Chapter 2: Estuarine Salinity Structure and Circulation

Transcription

1 Chapte : Estuaine Salinity Stuctue and Ciculatin W.R. Geye, Wds Hle Oceangaphic Institutin.. The Hizntal Salinity Gadient Estuaies shw a geat divesity f size, shape, depth, and fcing chaacteistics, but a geneal chaacteistic f estuaies is the pesence f a hizntal salinity gadient (Fig..). Nmally the salinity deceases fm the cean twad the head f the estuay due t feshwate input; in the case f invese estuaies, the salinity inceases in the landwad diectin due t excess evapatin (see Chaptes and 9). This salinity gadient is the key dynamical vaiable that makes estuaies diffeent fm any the maine lacustine envinment. The hizntal salinity gadient is the key diving fce f the estuaine ciculatin, which in tun plays a key le in maintaining salinity statificatin in estuaies. The cmbined influence f the estuaine ciculatin and statificatin detemines the fluxes f salt and fesh wate within the estuay, and thei intensity vaies with the stength f the feshwate inflw. Because f these dynamics, estuaies ae ften the mst stngly statified aquatic envinments, but they als tend t have vigus wate and salt exchange, due t the estuaine ciculatin. This chapte exples the cupled equatins invlving the estuaine ciculatin, statificatin, salt flux and the feshwate inflw. A maj utcme f this analysis is t eveal the essential imptance f hizntal salinity gadient in the estuaine ciculatin, statificatin, and salt balance, but als t find that the hizntal salinity gadient ultimately depends n the stength f the feshwate utflw and the intensity f mixing by tidal cuents... The Estuaine Ciculatin The fist knwn efeence t the estuaine ciculatin was cntibuted by Pliny the Elde in efeence t the vetically vaying flw in the Stait f Bsphus, which cnnects the highsalinity Mediteanean t the me backish Black Sea. He fund that as fishemen lweed thei nets, they wuld tug in the eastwad diectin nce they eached a cetain depth, at which they wee being swept by the deep, high-salinity inflw int the Black Sea. Nineteen hunded yeas late, Knudsen nted a simila bi-diectinal flw in the entance t the Baltic Sea. His name has been immtalized f his quantificatin f the salt balance, which will be discussed in sectin.4. In 95, Pitchad was the fist eseache t link the estuaine ciculatin t the fcing by

2 the hizntal density gadient, using bsevatins in the James Rive estuay t demnstate the mechanism. Pitchad pinted ut that the tidal cuents ae typically much stnge than the estuaine ciculatin, but if the vetically vaying hizntal cuents ae measued thugh the cuse f the tidal cycle and then aveaged, the esidual estuaine ciculatin wuld be evealed, as shwn in Fig.. In a nmal psitive estuay (see chapte ), i.e., ne with excess feshwate input, the nea-bttm flw is landwad. The stength f the estuaine ciculatin is typically 0.05 t 0.3 m/s (as measued by the tidally aveaged bttm inflw). The diving fce f the estuaine ciculatin is the hizntal salinity gadient s / x, which induces a vetically vaying pessue gadient. The pessue p gadient can be expessed as the cmbined influence f the suface slpe p s g g ( h z) x x x / x and s / x : whee ρ is the density f wate (dminated by salinity), β is the cefficient f saline cntactin, g is the acceleatin f gavity, h is the wate depth and z is the vetical cdinate measued upwad fm the bttm. Nte that the secnd tem n the ight-hand-side f (.), the. s / x tem, is ze at the suface and maximal at the bttm, iented in the diectin that acceleates the bttm wate int the estuay. The tidally aveaged suface slpe tilts in the the diectin fm the salinity gadient, with a magnitude lage enugh, elative t the salinity gadient, that the pessue gadient eveses smewhee clse t the middle f the wate clumn. Thus the suface wate is diven seawad and the bttm wate landwad. If the flw wee stating fm est (imagine the estuay was fzen and it suddenly melted), the pessue gadient wuld esult in acceleatin f the suface and bttm wates in ppsite diectins. This acceleatin wuld cntinue until sme the fce balanced the pessue gadient. The fce that is mst imptant f balancing the pessue gadient is the intenal stess ( mmentum flux) acting n the estuaine shea flw. Pitchad epesented the tubulent stess in tems f an eddy viscsity A z A u z. z whee τ is the stess (in units f fce/aea Pasacals) and u / z is the vetical shea f the hizntal flw. The units f A z ae length /time, just like the mlecula viscsity, althugh it is

