Boundary currents over shelf and slope topography

Journal of Marine Systems 19 Ž1999. 137–158

Boundary currents over shelf and slope topography Pieter Jacobs ) , Yakun Guo, Peter A. Davies Department of CiÕil Engineering, The UniÕersity of Dundee, Dundee DD1 4HN, UK Received 11 July 1997; accepted 23 March 1998

Abstract Laboratory experiments are presented from a modelling investigation into the influence of shelf and slope topography on f-plane surface and intermediate flows along ocean boundaries. The surface flows are formed from an upstream source by the release of fresh water into a rotating tank containing salt water, while for the intermediate-water counterpart flows, neutrally-buoyant fluid was released from a submerged source into stably-stratified Žtwo-layer. and quiescent receiving waters in solid body rotation. It is shown that the stability of these buoyancy-driven currents can be described satisfactorily by a combination of the dimensionless parameters Bu s N 2rf 2 , Ek s 2 nrfD 02 and Ro s U0rfL0 , where N and f are the buoyancy and Coriolis frequencies respectively, D 0 , L0 and U0 are the initial depth, width and velocity of the currents, respectively, and n is the kinematic viscosity of the fluid. Furthermore, comparison with physical models of surface and intermediate flows along a vertical wall and over a flat bottom reveals that the stability regimes are not significantly altered by the presence of shelf topography. Variation of the depth of the surface flows with respect to the total fluid depth above the underlying shelf is shown to have a significant effect on the velocity and density structure of these flows. When the depth and width ratios are small, the surface flow is not affected by the varying topography. However, when the current occupies a considerable height above the shelf and is at least as wide as the shelf, upper layer fluid is transported offshore through the bottom Ekman layer, where it is arrested above the sloping bottom. At this location, a deepening of the upper layer develops due to potential vorticity conservation of the lower layer, accompanied by a local alongshore velocity maximum. This shelf break front prevents significant offshore transport of upper layer fluid far beyond the shelf break, even in cases where the flow is unstable. Comparison of the intermediate currents with dynamically-similar currents above a flat bottom does not reveal a stabilising effect of the slope. For unstable intermediate currents, offshore transport is not prohibited Žas it is shown to be for surface currents over narrow shelves, due to the presence of the slope., and large scale instability patterns can extend over great distances from the slope. It is shown that the geostrophic nature of these currents is destroyed close to the sloping bottom. Here, the upper and lower density interfaces, denoting the vertical extents of the intermediate current, tilt sharply downwards. q 1999 Elsevier Science B.V. All rights reserved. Keywords: stratified flow; rotating flow; topography; shelf currents; buoyancy; geostrophy

1. Introduction )

Corresponding author. Centre for Water Research, University of Western Australia, Nedlands, Western Australia 6907, Australia. Tel.: q61-8-9380-1687; Fax: q61-8-9380-1015; E-mail: [email protected]

It has long been recognised that the physical, chemical and biological transfer processes occurring at the ocean margins are crucial determinants of the fluxes of energy across the boundary between the

0924-7963r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 7 9 6 3 Ž 9 8 . 0 0 0 5 6 - 6

138

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

coastal seas and the deep oceans. The transfers are, of course, two-way; on the one hand, the deep ocean is supplied with dissolved and particulate matter from the high productivity coastal seas and, on the other, the deep ocean waters export nutrients and dissolved trace elements in the reverse direction. Since the quantification of fluxes across the margins is a fundamental requirement for understanding and monitoring global climate change processes, there is a great need to determine the physical mechanisms responsible for the transport of the above elements. In particular, important questions remain concerning the passive Žor otherwise. nature of the sediment, nutrient, chemical and organic tracers. For example, in the context of the present study of slope currents flowing along the continental shelf, attention has been focused recently ŽBackhaus et al., 1994. upon the role of such currents in determining the spatial and temporal variability of the annual invasion of the northern North Sea by the copepod Calanus finmarchicus. Such an invasion is of crucial importance for the availability of food sources for demersal fish and fish larvae in the North Sea and Nordic Seas and the stability of the ecosystems in these regions ŽCushing, 1990; Richardson et al., 1995.. There is strong evidence to link the variability of the invasion with the spatial and temporal behaviour of the socalled Continental Shelf Jet ŽBackhaus et al., 1994. —the phenomenon of interest in this paper. Likewise, recent field measurements taken at the north east European Shelf as part of the OMEX programme have revealed the existence of strong slope currents and significant lateral transport of suspended matter ŽWollast and Chou, 1995., with strong vertical mixing of nitrate-rich deep water at the shelf front and significant vertical transport of organic carbon in the form of micro- and meso-zooplankton. Seasonal cycles of benthic activity closely mirror the seasonal fluxes of organic material to the sea bed and shelf edge topography and flow dynamics are known to provide preferential pathways for fluxes of sediment and organic matter ŽWeaver et al., 1997.. These and related examples confirm the coupling between physical model results of the type that are discussed here and the implications of such results for all components of the relevant marine system under consideration. Of particular significance is the

matter of lateral transport of energy and material away from the shelf edge to the deep ocean ŽWeaver et al., 1997., a mode that is linked closely to the structure, stability and variability of the along slope currents being modelled in this paper and not simply to sinking and overspilling processes at the edge. OMEX field data at the Goban Spur, showing the flux into the benthos of quickly-degrading organic material to be approximately twice that determined from the 3600-m sediment traps at that location suggest strongly that lateral fluxes of refractory matter is extremely important ŽWeaver et al., 1997.. Surface and intermediate-water boundary currents in coastal regions are often characterised by a large degree of variability. Observations of surface flows include the Norwegian Coastal Current ŽMysak and Schott, 1977; Johannessen et al., 1989., the Leeuwin Current ŽThompson, 1984; Godfrey and Ridgway, 1985; Griffiths and Pearce, 1985. and the Algerian Current ŽMillot, 1985.. An example of an intermediate flow along a continental shelf is that formed by the Mediterranean outflow into the Gulf of Cadiz ŽJungclaus and Mellor, 1997.. The northward continuation of this flow can be found as a jet flowing along the Portuguese, Galician, Armorican and Celtic slopes ŽPingree and Le Cann, 1990. as far as the continental slope west of Scotland ŽBackhaus et al., 1994. and beyond. The observed variability manifests itself primarily in the appearance of mesoscale meanders and eddies, caused by, for example, either Ži. spatial and temporal changes in the forcing of the flow, Žii. variations in the underlying bathymetry, or Žiii. the instability of the flow itself. Previous laboratory models have all concentrated on the behaviour of these flows along a straight vertical coastline and above a flat bottom Žsee Vinger and McClimans, 1980; Griffiths and Linden, 1981; Chabert d’Hieres ` et al., 1991 and Obaton, 1994 for baroclinic surface flows; Davies et al., 1991; Baey et al., 1995 for intermediate flows.. However, a common feature of the above-mentioned regions is the relative narrowness of the continental shelf, bounded on the offshore side by a steep slope. The influence of this topography on Ži. the stability and Žii. the density and velocity distributions of the currents is the main focus of this paper. Previous analytical descriptions of surface boundary flows are reported by Condie Ž1993. and Will-

