Dynamical Influences on the Maine Coastal Current

Daniel R. Lynch, Monica J. Holboke, Christopher E. Naimie

Dartmouth College, Hanover, New Hampshire, U.S.A.
31 August, 1995
Prepared for Continental Shelf Research

Abstract:

Background and Objective

The Gulf of Maine is a semi-enclosed coastal sea on the Northwest Atlantic shelf. (Figure 1). It is widely accepted that there occurs an easterly current along the northern margin of the Gulf (Bigelow, 1927; Bumpus and Lauzier 1965; Pettigrew 1994). Such an occurrence is qualitatively consistent with buoyancy inputs from freshwater runoff at the coast and the attendant along-coast frontal structure. The transport pathways within such a coastal current system are of intrinsic interest from several points of view (Townsend et al, 1987; Townsend, 1991; Franks and Anderson, 1992a,b.)

Also widely accepted is the occurrence of a large-scale cyclonic circulation in the interior Gulf and in particular over Jordan Basin in the eastern Gulf (Brooks 1985; Brown and Irish 1992, 1993). This is broadly consistent with a) barotropic throughflow of shelf water which enters at Southwest Nova Scotia and follows the topography around the Gulf; and b) a seasonal pattern of dense slopewater intrusion into and through the deep Gulf basins via the Northeast Channel, and the attendant baroclinic circulation.

These are generic coastal sea phenomena. In the present context, all give rise to easterly flow along the coast; all are seasonally modulated; and all exhibit complex variability. The details of their dynamical interactions in the Gulf of Maine, in the presence of local and regional wind, tide, and on real topography, are largely unexplored.

Our objective here is to investigate the dynamical influences on the Maine Coastal Current (MCC). Our method is to study model-generated circulation fields representative of climatological mean conditions in bimonthly ``seasons". We distinguish between local (freshwater runoff, local wind, tidal rectification) and remote (Gulf-wide wind response, throughflow from the Scotian Shelf, and basin-scale baroclinicity) influences. A central conclusion is that the MCC cannot be understood in local terms alone -- the remote, basin-scale circulation is an essential ingredient in the composite.

The Maine Coastal Current

We conceptualize the MCC as a composite of seven legs or segments and three branch points (Figure 2). The upstream, Eastern segment extends from Grand Manan basin to Penobscot Bay. Bisagni et al (1994) discuss a formational hypothesis for this branch, involving freshwater inflow from the Scotian Shelf and the Saint John River, with strong local tidal mixing in the Grand Manan area, which is consistent with observed sea surface temperature patterns and several previous studies.

South of Penobscot Bay a widely-reported offshore meander occurs (e.g. Brooks 1985). We identify this as the first of the three branch points, separating Eastern and Western segments of the MCC and originating the southward Jordan segment. This branching structure is consistent with the topography here, where the deep relief of Jordan and Wilkinson Basins is interrupted by a broad shoal. Other offshore steering mechanisms potentially operative here include geostrophic steering by the buoyant Penobscot outflow, and by the cyclonic circulation over Jordan Basin associated with slopewater intrusion. These effects respectively push and pull the Jordan segment offshore. Brooks and Townsend (1989) advanced the hypothesis that this branch point is controlled by the latter -- the ``slopewater steering" mechanism. Sea surface temperature analysis by Bisagni et al supports this hypothesis. More recently, Brooks (1994) suggests offshore steering by the Penobscot plume.

The Western segment of the MCC presumably originates as that portion of the Eastern segment which returns shoreward, plus a portion of the Penobscot River outflow. Following the Western segment, we encounter local contributions from the Kennebec, Androscoggin, Saco, and Merrimack Rivers, and arrive at the second branch point offshore of Cape Ann. At this point, the MCC is divided between an inshore, ``Massachusetts" branch and an offshore, ``Stellwagen" branch. This branch point was studied in detail as part of a comprehensive modeling investigation of Massachusetts and Cape Cod Bays. Blumberg et al (1993) studied the sensitivity of the Bays' circulation to local (using the present terminology) influences on modeled circulation patterns. One conclusion of that study was the importance of the offshore boundary conditions which in the present terminology are synonymous with both upstream inflow and the Gulf-wide circulation. Signell et al (1994) report similar conclusions based on hindcasting experiments with the same model -- basically, model skill deteriorated in regions where local influences were not dominant. Drifters released in the Bays (Geyer et al, 1992) demonstrate complex local behaviour with residence times of order 10 to 20 days in the Massachusetts segment of the MCC, with an extreme of 50 days. This segment rejoins the Stellwagen segment at its exit from Cape Cod Bay at Race Point.

Downstream, the Stellwagen segment undergoes another bifurcation into a ``Nantucket" segment exiting the Gulf at Great South Channel, and a ``Georges Bank" segment which either recirculates in the topographic cul-de-sac north of the Channel (herein the ``SCOPEX" gyre) or finds its way to the northern flank of Georges Bank. Drifter studies and related observations (Chen, 1992; Beardsley et al, 1993; Geyer et al, 1992; Chen et al. 1995) clearly illustrate this branch point and the two implied exit segments of the MCC. Brooks (1985) suggests that the Georges Bank segment itself bifurcates with one segment returning to Jordan Basin and the other transiting the northern flank of the Bank.