3 seveal des f magnitude lage. A pactical way f thinking abut the eddy viscsity is as a pduct f a tubulent velcity scale and a tubulent lengthscale. The magnitude f the eddy viscsity is set by the intensity f the tidal flw and the statificatin; values ange fm 0-4 t 0 - m /s in estuaies. The eddy viscsity vaies significantly in space and time due t vaiatins in fcing, but the mmentum balance can be appximated using a cnstant value that epesents an effective tidal aveage (althugh the estimate f its value is best btained a psteii). The equatin elating the pessue-gadient fcing t the estuaine ciculatin is a geatly simplified, tidally aveaged epesentatin f the hizntal mmentum equatin: s g g ( h z) A x x z whee the eddy viscsity has been assumed t be cnstant in the vetical t make the paamete dependence me clea. The magnitude f the suface slpe is cnstained by the mean utflw; if the ive flw is small cmpaed t the estuaine ciculatin (geneally a valid appximatin except f salt-wedge highly statified estuaies), then 3 s g g h.4 x 8 x and the slutin f the velcity is u z z.3 s 3 g h 3 u( z) x A z whee ς=z/h is a nn-dimensinal depth vaying fm 0 at the bttm t at the suface. The shape f the velcity pfile is shwn in Fig... This shuld be cnsideed a qualitative slutin the vetical stuctue f the velcity in actual estuaies diffes due t the spatial and tempal vaiatins f the eddy viscsity as well as the facts such as lateal advectin (nte cmpaisn with actual bseved pfiles in Fig..). Nevetheless equatin.5 yields the geneal shape and magnitude f the estuaine ciculatin, and it is a useful appximatin f analyzing the influence f the estuaine ciculatin n the statificatin and salt balance. In pactice it is difficult t assign an apppiate value t A z withut actually slving the time-dependent equatins with the inclusin f an advanced tubulence clsue. A simple 3

4 altenative t equatin.5 can be btained by eplacing A z with an equivalent expessin invlving the tidal velcity magnitude t, the depth h and a bttm dag cefficient C d : A z CdT h.6 48a whee the dag cefficient equates the magnitude f the bttm stess t the tidal velcity as C b d t (with typical values f C d ~ ) and a is a dimensinless cnstant yet t be detemined elated t the effectiveness f tubulent mmentum flux. Nte that this is an effective viscsity based n the tidally aveaged flw, and its value is significantly smalle than the maximum eddy viscsity that wuld ccu within a tidal cycle. Substituting this int equatin.5, the magnitude f the estuaine ciculatin can be detemined as e a s g h x C d t.7 This fmulatin indicates the paamete dependence f the estuaine ciculatin elative t the key vaiables: linealy with s / x, invesely with tidal velcity, and quadatically with depth. Cmpaisn with data fm the Hudsn Rive estuay veifies that equatin.7 pvides a easnable estimate f the vaiability, with a value f a f abut 0.3 (Fig..)..3. The Statificatin The vetical vaiatin f salinity, statificatin, is ne f the me cnspicuus chaacteistics f estuaies. Estuaine statificatin vaies cnsideably fm ne estuay t anthe, and ne way f classifying estuaies (Chapte ) is based n the stength f statificatin: well mixed, patially mixed, highly statified, and salt wedge. As a classificatin scheme this is nt vey eliable, hweve, as ne estuay may vay fm well-mixed t highly statified depending n the fcing cnditins. Estuaine statificatin is imptant f a numbe f easns it inhibits vetical mixing, which affects the dynamics and may lead t hypxia in the sub-pycncline wates. The statificatin als plays a fundamental le in the salt balance, which will be discussed in sectin.4. What cntls the statificatin in estuaies? What makes statificatin vay s much fm ne estuay t anthe and f ne estuay t vay fm well-mixed t highly statified? 4