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

mott and Collings Ž1997. for two- and three-layer models, respectively. The first of these studies Ži. explains that geostrophy and potential vorticity conservation Žof the upper layer. are sufficient to ensure that the surface layer does not extend far beyond the shelf break and Žii. shows that the depth of the upper layer decreases monotonically in the offshore direction. Willmott and Collings Ž1997. included a second active layer and showed that potential vorticity conservation in both active layers and geostrophicallybalanced interfaces create a local maximum in upper layer depth above the slope. In both cases, the presence of the shelf break is shown to arrest the offshore spreading of surface waters.

2. Physical system

shape of the flow at the source is triangular, then mass conservation requires that: L0 D 0 Q 0 s U0 . Ž 1. 2 From the geostrophic balance, a second relationship between the velocity and depth at the source can be derived, using the hydrostatic equation and the x-component of the momentum equation: gX D0 fU0 s Ž 2. L0 in which g X is the reduced gravity based on the density difference between the two layers. Combining Eqs. Ž1. and Ž2. gives the depth and the velocity at the source as a function of input parameters only: D0 s

2.1. Surface current U0 s Consider the situation of Fig. 1, in which a fresh water current flows over a layer of quiescent denser water in a uniformly rotating system ŽCoriolis parameter f .. The current is fed by an upstream source at a rate Q0 and has initial depth D 0 , width L0 and uniform velocity U0 , respectively. The flow is driven by an inertial-buoyancy balance in the along-stream direction while the cross-stream force balance is assumed to be geostrophic. If the cross-sectional

139

ž ž

1r2

2 Q0 f gX 2 Q0 g X f L20

/ /

Ž 3. 1r2

Ž 4.

Eq. Ž3. is used to define the appropriate Rossby radius of deformation according to: X

RD s

(g D f

0

s

ž

2 Q0 g X f3

1r4

/

.

Ž 5.

The bottom topography is formed by an idealised model of a continental shelf and slope with shelf width LS and height ZS . The profile of the slope,

Fig. 1. Physical system for surface current over a shelf and slope.

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

140

starting at the shelf break Žwith offshore coordinate y break ., can be described by: z shelf Ž y . s ZS cos 2 Ž p Ž y y y break . .

Ž 6.

The total height of the water in the tank is H, which makes the depth of the fluid above the shelf equal to HS s H y ZS . The mean kinematic viscosity of the working fluids is n , so the flow is determined by seven independent input parameters, namely Q0 , f, g X , L0 , n and the geometrical parameters LS and HS . From dimensional analysis, the flow can then be characterised by five dimensionless parameters, for example a Burger number Bu, an Ekman number Ek, a Rossby number Ro: Bu s Ek s

Ro s

N2 s

f2

gX 3

ž

2 Q0 f 5

U0 f L0

/

Ž 7.

g Xn

2n f D 02

1r2

s

s

Ž 8.

Q0 f 2

ž

2 Q0 g X f 3 L40

1r2

/

Ž 9. 2.2. Intermediate current

and two geometrical ratios: L0

Ž 10 .

LS D0 HS

s

2 Q0 f

ž / g X HS2

number thus defined is an important indicator for the description of the stability of the current ŽChabert d’Hieres ` et al., 1991.. Note that if we define Bu as the ratio of the squares of the Rossby radius of deformation and the initial width of the current L0 , then decreasing the initial width would increase Bu, implying a more stable flow ŽChabert d’Hieres ` et al., 1991, for this configuration.. But, from continuity, this would also result in a higher initial velocity U0 , which would increase the possibility of occurrence of barotropic instabilities. This is confirmed by the measurements of buoyant surface boundary currents by Vinger and McClimans Ž1980., who found shear instabilities for supercritical coastal currents over a flat bottom. So the Burger number, defined as above in Eq. Ž7., may be regarded conveniently as an indicator for the baroclinic stability characteristics of the flow. The barotropic effects are captured by the Rossby number, in the sense that a higher Rossby number would Žon the evidence of previous studies. indicate a more unstable flow.

1r2

Ž 11 .

with N the buoyancy frequency based on the upper layer depth D 0 . It is anticipated that the Burger

For the intermediate current experiments, consider the configuration of Fig. 2. A constant flux Q 0 of water with an intermediate density r 2 Žf Ž r 1 q r 3 .r2. is introduced at the interface of a two-layer system Ž r 1 , r 3 .. Again, the continuity condition at the source is described by Eq. Ž1.. The result of the geostrophy condition is also given by Eq. Ž2. after

Fig. 2. Physical system for an intermediate current along a slope.

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

141

Table 1 Parameter ranges for surface and intermediate current experiments and for some observed shelf currents

Shallow surface currents Deep surface currents Intermediate current Norwegian Coastal Current Leeuwin Current Algerian Current Celtic Slope Current

Bu

Ek

Ro

L0rLS

D 0rHS

h 3 rz S

128–3830 7–69 6–771 3600 9500 15 000 250

6.40 = 10y3 –1.23 = 10y1 5.56 = 10y4 –6.68 = 10y3 8.35 = 10y4 –7.79 = 10y2 1.2 = 10y3 5.4 = 10y4 1.7 = 10y3 1.0 = 10y3

0.46–2.02 0.10–0.92 0.05–1.95 0.02 0.02 0.08 0.04

0.7 1, 1.5 – 1.0 2.5 10 –

0.20–0.62 0.61–1.50 – 0.25–0.5 0.6–1.0 0.5–1.0 –

– – 0.67 – – – 0.8

The value of the kinematic viscosity for the laboratory observations was taken as 10y6 m2rs, while a value of 10y3 m2rs was assumed for the eddy viscosity of the oceanic cases.

