the bttm bundary layer. Abve the lg layer the phase in the bundary layer is advanced wing t an increase f the frictinal effect. The increase results frm an increased vertical shear in the hrizntal current magnitude (Figure 7) in spite f the reductin f the eddy viscsity magnitude. The phase abve the bttm bundary layer becmes lagged primarily because f reduced frictin. The increased phase difference between the near-bttm and the nearsurface currents was als fund frm in situ bservatins [Hwarth, 1998]. The change f current magnitudes and phases at U09 is similar t that at U01 since the M 2 tidal currents at bth lcatins dminate. The M 2 current prfiles at U04 where the diurnal currents and assciated frictin dminate (see Figure 9a) shw an verall increase f magnitudes ver the entire water clumn. The u phase is slightly advanced r unchanged, and the v phase is advanced thrughut the water clumn. As we can see, stratificatin is very effective in suppressing tide-generated turbulence ver the Newfundland Shelf. This

13 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF 11,419 U U " U01 in spring q2 (lo-4 m2/s 2) 2 5 loo I(m) v t ( 10-4 m2/s) Figure 12. Same as Figure 8 but fr the diagnstic summer and spring stratificatin cases. is mainly because tidal currents in this regin, thugh an im- present prgnstic run, s that barclinic tides cannt be genprtant current cmpnent, are relatively weak. The vertical erated and nntidal variability is nt invlved in the slutin. shear in the hrizntal current prfile is s small in general The nly difference between the prgnstic and diagnstic that weak stratificatin such as with an N f rad/s is able runs in this study is that the stratificatin suppressin f turt sufficiently reduce the turbulence generated by the shear. bulence changes with the evlutin f density in the frmer. Within 10 m frm bttm at U01, N is between and 0.01 The cmputed tidal elevatins with evlving vertical stratirad/s, larger in summer. The gradient Richardsn number ficatin shw little difference frm thse with fixed stratifica- (Ri = N2/(Ou/Oz) 2) is estimated 0.2 in spring and in tin. Nevertheless, there are appreciable changes in the mdel summer, s the turbulence is partially suppressed and the ver- tidal currents and mixing ver the shelf. tical eddy viscsity is reduced up t 1 rder f magnitude, a Cmparing the M 2 current prfiles at U01 frm the prglittle mre in summer than in spring. The reductin in bttm nstic (Figure 13) and diagnsticalculatins, we d nt see frictin velcities is ---30% in summer (Figure 10b) and slightly any qualitatively significant difference, even thugh sme smaller in spring (Figure 10c), cmpared with the baseline case change is f interest. The prgnstic run appears t agree (Figure 10a). Abve the 10-m bundary layer the Richardsn better with bservatins. The transitin between the bttm number is much higher, and the tidally induced turbulence bundary layer and the layer abve it is smther, with a slight there is essentially shut ff fr bth seasns. increase f the bundary layer thickness Prgnstic Run With Evlving Vertical Stratificatin Suppressin f turbulence fr the middle and upper water In the prgnstic run, density is allwed t evlve during the clumn in the p. rgnstic summer run is generally similar t mdel integratin in time, s that stratificatin affects tidal that in the diagnstic summer run, but the turbulent kinetic currents and is in turn affected by the tidal currents. The energy and the vertical eddy viscsity near the bed are much prgnstic mdel run is initialized with the climatlgical sum- larger in the prgnsticase fr a certain perid f an M 2 tidal mer density prfile and the summer diagnstic slutin. Dur- cycle (Figure 14), which is attributable t the evlutin f bth tidal currents and stratificatin and their interactins. It is als ing the mdel integratin frward in time, density is fixed at the lateral pen bundary, and its vertical gradient is set t imprtant t realize that in a prgnstic run that allws bazer at the sea surface and the bttm. The barclinic pressure rclinic tides they can be generated at the Grand Bank slpe gradients in the mmentum equatins are turned ff fr the and prpagate ut int the cean, where they give rise t