5 The key t the vaiability f statificatin is embdied in the equatin f lcal salt cnsevatin, which can be simplified f steady-state cnditins and mdest alng-estuay vaiatins in depth t s s u( z) K.8 x z z whee u(z) is the vetically vaying, tidally aveaged velcity, and K z is the eddy diffusivity f salt, with the same dimensins and simila magnitude t A z. It is nt immediately bvius why this equatin wuld dictate the statificatin. One way t illustate the balance me clealy is t integate equatin.8 fm the middle f the wate clumn t the suface (neglecting vetical vaiatins in s / x ), btaining s s e K z mid.9 x z whee is a cnstant f integatin appximately equal t 0.3 and s / z is the vetical gadient f salinity in the middle f the wate clumn. This equatin indicates that mean advectin f salt by the estuaine ciculatin is balanced by vetical mixing. The salinity f the uppe laye wuld decease due t seawad advectin f lwe-salinity wate, but vetical mixing caies highe-salinity wate up, balancing the effect f advectin (Fig..3). In the lwe laye, advectin wuld cause the salinity t incease, but vetical mixing tanspts lw-salinity wate dwnwad t maintain a steady state. As with the eddy viscsity, the eddy diffusivity can be epesented in tems f tidal velcity and depth (cf., equatin.6). Substituting this int equatin.9 and nting that s / z s / h, whee s is the tp-t-bttm salinity diffeence, we btain s e h s a x.0 C D t whee a is a cnstant that incpates and als depends n the shape f the salinity and velcity pfiles. The value f a was estimated fm Hudsn Rive data t be appximately 50. Cmbining equatin.0 with equatin.7 f the estuaine ciculatin, mid s g h x s a a C D t 3.. 5

6 This equatin indicates that the statificatin depends quadatically n the salinity gadient and invesely n the squae f the tidal velcity i.e., the statificatin is a lt me sensitive t changes in these fcing vaiables than is the estuaine ciculatin. The sensitive dependence f statificatin n the stength f the tides has been evealed in a numbe f studies f the sping-neap vaiatins in statificatin. Duing sping tides, tidal mixing is maximal, and equatin. pedicts that the statificatin shuld each a minimum, and vice vesa. Haas (977) fist dcumented the sping-neap vaiatins f statificatin due t vaiatins in tidal mixing in the sub-estuaies f Chesapeake Bay. Data fm the Hudsn estuay is used t test equatin., as shwn in Figue.4 (lwe panel). These data indicate that the actual statificatin is me sensitive t the sping-neap cycle than equatin. pedicts. The easn f this is that the intensity f mixing des nt just depend n the intensity f the tides; it als depends n the ambient statificatin. This is a cmplex tpic, which is teated in me detail in Chapte 7. Biefly, the paamete that best quantifies the imptance f statificatin n mixing is the gadient Richadsn numbe the ati f the statificatin t the shea. This can be appximated f scaling pupses by a nndimensinal ati f the vetical salinity diffeence t the tidal velcity: Ri T gsh.. T F Ri T >, mixing is stngly suppessed by the statificatin, and f Ri T < 0.5, mixing is elatively unaffected by statificatin. Mdels f mixing in statified bunday layes (e.g., Twbidge, 99) suggest that the mixing ate shuld depend n Ri -/. If equatin. is mdified by the additin f a fact t accunt f the Ri-dependence s aa' Ri / T s g x C D t h 3.3 the fit with the Hudsn Rive data is significantly impved (Fig..4). An explicit fm f s that includes the statificatin effect n tubulence is btained by cmbining equatins. and.3: 6