substituting the reduced gravity g X by the modified value: g X12 g X23 gX ' X Ž 12 . g 12 q g X23 with g X12 and g X23 the reduced gravitational accelerations for the interfaces between the upper and intermediate, and the intermediate and lower layers, respectively. Using this substitution in the equations of the dimensionless parameters Bu, Ek and Ro allows us to use the same definitions for these parameters to characterise the flow. However, for the intermediate flow experiments, the ratios Eqs. Ž10. and Ž11. are not significant. The appropriate geometric ratio is then that of the depth of the lower layer h 3 and the height of the shelf ZS , to indicate the vertical level of introduction of the intermediate flow with respect to the height of the shelf. The parameter ranges used in the present experiments are listed in Table 1, together with the equivalent values for some of the currents mentioned in Section 1. 2.3. Geostrophic conditions If we apply the thermal wind relation to the surface current described above then the velocity difference between the upper and lower layers can be expressed as: u1 Ž y . y u 2 Ž y . s y

g X d h1 f dy

Ž 13 .

where h1Ž y . is the upper layer depth, with h1 s Ž D 0 , 0. at y s Ž0, L0 . Žsee Fig. 2.. If we assume that the

velocity in the lower layer is negligible Ža condition which is fulfilled if the upper layer depth is small compared with the total depth., then the interface position can be calculated from the velocity profile u1Ž y . using h1 Ž y . s y

f

y

H u Ž y.d y g 0 X

1

qC

Ž 14 .

where the integration constant C can be evaluated from the directly measured interface depth at a certain radial position y. The same principle can be used to calculate the thickness of the intermediate current, provided that g X is replaced by either g X12 or g X23 for the upper or lower interfaces, respectively.

3. Experimental setup The experiments were conducted on the large rotating facility in the Coriolis Laboratory of the Institut de Mecanique de Grenoble ŽFrance.. The ´ platform supports a 13-m diameter, 1.2-m deep cylindrical tank, in which an azimuthally-symmetric model of a continental shelf and slope was placed against the outer wall for about three quarters of the circumference Žsee Fig. 3.. Three sets of experiments were investigated: relatively shallow surface currents Ž D 0rHS - 1., deep surface currents Ž D 0rHS ; 1., and intermediate currents along the slope. For the investigation of a surface flow over a continental shelf, the tank was filled Žwhile rotating. with a layer of salt water with known density r 2 to a total depth H. Subsequently, the tank was left to rotate for about 2 h so that any disturbances due to

142

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

Fig. 3. Sketch of rotating tank with model shelf and slope.

the filling process could die out. Then, at time t s 0, fresh water was introduced through the upstream source Žthe injector. at a rate Q0 . The resulting Lagrangian velocity was determined by recording the times at which the nose of the Ždyed. surface current passed equidistant marks on the side wall of the tank. The accuracy of these measurements increases with decreasing Lagrangian velocity Žsince the relative error in the time measurement decreases., but was generally between 4% and 11%. The supply of dye to the current was stopped and reinitiated regularly to allow for further measurements of the Lagrangian velocity. This velocity will be referred to as the nose velocity Žsee Fig. 4., although for the second and later determinations in an experiment this name is somewhat misleading. From the same video images, the stability of the boundary current can be observed. At some distance downstream from the end of the shelf and slope topography, an overflow sink was placed at a suitable height to collect and remove the water originally at the source, enabling the steady state flow to be observed for longer than typically 50 rotation periods. The presence of the sink also ensured that the total height H remained constant during the experiment. The experiments with the intermediate flow were set up in the same way as the surface current experiments described above, except that the tank was initially filled with a two-layer system. The density of the intermediate Žsource. water was approximately

the average of the densities of the upper and lower layers, respectively, to ensure symmetric conditions for the upper and lower interfaces. The intermediate water was collected downstream of the topography by a submerged sink. The Eulerian velocity field was determined with a CCD camera and an S-VHS video recorder. Small, neutrally-buoyant particles were added to the surface or intermediate water and illuminated by a horizontal laser sheet. A field of view of 42 = 32 cm was obtained, so in order to be able to measure the

Fig. 4. Top view of a surface current over shelf and slope topography, indicating the ŽLagrangian. nose velocity and the Eulerian alongshore velocity profile.

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

velocity profile to the full radial extent of the flow, the camera was moved to adjacent radial positions. This system was used at two downstream positions Ž6.1 and 14.8 m from the injector; due to the decrease in effective tank radius, these positions were 5.0 and 12.1 m for intermediate currents.. Final determination of the Eulerian velocity was carried out using DigImage particle tracking software ŽDalziel, 1995., with which, for the present flows, an accuracy of about 5% can be reached. The vertical distribution of the density was measured using a set of 9 to 18 ultrasonic probes of the type described by Fleury et al. Ž1991. with temperature and pressure influences assumed to be negligible compared with those associated with the salinity changes of the fluid. These probes were distributed along a radial line and could be moved to any desired azimuthal position. Density profiles were taken by automatically moving the probes vertically through the water column with a vertical definition of about 1 mm. The signals of the probes were only used in a relative manner, so that the interface positions were determined by observing Žabrupt.

143

changes in the density profiles, rather than locating specific prescribed density surfaces.

4. Results 4.1. Shallow surface current (D0 r HS - 1) Seven experiments were carried out for surface currents that occupied a small part of the total depth over the shelf. From the overhead video images it was observed that the surface currents stayed confined to the shelf region. The presence of the shelf and slope had therefore a negligible influence on the structure of the currents, enabling them to be treated as surface flows over a flat bottom. Obaton Ž1994. experimentally determined a critical value for the Ekman number Ek of 6 = 10y3 for such flows, above which surface currents are stable. Table 1 shows that the present values of Ek are well above this critical value. Indeed, all the flows were found to be stable, in the sense that no large meander-like perturbations ŽVinger and McClimans, 1980. devel-

Fig. 5. Dimensionless plot of the nose velocity against time for a shallow surface current. Experimental parameters are Bu s 181, Ek s 0.0128, Ro s 0.46, D 0rHS s 0.44 and L0rLS s 0.7. The times in the legend indicate the times at which each measurement was started by reinitiating the supply of dye to the source fluid.