14 11,420 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF O u-amplitude (cm/s) u-phase (degree) -1 lo 20 v-amplitude (cm/s) i v-phase (degree) Figure 13. Cmputed vertical prfiles f M 2 currents at U01' prgnstic (slid line) versus diagnstic (dashed line) runs. Crsses are the in situ bservatins. significant vertical shear and hence turbulence in the water clumn abve the bttm bundary layer Bttm Rughness Height In the present mdel the bttm frictin stress is related t the currents at the lwest current level, the height f which varies with the lcal water depth. The drag cefficient is inversely prprtinal t the square f the lgarithmic rati f the height t the bed rughness height. An accurate bed rughness height is difficult t determine, s we have used a unifrm m as a base value in the baseline mdel and the strati- ficatin cases. A hrizntally variable rughness height is desirable if bed types and frms are knwn well (e.g., Aldridge and Davies [1993] in an eastern Irish Sea mdel). As a simple sensitivity study we have cnsidered a hmgeneus case with an increase f the bed rughness height t 0.02 m. The increase f the bttm rughness height reduces the near-bttm current at all the three sites (Figure 7), but the near-surface current is increased at the shallw site U01 and decreased at the deep site U04 and unchanged at the intermediate-depth site U09. The increase results in a slightly larger bttm frictin velcity at U01 (Figure 9b) wing t an in-._ *, M 2 Cycle M 2 Cycle Figure 14. Cmputed twice turbulent kinetic energy q2 and vertical eddy viscsity 't at - = -0.9 at U01: prgnstic (slid line) versus diagnstic (dashed line) runs. crease f the mdel drag cefficient in spite f the reductin f the near-bttm current. The phase reductin is relatively mre nticeable near the bttm. The reductin represents an earlier current turn, e.g., frm fld t ebb, in the sensitivity case than the baseline case. Overall, these changes are nt significant, suggesting limited influences f the bttm rughness height n the cmputed currents. Lw sensitivity f the tidal respnse t variatins in the bttm rughness height was als reprted in literature [e.g., Oey et al., 1985] Cmputatin With a Single Cnstituent In sectin 3 and 4 the results are decmpsed using the harmnic analysis frm the baseline mdel results with the five tidal cnstituents cmputed simultaneusly. In sme existing castal mdeling effrts the cmputatin is carried ut fr a single cnstituent. Figure 7 shws sme differences fr the dminant M 2 cnstituent between the multicnstituent simulatin and a single-cnstituent (M 2 nly) cmputatin. It is evident that the single-cnstituent cmputatin underestimates the current except near the bttm. The single-cnstituent cmputatin des nt include the cntributin f the ther fur cnstituents t bttm frictin. The cnsequences are thinner bttm bundary layers (see Figure 7) and reduced bttm frictin velcities (nt shwn). The cntributin f ther flw cmpnents t frictin fr a single tidal cnstituent cmputatin was cnsidered by estimating the frictin cefficients based n this tidal cnstituent and the ther flw cmpnents (M. C. G. Freman et al., persnal cmmunicatin, 1999) r by impsing backgrund frictin cefficients [e.g., Han et al., 1999]. Nte that the relative change is larger at U04 than at U01, which can be attributed t the significance f the diurnal tidal currents at U04 (see Figure 9a) where the single M 2 cmputatin significantly un- derestimates the frictinal effect. The ptential cntributin f the fur ther cnstituents thrugh the nnlinear advective prcess is als cnsidered. We have made tw 37-day mdel runs with and withut the nnlinear advective terms in the mmentum equatins. A harmnic analysis f the mdel results indicates negligible differences f <0.1 cm/s in the M 2 current amplitude at U01. As anther check, we have perfrmed a slightly different harmnic analysis f the nnlinear mdel results. This