7 s a a' 4 D 4 3 s g h x C 6 T 7 Nte the exteme sensitivity f the statificatin t the tidal mixing accding t this fmulatin, as well as the sensitivity t the hizntal pessue gadient and depth. The Hudsn data pvide sme suppt f the sensitivity t tidal velcity, but equatin.4 appeas t veemphasize the dependence n hizntal salinity gadient, based n bsevatins and mdel esults. The cnsequences f this statificatin-dependence n the veall estuaine balance ae discussed in Sectin The Salt Balance If an estuay is in steady state, then the amunt f salt being tanspted past any csssectin has t be ze (except in the highly unusual case that thee ae significant suces f salt in the wateshed). Cnsideing a css-sectin within the estuay with sme tidally aveaged value f salinity s 0, the feshwate utflw Q (vlume pe time) will cause a seawad tanspt Q salt = Q s. In de t maintain a steady state, thee must be mechanisms that tanspt salt int the estuay, t cmpensate f the advective lss due t the ive utflw. Knudsen s analysis f the estuaine ciculatin f the Baltic Sea pvides the essence f the estuaine salt balance. Knudsen s elatin cnsides the integated cnsevatin f vlume and salt in a basin that has a iveine suce f fesh wate and exchange flw with the cean (Fig..5). Vlume and salt cnsevatin yield Q Q Q Q s Q s whee Q and Q ae the vlume tanspts in the uppe and lwe layes (the uppe laye being diected seawad and the lwe laye landwad). Cmbining the tw leads t Knudsen s elatin: Q s Q s If Q >>Q (which is geneally the case f patially mixed and well-mixed estuaies), then.5.6 s s s, and Knudsen s elatin can be estated using e.7 s a s e 7

8 whee u Q / A cs (the utflw velcity assciated with the ive dischage, A cs being the lcal css-sectinal aea f the estuay), and a is cnstant equal t appximately 0.5. Equatin.7 indicates that the tendency f salt t be caied ut f the estuay by the feshwate utflw is balanced by the net input f salt due t the estuaine ciculatin. The stnge the estuaine ciculatin, and the lage the vetical salinity diffeence, the me salt is tanspted int the estuay. Equatin.7 epesents the steady-state balance, and it nly cnsides the influence f the estuaine ciculatin n the salt balance. The salt cntent f estuaies is nt actually cnstant in time, because a numbe f facts cause the left-hand and ight-hand sides f equatin.6 t change. The magnitude and causes f thse vaiatins will be discussed in sectin.6. This equatin als leaves ut anthe cntibut t the hizntal salt flux: the hizntal dispesin f salt (tidal dispesin), which is due mainly t tidal stiing. Tidal dispesin is paticulaly imptant in sht estuaies, in which the length f the salt intusin is cmpaable t the tidal excusin distance (5 5 km), and als in egins f abupt changes in estuaine css-sectin. But in lage estuaies (>30 km lng) and away fm maj changes in css-sectinal gemety, the salt tanspt induced by estuaine ciculatin geneally dminates ve tidal dispesin, and equatin.7 is a gd epesentatin f the time-aveaged salt balance..5. The Cupled Equatins The key t the dynamics f estuaies is that the glbal salt balance has t be satisfied at the same time that the lcal mmentum and salinity equatins ae in balance. This cmbinatin f equatins f estuaine ciculatin, statificatin and salt balance leads t a cnstaint n the hizntal salinity gadient, which is in essence the maste vaiable cntlling the estuaine dynamics. Fist we will cnside the fmulatin in which the influence f statificatin n mixing is neglected, as it leads t a esult that is ften nted in the liteatue. Cmbining equatins.7,. and.7, we btain Then, slving f s a a a g s / x, we btain s x C 3 d t 3 h 5.8 8