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

144

oped on the frontal boundary separating the surface and receiving waters. At later stages in the experiments, the nose detached from the coast, due to the presence of small anticyclonic eddies close to the coast, originating from the lower layer Ždescribed in more detail below, see also Chabert d’Hieres ` et al., 1991 and Obaton, 1994.. However, these small-scale eddies did not have a significant influence on the stability of the surface current itself. Observations of the Lagrangian along-shelf nose velocity of a baroclinic surface current as a function of time indicate Žsee Fig. 5. that the appropriate scale for the initial velocity is given by that of the first baroclinic mode, which can be expressed in terms of the initial parameters as: U) s g X D 0 s f L0 U0 s Ž 2 Q 0 fg X .

(

(

1r4

Ž 15 .

The Lagrangian nose velocity becomes smaller than U) within approximately one rotation period, indicating that the flow is subcritical. Furthermore, the current slows down when it flows further down-

stream. This decline in Lagrangian velocity has also been described by Davies et al. Ž1993. for similar coastal currents. They developed a scaling for this decline, based on a balance between friction and pressure gradient forces, producing a time dependency of ty1 r4 . However, their experiments resulted in a power of t between y0.38 and y0.81, while Fig. 5 indicates a power of y0.48 " 0.02. The results of all shallow surface currents were in the range y0.47 " 0.02 to y0.71 " 0.03 Žwith an average value of y0.56 " 0.09., confirming the empirical values of Davies et al. Ž1993.. If the flow rate is constant within the current Žthat is, if no mixing occurs., then a decline in nose velocity indicates that the cross-sectional area of the flow must increase downstream. This can be achieved by an increase in depth andror in width. An example of an Eulerian along-shelf velocity profile Žas function of the radial distance. is given in Fig. 6. Each instantaneous measurement, indicated by a different symbol, results from a temporal aver-

Fig. 6. Eulerian alongshore velocity as function of offshore distance for the same experiment as in Fig. 5. Measurements are taken at x s 6.1 m between t s 20 T and t s 22 T. The shelf break is at 100 cm from the vertical wall.

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

age Žof 3 s. of the velocity data. The time difference between the first and last measurement in Fig. 6 was about two rotation periods. However, the data do not drift significantly over this period, indicating that the flow is stable. The tracking data have also been averaged spatially over the width of the field of view Ž42 cm; in the direction of the flow.. The along-shelf, jet-like velocity profile is then used to calculate the vertical position of the density interface, with Eq. Ž14.. The result is shown as the solid line in Fig. 7, in which the results from the Ždirect. density measurements are indicated by the triangular symbols. The averaged depth of the interface at yrLS s 0.3 has been chosen as the reference for the determination of the associated integration constant. ŽNote that the computation of the shape of the interface is fairly robust, because of the tight polynomial fit of the velocity data; the vertical offset of the curve, however, depends on the choice of the integration constant and therefore introduces an estimated error of "0.5 cm.. The density measurements

145

show no strong influence of the increasing depth beyond the shelf break. The flow is essentially in geostrophic balance. For the case illustrated in Figs. 5–7, the calculated interface position indicates a depth at the wall Žat x s 6.1 m. of 2.7 " 0.5 cm, while the flow depth at the injector Žat x, y s 0. is set at 3.5 cm. Thus, the flow depth decreases between these downstream positions. The ratio of the depths at x s 6.1 m Žcalled D). and D 0 is independent of the initial conditions, and its average value for this downstream position over all the experiments gives D) s Ž0.65 " 0.09. D 0 . The observed decrease in Lagrangian velocity must be accompanied by an increasing cross-sectional area of the flow Žin the absence of interfacial mixing.. The above data indicate that the depth decreases downstream, so the only way in which an increase in cross-sectional area can be achieved is through an increase in horizontal width. This width cannot be measured from the overhead recording of

Fig. 7. Directly measured Ž\. and calculated Žsolid line. interface position for the same experiment as in Fig. 5. The free surface is indicated by the horizontal line at z s 38 cm. The direct measurements were taken at x s 6.4 m between t s 19 T and t s 27 T.

146

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

the surface dye patterns, since Ekman layer transport Žfrom wind shear due to the rotation of the tank under the quiescent air mass above it. can significantly obscure these measurements ŽJacobs, 1996.. Therefore, the width of the current is defined as the halfwidth L1r2 of the radial profile of the Eulerian alongshelf velocity uŽ y ., where L1r2 is the width of the jet for which u s u maxr2 and u max is the maximum Žpeak. velocity of the profile, situated at y s L max . For a detailed analysis of the dependency of these parameters on the initial conditions, the reader is referred to Jacobs Ž1996.. As stated above, the profile of Fig. 6 is a typical example for the relatively shallow surface currents. The velocity maximum was in all cases situated around yrLS s 0.1 from the vertical wall. However, a detailed comparison of the measurements made at the two different downstream stations showed an increase in Lmax , indicating that the flow detaches from the coast Žas mentioned above.. This detachment results from the lower layer gaining anticyclonic circulation Ždue to relatively greater vortex tube compression at the wall by the presence of the upper layer.. Subsequently, a small but significant reverse flow is formed along the wall which interacts with the main surface flow to form the small anticyclonic eddies attached to the coast Žalso described by Chabert d’Hieres ` et al., 1991.. This process is enhanced by the strong horizontal shear in the upper layer flow close to the wall Žsee Fig. 6.. Comparison of the halfwidth of the flow, measured at the two downstream positions show a decrease in halfwidth with downstream distance of about 15%. So, since the observed decrease in nose velocity cannot be explained by an increasing flow width, other processes Žsuch as interfacial mixing. must operate to slow down the current. Friction effects on the solid boundary and on the interface also account for the observed reduction in Lagrangian velocity. 4.2. Deep surface currents (D0 r HS ; 1) Seven experiments were carried out with D 0rHS ; 1; for one of these experiments, the initial width of the current was decreased to the shelf width Ž L0rLS s 1. to investigate the influence of an increase in Ro Žfrom 0.41 to 0.92. on the stability of