analysis includes additinal shallw water cnstituents, m 4 and MS 4. The analyzed m 4 and MS 4 current magnitudes are <0.1 cm/s at U01. Therefre the nnlinear advective prcesseseem unlikely t be a factr causing the difference between the singlecnstituent and multicnstituent cmputatins at U01. Nte that the nnlinear interactin here refers t the advective m- mentum exchange amng the five tidal cnstituents. The nnlinear interactin between the tidal current and density- r wind-driven current is nt cnsidered in this study (n wind stress impsed at the sea surface and n barclinic pressure gradients included in the hrizntal mmentum equatins). Surely, the nnlinear effect amng the five tidal cnstituents in the very nearshre regin (e.g., inlets and embayments) may be significant. Hwever, with the present hrizntal reslutin the nearshre bttm tpgraphy is nt well reslved. Furthermre, the mdel M 4 and MS 4 current magnitudes at U01 are fund t be cnsistent with estimates frm mred measure- ments (<0.3 cm/s [see Rss et al., 1988]), prviding bservatinal evidences f the weak nnlinear advective effects amng the majr tides ver the Newfundland Shelf. It fllws that ne shuld (if pssible) include majr tidal

15 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF 11,421 cnstituent simultaneusly in a tide mdel t accunt fr the nnlinear effects thrugh the bttm frictin and the advective mmentum exchange amng the majr tidal cnstituents. Fr the Newfundland Shelf away frm castal embayments and inlets the nnlinear interactin thrugh the advective exchange seems weak frm the present mdel results and available mred measurements. 7. Cnclusins We have implemented a 3-D hydrdynamic mdel with adequate capability f reprducing tidal elevatins and currents References fr the M2, 52, N2, ml, and O cnstituents ver the Newfund- Aidridge, J. N., and A.M. Davies, A high-reslutin three-dimensinal land Shelf. The cmputed tidal elevatins are in very gd hydrdynamic mdel f the eastern Irish Sea, J. Phys. Oceangr., 23, , agreement with in situ bservatins fr the five cnstituents. Blumberg, A. F., A primer fr ECOM-si, HydrQual, Mahwah, N.J., The simulated semidiurnal tidal currents agree well with in situ bservatins within bservatinal uncertainty, while the mdel Brethertn, F. P., R. E. Davis, and C. B. Fandry, A technique fr diurnal tidal currents shw ntable discrepancies. bjective analysis and design f ceangraphic experiments applied t MODE-73, Deep Sea Res., 23, , The M 2 tidal currents dminate tidal current variability ver Crawfrd, W. R., and R. E. Thmsn, Cntinental shelf waves f the Newfundland Shelf, especially ver the shallw uter diurnal perid alng Vancuver Island, J. Gephys. Res., 87, shelf areas such as Sutheast Shal. The diurnal tidal currents 9522, are generally weak but intensified in sme uter shelf and shelf Cummins, P. F., and L.-Y. Oey, Simulatin f bartrpic and barclinic tides ff Nrthern British Clumbia, J. Phys. Oceangr., 27, break znes. The intensificatin appears f a nn-kelvin wave , rigin and is prbably assciated with first-mde cntinental Davies, A.M., A bttm bundary layer-reslving three dimensinal shelf waves at diurnal frequencies. tidal mdel: A sensitivity study f eddy viscsity frmulatin, J. Phys. The present study indicates significant vertical and hrizn- Oceangr., 23, , Davies, A.M., and J. N. Aidridge, A numerical study f parameters tal variatins f magnitudes f the turbulent kinetic energy and influencing tidal currents f the Irish Sea, J. Gephys. Res., 98, vertical eddy viscsity ver the Newfundland Shelf. Large , vertical viscsity and bttm frictin velcity magnitudes are Davies, A.M., and J. E. Jnes, A three dimensinal mdel f the M2, assciated with strng currents in shallw regins, where S2, N2, K, and Oh tides in the Celtic and Irish Seas, Prg. Oceangr., 29, , strng vertical shears prduce large turbulent kinetic energy. Davies, A.M., S.C. M. Kwng, and R. A. Flather, A three dimensinal Fr the stratificatin cases the turnff f the barclinic pres- mdel f diurnal and semi-diurnal tides n the Eurpean