9 s x / 3 / 3 s / 3 / 3 5/ 3 a a a g h C d t Equatin.9 indicates that f steady-state cnditins, the hizntal salinity gadient depends n the ne-thid pwe f the ive flw and the fist pwe f the tidal velcity. These scaling elatins ae cnsistent with the Hansen and Rattay (965) slutin f the advectin-dminated limit, the Chatwin (976) slutin f patially mixed estuaies, and the MacCeady (999) slutin f advectin-dminated estuaies. The essential finding is that the salinity gadient is elatively insensitive t vaiatins in ive flw, altenatively that the estuaine salt flux is paticulaly sensitive t the salinity gadient. Nw cnsideing the slutin f the hizntal salinity gadient when the Richadsnnumbe dependence n vetical mixing is included, we stat with equatin.4 f Δs in cmbinatin with equatins.7 and.7 and btain.9 s x 7 / 5 t / 5 / 5 s / 5 a a ' a / g 4 / h C d.0 When the influence f vetical mixing is included, the salinity gadient is even less sensitive t vaiability f ive flw, i.e., the estuay is stiff (think f a steel sping) with espect t vaiatins in ive flw. Mnismith et al. (00) fund even geate stiffness in the salinity /7 gadient f nthen San Fancisc Bay, btaining a dependence. This may be in pat due t vaiatins in gemety alng the estuay, but the influence f statificatin n mixing is likely an imptant cntibut t the estuaine espnse t vaiatins in ive flw. The expessin f s/ x can be substituted back int the equatins f e and s t btain expessins f the estuaine ciculatin and statificatin in tems f the fcing vaiables t and, fist withut cnsideing the Richadsn-numbe effect: e a / 3 / 3 / 3 gs h aa. s a s a a / 3 / 3 gs h / 3 These equatins eveal the supising esult that f the steady-state balances, the estuaine ciculatin and statificatin d nt depend n the tidal velcity, even thugh equatins.7 and. 9

10 . clealy indicate the invese dependence n tidal mixing. This paadxical esult is due t the vaiatin f hizntal salinity gadient with tidal velcity (equatin.9), which exactly cmpensates f the vaiatins in tidal mixing. Real estuaies d shw lage vaiatins due t changes in tidal mixing this is because the steady-state assumptin is vilated in the spingneap cycle me n this in the next sectin. F the case in which Richadsn-numbe effects ae cnsideed, we get slightly diffeent equatins f e and s: e / 5 a 5 5 / 5 gs / / h T a a.3 s a s aa / 5 / 5 T 4 / 5 gs h / 5 These equatins indicate that the estuaine velcity e inceases with inceasing ive flw (as expected), and als inceases with inceasing tidal velcity (nt expected). Statificatin is fund t be slightly me sensitive t ive flw than in the case withut the Richadsn-numbe dependence, and als it is fund t vay invesely with tidal velcity. Althugh the physics wuld suggest that equatins.3 and.4 pvide a me ealistic epesentatin f the vaiability f estuaine ciculatin and statificatin, thee have nt been adequate analyses f these quantities amng diffeent estuaies t pvide a definitive assessment. An analysis f statificatin amng a wide vaiety f estuaies (Fig..6) indicates that the simple pwe law pedictin f equatin. des a bette jb than equatin.4 f pedicting the wide ange f statificatin bseved in estuaies, even thugh it has a me simplified theetical basis. Thee ae the facts such as estuaine gemety and tempal vaiability that ae nt included in the they that cntibute t the actual vaiability amng estuaies. These equatins shuld be egaded at this time as pviding guidance f the intepetatin f vaiability amng estuaies and within a paticula estuay Tempal Vaiability f the Estuaine Salinity Stuctue and Ciculatin The cmbined equatins pesented in the pevius sectin ae based n a steady-state salt balance, meaning that the estuay neithe gains n lses salt. An estimate f the timescale f 0