the flow Žsee Table 1.. The values for Ek for these experiments are all below the critical value of 6 = 10y3 ŽObaton, 1994., contrary to the shallow flow cases. So, unstable flow can be expected on the basis of the critical Ekman number criterion. However, unstable flow occurred only for low values of Bu Ž- 10. and for high values of Ro Ž) 0.8.. For all three cases of unstable flow, the current was found to meander through a regular pattern of cyclonic and anticyclonic eddies Žsee Fig. 8.. The anticyclones were attached to the coast, while the cyclones were positioned above the slope. A similar cyclonicranticyclonic eddy pair was also observed in the Norwegian Coastal Current ŽJohannessen et al., 1989.. This pattern is explained by the detachment of the current at the coast, as observed in the wide shelf case and described above. After this detachment, the flow enters the slope region, since the shelf width is of the same order as the width of the current. Above the slope, the upper layer increases its depth as a result of the potential vorticity conservation in the bottom layer Žsee below and Willmott and Collings, 1997.. Then, to conserve its own potential vorticity, the upper layer flow must gain cyclonic vorticity, thus creating the observed cyclonic eddies. From the overhead video images, an estimate is made of the wavelength of the meander pattern. The result are given in Table 2. Although the absolute values of the wavelength are very similar for all experiments, scaling them by the Rossby radius, as defined in Eq. Ž5. reveals important differences. For low values of Ro Žcoinciding with low values of Bu., the dimensionless wavelength is found to be very similar to that reported by Condie and Ivey Ž1988., who found a value of 0.83 " 0.11. They compared this result to the experimental values of 1.1 " 0.3 of Griffiths and Linden Ž1982., 1.16 " 0.27 of Chia et al. Ž1982. and 1.14 of Narimousa and Maxworthy Ž1987. by using a mean depth, rather than the depth at the wall, in the definition of R D . Note that here the definition of the Rossby radius is based on the initial depth at the wall. The value of R D will decrease if the actual depth is used, since the depth of the intrusion decreases downstream as well as cross-stream. If we assume that the local depth is of the order 0.5Ž D 0 ., then the results for experiments Sur22 and Sur24 are 1.0 and 1.2, respectively, in good agreement with the values cited above. Kill-

P. Jacobs et al.r Journal of Marine Systems 19 (1999) 137–158

147

Table 2 Results of wavelength measurements

Fig. 8. Top view of an unstable, relatively deep surface current. The coast is situated at the right of the picture, while the shelf break is indicated by the dashed line. The instability pattern is characterised by large anticyclonic eddies near the coast Žthe darker patches.. The surface flow itself is from bottom to top and meanders across the shelf Žlighter shades.. The grey scale gives an indication of the flow evolution: the continuous supply of red dye at the source was stopped; after this, the introduced fresh Žsurface. water was not coloured. The figure therefore indicates that the surface current has a higher downstream velocity than the eddy pattern. The shelf width is 50 cm, and the distance between the thick Žnear-horizontal. lines at the coast is approximately 123 cm. The eddy in the centre of the picture is positioned approximately 19.8 m downstream of the source at t s 24.5 rotation periods. Bu s 7.0, Ek s 5.56=10y4 , Ro s 0.18, D 0 r HS s1.50, L0 r LS s1.5 and R D s 32 cm.

Experiment

Ro

Bu

R D Žm.

l Žm.

l r2p R D

Sur22 Sur24 Sur27

0.177 0.145 0.922

7.0 8.5 48.3

0.32 0.29 0.48

1.45"0.15 1.53"0.09 1.42"0.13

0.73"0.08 0.85"0.05 0.47"0.04

worth et al. Ž1984. obtained a theoretical prediction for the wavelength of 1.15 for waves that extract energy from both the vertical and horizontal shears Žmixed barotropicrbaroclinic instability.. However, Pedlosky Ž1987. showed that pure baroclinic waves have a typical wavelength of roughly five times the Rossby radius of deformation, a scale that accords well with the results of experiments Sur22 and Sur24. It is therefore concluded that the instabilities found in these two experiments originate from a mixture of baroclinic and barotropic effects, with a dominating baroclinic component. In the Algerian Current, the local value of the Rossby radius of deformation is about 20 km, while eddies with a diameter of 100 km have been observed ŽMillot, 1985.. For the Norwegian Coastal Current these values are found to be 10 km and 60–100 km, respectively ŽIkeda et al., 1989.. Thus, the experiments are in good agreement with these field observations. The analysis of satellite images of the Leeuwin Current by Griffiths and Pearce Ž1985. indicated a dimensionless wavelength of 2.18 " 0.53, substantially greater than the values found in the experiments. Griffiths and Pearce Ž1985. mentioned that non-linear interactions between perturbations of differing amplitudes or wavelengths could be the reason for the observed large separation of the eddy structures. However, the dimensionless diameter of the eddies measured 1.19 " 0.14 which agrees with the above mentioned scale. Note that in the experiments these two quantities are essentially the same, since neighbouring eddies are only separated by the thin surface current. The dimensionless wavelength of the instabilities in experiment Sur27, with a relatively high value of Ro, is much smaller. The length scale of barotropic instabilities is usually smaller than that of baroclinic instabilities. Furthermore, a necessary condition for barotropic instability on an f-plane is that the second order derivative of the velocity profile vanishes somewhere in the domain. This criterion is certainly

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fulfilled for all surface currents investigated here. Finally, the higher value of Ro indicates a higher horizontal velocity shear. This indicates that the barotropic component in the instability process has increased. Thus, the initial width of the current L 0 can have an explicit effect on the appearance and stability of the current, and the combination of ŽBu; Ro. is useful to distinguish flow regimes in terms of barotropic and baroclinic instability mechanisms. Note that both types of instabilities have been identified at different latitudes in the Norwegian Coastal Current ŽJohannessen et al., 1989; Ikeda et al., 1989.. The decline in Lagrangian nose velocity was slower than in the shallow flow case. The appropriate power of t was found in the range between y0.22 " 0.04 and y0.51 " 0.08 Žwith an average value of y0.34 " 0.09.. This can be explained by the observation that in the present case the initial velocities are much lower than in the shallow flow case Žfor similar values of Ro. because the discharge rate is of the same order of magnitude, but the depth

is greatly increased. Also, since the value of D 0rHS is close to or larger than unity, bottom friction effects will also reduce the initial velocity. The influence of the shelf break and slope is apparent from the Eulerian velocity profile in Fig. 9. As before, this profile has been constructed from the recordings of particle motions at four adjacent radial camera positions of a flow which was stable over the duration of the experiment. The obtained tracking data have been averaged spatially Žover the width of the field of view; 42 cm. and temporally Žover 3 s.. Fig. 9 shows that the current splits into two noses, one close to the wall and one above the slope. It should be noted that the initial intrusion of the surface current Žduring the transient phase of flow. did not show such a structure. This profile is typical for all stable deep surface flows. In some cases Žmost notably when the volume flow rate of the current Q 0 is increased., the local offshore velocity maximum over the slope is higher than the coastal velocity maximum over the shelf. Similar upper layer veloc-

Fig. 9. Eulerian alongshore velocity as function of offshore distance for a deep surface current. Measurements are taken at x s 6.1 m between t s 19 T and t s 25 T. The shelf break is indicated by the dashed line at y s 50 cm, and the foot of the slope by the dash–dotted line at y s 100 cm. Bu s 48.3, Ek s 0.00334, Ro s 0.41, D 0rHS s 0.86 and L0 rLS s 1.5.