Shelf, J. sure gradient terms in the mmentum equatins influences Gephys. Res., 102, , bth the diagnstic and prgnstic mdel slutins. In the de Margerie, S., and K. D. Lank, Tidal circulatin f the Sctian Shelf and Grand Bank, Cntract Rep. 08SC.FD901-5-X515, Dept. Fish. diagnstic runs the specified time-invariant vertical stratificaand Oceans, Ottwa, Ontari, Canada, tin affects the tidal current prfile nly thrugh suppressing de Yung, B., and C. L. Tang, Strm-frced barclinic near-inertial turbulence. In the prgnstic run the vertical stratificatin can currents n the Grand Bank, J. Phys. Oceangr., 20, , evlve, but barclinic tides are nt generated withut the ba- Flather, R. A., A numerical mdel investigatin f tides and diurnal rclinic pressure gradients, s the nly difference is that the perid cntinental shelf waves alng Vancuver Island, J. Phys. Oceangr., 18, , stratificatin suppressin f turbulence changes with the ev- Freman, M. C. G., and R. F. Henry, The harmnic analysis f tidal lutin f density in the prgnstic run. The prgnstic results mdel time series, Adv. Water Resur., 12, , seem mre prmising, althugh the imprvement is very md- Freman, M. C. G., R. F. Henry, R. A. Walters, and V. A. Ballantyne, est. The diagnstic and prgnstic slutins indicate that the A finite element mdel fr tides and resnance alng the nrth cast f British Clumbia, J. Gephys. Res., 98, , tidally induced turbulence in shallw waters is significantly Garrett, C. J. R., J. R. Keeley, and D. A. Greenberg, Tidal mixing reduced by a stable vertical stratificatin where a sufficient versus thermal stratificatin in the Bay f Fundy and Gulf f Maine, density gradient cincides with a significant velcity shear in Atms. Ocean, 16, , the vertical. This des nt ccur in the deep cean where tidal Gdin, G., Ctidal charts fr Canada, Manuscr. Rep. Set. 55, 93pp., Mar. Sci. Dir., Dept. Fish. and Oceans, Ottawa, Ontari, Canada, currents and bttm-generated turbulence are weak. Turbu lence is substantially reduced in the bttm bundary layer and Han, G., Castal tides and shelf circulatin by altimeter, Oceancmpletely suppressed abve it. Effectiveness f the stratifica- graphic Applicatin f Remte Sensing, edited by M. Ikeda and F. tin in suppressing tidally generated turbulence is attributable Dbsn, chap. 4, pp , CRC Press, Bca Ratn, Fla., Han, G., M. Ikeda, and P. C. Smith, Annual variatin f sea-surface t weakness f the regin's tidal currents, which are imprtant slpes ver the Sctian Shelf and Grand Banks frm Gesat altimcmpared with ther current cmpnents in the Grand Banks etry, Atms. Ocean, 31, , regin. Han, G., M. Ikeda, and P. C. Smith, Oceanic tides ver the Newfund- The tidal elevatins are hardly influenced by the vertical land and Sctian Shelves frm TOPEX/Pseidn altimetry, Atms. Ocean, 34, , stratificatin, but the tidal currents in shallw areas are sensi- Han, G., J. W. Lder, and P. C. Smith, Seasnal-mean hydrgraphy tive t it. The stratificatin reduces the vertical current gradi- and circulatin in the Gulf f St. Lawrence and n the eastern ent in the upper and middle water clumn and significantly Sctian and suthern Newfundland Shelves, J. Phys. Oceangr., 29, increases the gradient in the bttm bundary layer. Tidal current magnitude decreases in the lg layer, increases substantially in the rest f the bttm bundary layer, and decreases abve the bundary layer. The phase f tidal currents is als subject t change, with a ntable advance in the bttm bundary layer due t an increase in the frictinal effect. Acknwledgments. I thank J. Lder and H. Sandstrm fr helpful cmments n an early versin f the manuscript and R. Hendry, M. Ikeda, B. Petrie, and P. C. Smith fr discussins. Cnstructive suggestins and cmments were received frm tw annymus reviewers. The wrk is partially funded by the Canadian Panel f Energy, Research and Develpment (PERD) , Han, G., R. Hendry, and M. Ikeda, Assimilating TOPEX/Pseidn derived M 2 tide in a primitive equatin mdel, Cnt. Shelf Res., 20, , Hllway, P. E., A numerical mdel f internal tides with applicatin