11 which that assumptin is valid can be appximated by the flushing timescale, which can be estimated as the ati f the length f the salinity intusin L t the estuaine velcity: T L / F E F the Hudsn estuay, that timescale is appximately 0 days; f the Chesapeake, clse t 30, and f the Clumbia Rive estuay, clse t day. If the fcing ccus at timescales cmpaable less than the esidence time, then the salt balance will nt keep up with thse changes, and s s/ x will adjust t the aveage fcing cnditins athe than thei sht-tem vaiatins. This des nt invalidate the cupled equatins, but it means that they shuld be cnsideed a epesentatin f the cnditins aveaged ve the flushing timescale. A maj cntibut t tempal vaiability in estuaies is the ftnightly vaiatin f tidal amplitude, mentined ealie in cntext with statificatin vaiatins. F lage estuaies such as the Hudsn the Chesapeake, s/ x emains nealy cnstant thugh the ftnightly cycle, s the vaiatin f statificatin is nt pedicted by the cupled equatins (equatin..4), but athe by the lcal statificatin balance (equatin..4). Indeed the lage spingneap vaiability f the statificatin in the Hudsn estuay (Fig..4) indicates a significant amplificatin f the tidal vaiatin, cnsistent with equatin.4. In estuaies that ae shte and have faste espnse times, s/ x will incease duing sping tides, patially ffsetting the influence f inceased mixing. Othe facts, such as changes in ive flw and wind fcing, als cntibute t tempal vaiability in estuaies, with the same caveat that they may ccu at timescales faste than slwe than the espnse time f the estuay, and thei influence n the estuaine egime will depend n the elative timescales. The influence f tempal vaiability (including tides as well as lwe-fequency pcesses) n the time-aveaged estuaine egime is ne f the mst imptant tpics in estuaine physics. Chaptes 4, 5 and 9 examines these time-dependent pcesses Estuaine Classificatin Hansen and Rattay (966) develped a scheme f estuaine classificatin called a statificatin-ciculatin diagam, which has been the mst cmmnly used appach ve the last fu decades. The Hansen-Rattay appach is intended as a diagnstic tl given the bseved statificatin and ciculatin, what ae the pcesses espnsible f salt flux? Anthe

12 appach t classificatin is the pgntic appach, in which the estuay is classified based n fcing vaiables, and the pupse f the classificatin is t pedict the estuaine egime based n thse fcing cnditins. Due t the cmplexity f the pcesses and vaiability within and amng estuaies, the pgnstic appach culd at best pvide a ugh estimate f the cnditins f a paticula estuay the quantitative pedictin f estuaine pcesses is difficult even with a high-eslutin numeical mdel. Nevetheless, the cupled equatins pvide a stating pint f a pgnstic classificatin f estuaies. This analysis suggests that the feshwate velcity R and tidal velcity T ae maste vaiables that may pvide the famewk f such a pgnstic appach, as illustated in Figue.7. Me stngly statified estuaies appea n the uppe pat f the diagam, and weakly statified n the lwe pat. The length f the estuay and flushing timescale depend invesely n s/ x (equatin.9.0), s the lwe left cne f the diagam indicates lng and slw-flushing egimes, wheeas the uppe ight cne is sht, apidly flushing systems. Estuaies at simila pints in the diagam wuld be expected t have simila dynamics, at least in a geneal sense. This famewk des nt accunt f vaiatins in estuaine gemety e.g., vey deep vs. vey shallw, vey wide vs. vey naw systems. Als, the issue f time-dependence is nt epesented in this diagam. Me eseach is equied t assess the geneal applicability f this famewk, and t detemine what the vaiables shuld be cnsideed t yield a easnable pedictin f the estuaine egime. Refeences Chatwin, P.C., 976. Sme emaks n the maintenance f the salinity distibutin in estuaies. Estuaine and Castal Maine Sci., 4, Clias, McGay, N. and C.A. Banes, 974. Atlas f physical and chemical ppeties f Puget Sund and its appaches. nivesity f Washingtn Sea Gant Pub. WSG 74-, 85 pp. Geye, W.R., J.D. Wduff and P. Taykvski, 00. Sediment tanspt and tapping in the Hudsn Rive estuay. Estuaies, 4, Haas, L. W., 977. The effect f the sping-neap tidal cycle n the vetical salinity stuctue f the James, Yk and Rappahannck Rives, Viginia,.S.A. Estuaine and Castal Maine Sci., 5,