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ity profiles have also been reported by Willmott and Collings Ž1997. in an analytical study of shelf break fronts, although in their case the profile did not show a maximum over the shelf. The velocity profiles in this analytical model are a result of the conservation of potential vorticity in each of the two active layers and are influenced by the velocity and depth of the upper layer at the coast, as well as the cross-sectional area of the upper layer, a parameter which is directly linked to the rate of discharge of upper layer fluid Ž Q0 .. Fig. 2 of Willmott and Collings Ž1997. indicates that for increasing upper layer area, the upper layer depth increases above the slope Žat a local depth maximum. while the profile above the shelf remains virtually unchanged. Through conservation of potential vorticity, this will increase the alongslope velocity of the local maximum over the slope, in qualitative agreement with the present experimental results. The density measurements ŽFig. 10a. show an interface depression that is associated with the second nose of the current Žover the slope.. The depths are averaged at each downstream position over the time indicated in the legend. It is clear that the upper layer deepens with time at a fixed downstream position. Also, the upper layer is deeper at x s 14.6 m than at x s 7.9 m, but the data further downstream are obtained at a later time. The only way in which the downstream spatial structure of the flow could be determined is from simultaneous measurements at different downstream positions, a procedure that could not be adopted in these experiments. The data from the ultra-sonic probes above the shelf were not conclusive, due to the relatively high values of the ratio D 0rHS . In these cases the upper layer approaches the bottom boundary Žthe shelf., where increased mixing due to bottom friction might erode the interface and thus make the detection more difficult. Note that the Ekman layer thickness in the cases presented here varied from 3 to 6 mm Žwith n equal to 10y6 m2rs.. When the depth ratio is larger than unity, a certain part of the shelf will be totally occupied by fresh water, thus making the interface vanish completely. In Fig. 10b, measurements of the upper layer depth at offshore positions yrLS s 1.2, 1.4 and 1.6, respectively, are averaged, scaled by the initial depth from Eq. Ž3., and plotted against Ro. All measure-

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ments were taken at x s 7.8 m between approximately t s 23 T and t s 32 T elapsed times. The ratio of upper layer depth and initial depth is independent of the initial parameters for all offshore positions Žmeasurements were also made at other values of y, but not shown here for clarity of the graph.. Furthermore, the maximum upper layer depth was always at yrLS s 1.6. These vertical density structures agree well in a qualitative sense with Ži. observations of the West Spitsbergen Current before it becomes subject to strong surface cooling ŽPlate 2a of Boyd and D’Asaro, 1994. and Žii. the model of Willmott and Collings Ž1997. in which the deepening of the upper layer above the slope was explained by conservation of potential vorticity in their second Žs middle. layer. In the model, the maximum depression seems to be linked to the point where the interface between the second and third layer intersects the slope. In nearly all cases, this is also the point where the vertical level of this second interface is lowest. The present experiments show that variation of the rotation rate f and the upper layer flow rate Q0 do not significantly alter this structure. Even when the upper layer current is unstable, the self-similar structure still occurs, with the maximum depression positioned approximately above the middle of the slope. There are two main differences between the analytical model of Willmott and Collings Ž1997. and the experiments described here. Firstly, although the lower layer in their model is quiescent, the interface between this layer and the middle layer is not rigid, and can therefore account for changes in the second layer depth, obviously together with the bottom topography. In the experiments, the second Žlower. layer depth can only be changed by variation of the upper interface and the bottom topography. Secondly, the angle of the model bottom increases monotonically, while the angle of the slope in the experiments decreases below mid-level. Note that the maximum depth of the upper layer was always found close to this point, at Ž yrLS , zrHS . s Ž1.5, 0.5.. Despite these differences, the resulting structure of the upper layer resembles closely the solution of Willmott and Collings Ž1997.. Comparison of the width of the current at two downstream positions for the stable cases show that, in contrast to the shallow flows, the width increases

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Fig. 10. Ža. Spatial and temporal evolution of the upper layer over the slope during one experiment for x Žin m., t Žin min. as indicated. Note that the free surface was at z s 38 cm, while the slope extended between y s 50 and 100 cm. Bu s 69, Ek s 0.00348, Ro s 0.70, D 0rHS s 0.95 and L0 rLS s 1.5. Žb. Ratio of upper layer depth and initial depth, as function of Ro for the offshore positions indicated Žin cm.. The solid, dashed, and dash–dot lines are the averages for y s 60, 70 and 80 cm.

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Žwith about 11% between x s 5.6 and 13.6 m. going downstream. Combined with the observation that the depth of the upper layer above the slope increases with time, it can be concluded that the flow migrates towards the shelf break. Clearly, the increased initial depth forces upper layer fluid into the bottom boundary ŽEkman. layer, in which it is transported offshore, in a similar way to the offshore transports described by Chapman Ž1986., Wright Ž1989. and Gawarkiewicz and Chapman Ž1992.. Indeed, observations showed that dye streaks on the shelf floor were positioned under an angle of roughly 458 to the left of the downstream direction. When the total depth increases over the slope, frictional effects on the flow are reduced, therefore causing the flow to follow the isobaths ŽChapman, 1986. and creating the convergence zone close to the shelf break. The specific shape of the interface between the two layers is then determined by potential vorticity considerations for the lower layer. 4.3. Intermediate current In the 11 experiments performed with the physical system of Fig. 2, unstable flow is found when Bu is smaller than 35 for the range 0.8 = 10y3 - Ek - 10 = 10y3 Žthis is not in conflict with the critical value for Ek of 6 = 10y3 for surface currents, since Ek intermed.f 0.5 = Ek surface , because of the modified definition of g X .. The results can be compared with those of the flat bottom equivalent described by Baey et al. Ž1995.. In general, the two sets coincide in the regime diagram, indicating that the presence of the slope does not alter significantly the stability characteristics of the intermediate water flow. However, certain experiments from Baey et al. Ž1995. showed stable flow within a certain distance from the injector, downstream of which a series of cyclonic vortices formed, attached to the wall. This type of flow has not been observed in the present experiments. Eddies and meanders always started close to the injector and travelled downstream with a phase speed smaller than the speed of the current. Unstable currents were all marked by the formation of dipolar structures on their offshore edge, of which the anticyclonic part was usually the stronger Žsee Fig. 11.. These dipoles moved away from the slope, in a