16 11,422 HAN: TIDAL CURRENTS AND MIXING OVER THE NEWFOUNDLAND SHELF t the Australian nrth west shelf, J. Phys. Oceangr., 26, 21-37, Hwarth, M. J., The effect f stratificatin n tidal current prfiles, Cnt. Shelf Res., 18, , Huthnance, J. M., L. A. Mysak, and D.-P. Wang, Castal trapped waves, in Barclinic Prcesses n Cntinental Shelves, Castal Estuarine Sci., vl. 3, edited by C. N. K. Mers, pp. 1-18, AGU, Washingtn, D.C., Kitaigrdskii, S. A., The lcatin f thermal shelf frnts and the variability f the heights f tidal benthic bundary layers, Tellus, Ser. A, 44, , LeBlnd, P., and L. Mysak, Waves in the Ocean, Oceangr. Ser., vl. 20, Elsevier Sci., New Yrk, LePrvst, C., M. L. Genc, F. Lyard, P. Vincent, and P. Canceil, Spectrscpy f the wrld cean tides frm a finite element hydrdynamic mdel, J. Gephys. Res., 99, 24,777-24,798, Lder, J. W., and D. A. Greenberg, Predicted psitins f tidal frnts in the Gulf f Maine regin, Cnt. Shelf Res., 6, , Lynch, D. R., and C. E. Naimie, The M2 tide and its residual n the uter banks f the Gulf f Maine, J. Phys. Oceangr., 23, , Maze, R., Generatin and prpagatin f nnlinear internal waves induced by the tide ver a cntinental slpe, Cnt. Shelf Res., 7, , Melir, G. L., and T. Yamada, Develpment f a turbulence clsure mdel fr gephysical fluid prblems, Rev. Gephys., 20, , Oey, L.-Y., G. L. Melir, and R. I. Hires, A three-dimensinal simulatin f the Hudsn-Raritan estuary, part I, Descriptin f the mdel and mdel simulatins, J. Phys. Oceangr., 15, , Petrie, B. D., Aspects f the circulatin n the Newfundland cntinental shelf, Can. Tech. Rep. Hydrgr. Ocean Sci. 11, 78 pp., Ottawa, Ontari, Petrie, B. D., Current meter and tide gauge bservatins frm Avaln Channel, , Can. Tech. Rep. Hydrgr. Ocean Sci., 102, 89 pp., Ottwa, Ontari, Petrie, B. D., K. D. Lank, and S. de Margefie, Tides n the Newfundland Grand Banks, Atms. Ocean, 25, 10-21, Prctr, R., and A.M. Davies, A three dimensinal mdel f tides ff the nrth-west cast f Sctland, J. Mari. Syst., 7, 43-66, Rss, C. K., J. W. Lder, and M. J. Graca, Mred current and hydrgraphic measurements n the Sutheast Shal f the Grand Bank 1986 and 1987, Can. Tech. Rep. Hydrgr. Ocean Sci., 71, 132 pp., Ottwa, Ontari, Schwiderski, E. W., On charting glbal cean tides, Rev. Gephys., 18, , Smagrinsky, J., General circulatin experiments with the primitive equatins, I, The basic experiment, Mn. Weather Rev., 91, , Sulsby, R. L., The bttm bundary layer f shelf seas, in Physical Oceangraphy f Castal and Shelf Seas, Oceangr. Ser., vl. 35, edited by B. Jhns, pp , Elsevier Sci., New Yrk, Stigebrandt, A., A nte n the lcus f a shelf frnt, Tellus Ser. A, 40, , Thmsn, R. E., and W. R. Crawfrd, The generatin f diurnal perid shelf waves by tidal currents, J. Phys. Oceangr., 12, , Xing, J., and A.M. Davies, Applicatin f three dimensinal turbulence energy mdels t the determinatin f tidal mixing and currents in a shallw sea, Prg. Oceangr., 35, , Xing, J., and A.M. Davies, Applicatin f turbulence energy mdels t the cmputatin f tidal currents and mixing intensities in shelf edge regins, J. Phys. Oceangr., 26, , 1996a. Xing, J., and A.M. Davies, Applicatin f a range f turbulenc energy mdels t the determinatin f M 4 tidal current prfiles, Cnt. Shelf Res., 16, , 1996b. Xing, J., and A.M. Davies, The influence f mixing length frmulatin and stratificatin upn tidal currents in shallw seas, Estuarine Castal Shelf Sci., 42, , 1996c. Xing, J., and A.M. Davies, A three-dimensinal mdel f internal tides n the Malin-Hebrides shelf and shelf edge, J. Gephys. Res., 103, 27,821-27,847, 1998a. Xing, J., and A.M. Davies, Influence f stratificatin upn diurnal tidal currents in shelf edge regins, J. Phys. Oceangr., 28, , 1998b. Zilitinkevich, S., and D. V. Mirnv, A multi-limit frmulatin fr the equilibrium depth f a stably stratified bundary layer, Bundary Layer Meterl., 81, , G. Han, Fisheries and Oceans Canada, Bedfrd Institute f Oceangraphy, P.O. Bx 1006, Dartmuth, Nva Sctia, Canada B2Y 4A2. (ghan@emarid.bi.df.ca) (Received December 9, 1998; revised September 22, 1999; accepted December 22, 1999.)