13 Hansen and Rattay, 965. Gavitatinal ciculatin in staits and estuaies, J. Maine Res., 3, 04-. Hansen, D. V., and M. Rattay, J., 966. New dimensins in estuay classificatin. Limnl. and Oceang.,, MacCeady, P., 999. Estuaine adjustment t changes in ive flw and tidal mixing. J. Phys. Oceang., 9, Mnismith, S.G., W. Kimmee, J.R. Buau, and M. Stacey, 00. Stuctue and flw-induced vaiability f the subtidal salinity field in nthen San Fancisc Bay. M. Phys. Oceang., 3, Pitchad, D.V., 95. Salinity distibutin and ciculatin in the Chesapeake Bay estuaine system. J. Maine Res., 5, Twbidge, J. H., 99. A simple desciptin f the deepening and stuctue f a stably statified flw diven by a suface stess. J. Gephys. Res., 97, 5,59-5,543. 3

14 Figue.. Tw estuaine css-sectins shwing salinity distibutins. The uppe panel is Puget Sund (Washingtn State, fm Clias et al., 974), ne f the lagest estuaies in Nth Ameica. The lwe panel is the Nth Rive (Mashfield, MA), a vey small estuay. In bth cases thee is a hizntal salinity gadient (saltie twad the cean) that pvides the diving fce f the estuaine ciculatin. The exteme diffeence in the stength f the salinity gadient between the tw egimes is elated t the exteme diffeence in depth as well as the elative stength f feshwate inflw. Figue.. Vetical pfiles f cuents in the Hudsn Rive estuay duing maximum fld (blue), maximum ebb (geen), tidal aveage (ed), and the theetical pfile (dashed). Based n bsevatins fm Geye et al. (00). Figue.3. Schematic css-sectin f an estuay shwing the influence f advectin and vetical mixing n the lcal salt balance. The ed lines ae ishalines, and the blue lines and aws indicate the estuaine ciculatin. In Bx A (uppe laye ), hizntal advectin causes a eductin f salinity, but vetical mixing cmpensates by eplacing lw-salinity wate with undelying high-salinity wate. The elative les f advectin and mixing ae evesed in Bx B (lwe laye). Figue.4. Time seies bsevatins fm the Hudsn Rive in the fall f 995 shwing ftnightly and mnthly vaiatins in tidal velcity amplitude (uppe panel), estuaine velcity (middle panel) and statificatin (lwe panel). The theetical pedictins f estuaine velcity and statificatin ae als shwn, based n bseved values f T and s/ x. Figue.5. Schematic css-sectin f an estuaine basin t illustate Knudsen s elatin f the salt balance. The salinity is assumed t be in steady state, which may nly be valid f lng time-scales (weeks t mnths) f lage estuaies. Figue.6. Estuaine statificatin pltted as a functin f feshwate velcity f a vaiety f diffeent estuaies. Equatin pvides a easnable fit t mst f these bsevatins. At high values f R, the statificatin asympttically appaches a value f, cnsistent with the salt-wedge egime. Figue.7. A famewk f pgnstic estuaine classificatin. The axes ae the fcing vaiables: tidal velcity and feshwate velcity, nn-dimensinalized by a densimetic velcity scale. Statificatin vaiatins ae mainly epesented by the vetical psitin n the 4

15 diagam. The length and flushing times depend n bth paametes. Additinal eseach may lead t a me quantitative appach using this famewk..a,b 5

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