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manner also described by Vinger and McClimans Ž1980. for surface baroclinic flows, and were thus responsible for substantial offshore transport rates of intermediate water. Similar instability patterns for an intermediate current were found by McCreary et al. Ž1991. in a numerical model of coastal upwelling. By variation of the model characteristics, they concluded that the instability pattern was caused by a combination of frontal and baroclinic instability mechanisms. However, experiments in a homogeneous fluid by Etling et al. Ž1993. and Stern et al. Ž1997. have shown that dipolar instabilities can also be formed from a barotropic coastal jet, indicating a shear flow ŽKelvin Helmholtz type. instability. In both experimental models, dipolar Žmushroomshaped. instabilities formed and separated from the coastal current. However, there was no evidence in these experiments of recirculation of fluid towards the coast by the anticyclonic part of the dipole, as was observed in our experiments ŽFig. 11.. This recirculation re-establishes the boundary current along the slope, after which another separation further downstream can occur. Stern et al. Ž1997. predicted the downstream location of the separation point from the Ekman spin-down time S E Žbased on the total fluid depth. and the current velocity as Xsep ; S E UC . For our experiments, this estimate ranged from 6.3 to 27.7 m Žwith S E based on the intermediate layer depth from Eq. Ž3. and UC the maximum downstream velocity measured from the Particle Tracking data., while from the video records all first separation points in the unstable experiments were found to be between 5.0 and 8.0 m downstream from the source. Since in our experiment all necessary conditions were present for frontal, baroclinic and barotropic instability mechanisms, it is impossible to conclude what the dominant instability mechanism is in the present experiments. However, in the light of the above it seems plausible that a combination of the three mechanisms was responsible for the instability patterns. Five different measurements from the same experiment of the Lagrangian nose velocity showed a higher initial nose velocity for the later intrusions ŽŽ1.5 " 0.1.U) compared to Ž1.2 " 0.1.U) for the initial intrusion.. This increase is due to the fact that the receiving water conditions for the initial intrusion Ža two-layer system. differ from those existing for

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Fig. 12. Eulerian alongslope velocity as function of offshore distance for an intermediate current along a slope. Measurements are taken at x s 5.7 m between t s 12 T and t s 14 T. Bu s 31.8, Ek s 0.00318, Ro s 0.65 and h 3rZS s 0.67.

fluid discharged subsequently. For the latter, the receiving water density structure is essentially that of a three-layer flow. Also, the initial intrusion is observed to lose some of its mass flux onto the shelf region through mixing. This process became less well developed, since later additions of dye did not show any spillage of intermediate water onto the shelf. So the total mass flux during the later measurements is higher than for the initial intrusion. The deceleration of the initial nose velocity was weaker than found for the surface flows. Here, fitting the data resulted in powers of t ranging from y0.08 " 0.02 to y0.46 " 0.07 Žwith an average of y0.16 " 0.12.. The relatively low initial velocity of the intermediate flows Žin an absolute sense. is the main

reason for this difference: the intermediate flows left the injector with a nose velocity between 3.3 and 5.3 cmrs, while for the surface flows the initial velocity was between 5.0 and 8.8 cmrs. Fig. 12 shows an Eulerian alongshelf velocity profile for an intermediate current. This profile is used, with Eq. Ž14., to calculate the vertical shape of the vein of intermediate water as a function of the offshore distance. For this, the motions in the upper and lower layers have been neglected and, by implication, assumed to be quiescent. Results of this calculation are compared with the Ždirect. probe measurements in Fig. 13. The results of the probe measurements at a reference station far from the wall Ž yrWS s 0.8, with y s 0 the point where the Žundis-

Fig. 11. Top view of an unstable intermediate current along a slope. The sloping sidewall is situated at the bottom of the picture. The instability pattern is characterised by a large dipolar vortex. Intermediate fluid flows from left to right until it detaches from the slope at a downstream distance Xsep s 6.0 m at t s 9.9 rotation periods Ža. and t s 10.9 rotation periods. Recirculation towards the slope can be seen at the edge of the anticyclonic part of the dipole Žtop right part of the photo.. The distance between the black lines at the level of the intermediate water is approximately 110 cm. Bu s 6.1, Ek s 8.35 = 10y4 , Ro s 0.24, h 3rZS s 0.67, D 0rZS s 0.69 and R D s 34 cm.

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Fig. 13. Directly measured Ž\. and calculated Žsolid lines. interface positions for the same experiment as in Fig. 12. The direct measurements were taken at x s 7.0 m between t s 12 T and t s 16 T. The position of the interface of the initial two-layer system is indicated by the dotted line. The dashed–dotted lines indicate the local normal direction to the slope.

turbed. interface intersects the slope and WS the width of the slope. have been used to determine the integration constants in Eq. Ž14.. There are three striking aspects of Fig. 13. Firstly, the intermediate water is not symmetrically distributed around the level of the initial interface between the upper and lower layer, because the density of the intermediate water is not exactly the average of the densities of the upper and lower layers. Secondly, far away from the slope, the intermediate water layer approaches a constant depth of 3.5 cm, representing the limited sharpness of the initial undisturbed interface, formed during the filling process. The depth of this layer will also be increased by transport of water from the Ekman layers at the upper and lower interfaces of the intermediate water. Thirdly, and most notably, the upper and lower interfaces deviate from the geostrophically-balanced slopes close to the rigid sloping wall. In the absence of flow, salinity interfaces tend to intersect rigid boundaries perpendicularly since the transport of salt

normal to the boundary must vanish. This results in the generation of a weak diffusive-driven flow, which will be present even if the fluid bound by the interfaces is in motion. This flow may become locally important because of the relatively long experiment duration. It is also noted that in the analytical derivation of the interface positions it is assumed that both the top and bottom layers are quiescent. The simultaneous release of lines of dye in all three layers revealed, however, that the velocities in the top and bottom layer are not zero, although they are at least an order of magnitude smaller than the velocity of the intermediate layer. In several cases, it was observed that the flow in the top and bottom layers opposed the direction of the intermediate flow. Finally, Fig. 14 shows the depth of the intermediate layer Žfor stable flows only. at yrWS s 0.3, scaled by the initial depth at the wall, from Eq. Ž3. and using Eq. Ž12.. Again, as was shown for the surface flows, this parameter is a good scaling parameter for the depth of the current. A decrease in

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Fig. 14. Ratio of intermediate layer depth at Ž x, y . s Ž5.2, 0.15 m. from the sloping wall Žat z s 0.20 m. and the initial depth at the wall, from Eq. Ž3..

intermediate layer depth with distance from the injector, as found for the relatively shallow surface currents, is not confirmed here. The scattering of the data in Fig. 13 is due to the fact that the measurements were taken over a wide range of experimental times. The deviation from geostrophy, as discussed above, will also increase this, since the radial position where the measurements were taken is relatively close to the sloping wall. The horizontal line indicates the average of the data shown, at h 2rD 0 s 1.07 " 0.11.

5. Concluding remarks A physical model has been described in which the influence of idealised shelf and slope topography on various types of coastal currents is investigated. The stability regimes of these currents can be described by three dimensionless characteristic numbers: the Burger number Bu, the Ekman number Ek and the

Rossby number Ro. The experimental flows were unstable for low values of Bu and Ek, or when Ro is sufficiently high, confirming the experimental results of Obaton Ž1994. and Baey et al. Ž1995.. This indicates that the presence of the shelf break does not have a significant influence on the stability regimes. However, in the unstable surface flows, the presence of the shelf break affected the instability pattern by inhibiting substantial offshore transport of upper layer fluid far beyond the shelf break. The resulting flow was characterised by a regular array of anticyclonic eddies near the coast, and smaller cyclonic eddies above the slope. The wavelength of these instabilities agrees well with previously published results ŽGriffiths and Linden, 1982; Chia et al., 1982; Narimousa and Maxworthy, 1987; Condie and Ivey, 1988. for flows with low values of the Rossby number, as well as with several field observations: the instabilities were concluded to be of a mixed baroclinicrbarotropic nature. However, for one experiment, the value of Ro was increased, thus increasing the available

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horizontal shear in the flow. The wavelength of the instabilities in this experiment was considerably smaller, indicating an increased influence of barotropic processes in the origin of the instability ŽVinger and McClimans, 1980.. Unstable intermediate currents were characterised by large offshore transports through subsurface dipoles, as reported by McCreary et al. Ž1991. in a model of coastal upwelling. The total depth H has not been found to be a determining parameter of the problem, other than in the ratio of surface current depth to the depth over the shelf Ž D 0rHS ., which discerns the shallow and deep surface currents. In contrast, the study of Vinger and McClimans Ž1980. did indicate an influence of the total depth, However, there are difficulties in comparing that study with the present work because of the different parameter ranges of Bu and, especially, the ratio R D rH Žwhich is approximately unity for the experiments of Vinger and McClimans Ž1980., while for the case investigated here the range was 3.0 - R D rH - 12.5.. The work of Vinger and McClimans Ž1980. and Chabert d’Hieres ` et al. Ž1991. may suggest that the fluid depth may be a controlling variable for cases in which Bu is sufficiently small ŽOŽ1... The surface and intermediate flows were introduced in a near-geostrophic balance. Measurements showed that the initial velocity of the nose of the current can be approximated by the velocity U) s Ž2 Q0 fg X .1r4 . Further downstream the Lagrangian nose velocity decreased. The strength of this deceleration depended on the absolute value of the initial velocity, as well as on the relative depth of the current. This decrease in Lagrangian velocity was, in the case of relatively shallow surface flows, accompanied by a decreasing cross-sectional area of the flow. The associated mass loss is attributed to interfacial mixing. The relatively deep surface currents widened downstream as a result of offshore transport in the bottom ŽEkman. boundary layer. The Eulerian velocity profiles for the shallow surface currents and for intermediate currents along a sloping wall did not show any influence of the varying bottom topography. In these cases, the flow was observed to have a jetlike structure, with the maximum velocity of the profile close to the coast or

sloping wall. When the depth of the upper layer was of the same order of magnitude as the total, however, a second velocity maximum was created, positioned above the sloping part of the bottom topography, indicating the presence of a shelf break jet. This velocity maximum coincided with a local maximum in the upper layer depth, in agreement with the analytical model of Willmott and Collings Ž1997.. This depression of the density interface is attributed to conservation of potential vorticity in the lower layer. The obtained Eulerian velocity profiles have been used to calculate the position of the interfaces between the active and passive layers as a function of the offshore distance, to be compared with the directly measured interface positions from the probe measurements. Agreement was found between the measured and calculated interface positions for the shallow surface currents since in this case the induced velocities in the lower layer could be neglected. This was also the case for the intermediate flows, in which the upper and lower layer depths were both larger than the depth of the intermediate layer itself. However, large deviations from the geostrophic conditions were found close to the sloping bottom. Here, the upper and lower interfaces both sloped down strongly. These deviations resulted from the perpendicular intersection of density Žhere: salinity. interfaces at solid boundaries because of the prohibited normal mass transport. The present work highlights some of the instability mechanisms of surface and intermediate boundary currents. It is clear that substantial offshore transport, shown here to be caused by the instability patterns of these currents, will carry significant amounts of biological and chemical matter away from the shelf and slope region into the deep ocean. However, the experimental results on the surface currents also showed that the underlying bottom topography can, in the case of unstable currents, reduce or even completely prevent this offshore transport.

Acknowledgements Thanks to Gabriel Chabert d’Hieres, Dominique ` Renouard, Henri Didelle and Rene´ Carcel for fruitful

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discussions about and help in performing the experiments at the Coriolis Laboratory of the Institut de Mecanique de Grenoble. Jean-Michel Baey kindly ´ provided the basic computer code for the analysis of the density data. The financial support provided by Ži. the EU MAST programme Žunder MORENA project contract no. MAS2-CT93-0065. and Žii. the NERC LOIS Shelf Edge Study ŽSES. are acknowledged with gratitude. Access to the rotating table facility of the Coriolis Laboratory was made possible by a grant from the EU ‘Grands Instruments’ programme Žcontract ERBCHGECT-920015.. The authors are also grateful to Drs. David Chapman and Scott Condie for useful discussions on the interpretation of the surface flow experiments.

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