This classification of the circulation into segments and branch points is offered as a conceptual framework. During a given period of analysis, the MCC and all its complexities may be characterized by

• the existence, location, and relative strength of the branch points;
• the along-shelf transports, speeds, and Lagrangian transit times in the segments; and
• the attendant 3-D cross-shelf exchanges along the various segments.

The present study is a first step toward a description of climatological mean conditions. Our intent is to provide a comprehensive baseline sufficient to support more detailed studies of individual features and variability. Of special interest at this stage is the identification of the relative contributions of the various dynamical influences on the principal MCC features.

Prognostic Finite Element Model

We employ a state-of-the-art finite-element circulation model, described in detail in Lynch et al. [1995]. The model is three-dimensional (hydrostatic) with a free surface, partially mixed vertically, and fully nonlinear. It transports momentum, heat, salt, and two turbulent variables in tidal time. Both barotropic and baroclinic motions are resolved in tidal time.

Vertical mixing is represented by a level 2.5 turbulence closure scheme [Mellor and Yamada, 1982; Galperin et al., 1988; Blumberg et al. 1992]. Horizontal mixing is represented by a mesh- and shear-dependent eddy viscosity similar to Smagorinsky (1963).

The horizontal coordinate system is Cartesian, on an f-plane. Variable horizontal resolution is facilitated by the use of unstructured meshes of conventional linear triangles. In the vertical, a general terrain-following coordinate system is used, with a flexible ``moving finite element" approach to nonuniform vertical discretization [Lynch 1982]. This allows continuous tracking of the free surface and proper resolution of surface and bottom boundary layers. The composite result is a 3-D mesh of 6-node linear prism elements which stretch and shrink vertically with the water column in tidal time.

The following notation is used, identical to Lynch et al. [1995]:

is the fluid velocity, with Cartesian components ,
is the free surface elevation,
is the streamfunction for tidally-averaged transport,
is the bathymetric depth,
is the total fluid depth, ,
is the fluid density; is a reference value,
is the fluid temperature,
is the fluid salinity,
is the turbulent kinetic energy,
is the turbulent mixing length,
are the turbulent vertical mixing coefficients,
are non-advective horizontal exchanges of momentum, heat, salt, and turbulence
g is gravity,
is the Coriolis vector, directed vertically with magnitude f
is the gradient operator; is its horizontal part,
is the material derivative following the fluid motion,
are the horizontal Cartesian coordinates,
z is the vertical coordinate, positive upward; ,
t is time.

Relative to Lynch et al. [1995], the only addition to the model is the incorporation of source terms to allow fluid discharges along the horizontal boundaries or within the water column. The following source notation is therefore introduced:

is a distributed mass source rate (fluid mass/time/unit volume);
is the volumetric source rate (fluid volume/time/unit volume);
, , , , are the properties of the source fluid;
is net Precipation at the free surface (fluid volume/time/unit area);
is the potential function for tidally-averaged transport,

Using this notation, the governing equations are:

Continuity:

and transport equations for horizontal momentum, heat, salt, and turbulence:

The volumetric source is introduced in the continuity equation, and each transport equation shares the same source term structure. This form is the analytic consequence of using the ``nonconservative" form of the transport equations [Lynch, 1986] and is elaborated in Appendix I. A neutral source is one with properties identical to the ambient fluid properties. In that case, it is easy to see that the direct impact of the source vanishes, leaving only the kinematic effect on the velocity field represented in the continuity equation.

Density is related to temperature and salinity by the equation of state [Gill, 1982]. The vertical turbulent mixing coefficients are given by

where is a constant and the stability functions and are algebraic functions of the local stratification [Galperin et al. 1988]. Additional constraints from Galperin et al.[1988] are enforced on mixing length (stable conditions) and stratification (unstable conditions). For periodic solutions, the transport streamfunction and potential are defined by

with T the tidal period. (See Appendix II.) Finally, the non-advective horizontal exchanges , , etc. are all expressed in nonlinear, spatially-variable Laplacian forms. (See Lynch et al., 1995 for details).

We solve these equations subject to conventional horizontal boundary conditions. On wet boundaries, the free surface elevation (tidal + residual elevation) is specified. On landward boundaries, there is no normal flow. In either case, no tangential stress is exerted on the fluid. Similarly for T, S, and , nonadvective exchanges are set to zero on all boundaries. Boundary conditions on are as specified in Lynch and Naimie [1993]: on landward boundaries and across the Bay of Fundy, and natural conditions are enforced on the seaward boundary. The dual of these is enforced on the potential . (See Appendix II.)

Vertical boundary conditions are posed as follows. For the horizontal velocity, the atmospheric shear stress is specified at the surface. At the bottom we use a conventional quadratic slip condition relating shear stress to the bottom velocity. Atmospheric heat input is specified at the surface. At the bottom, heat flux is assumed negligible. Analogous no-flux conditions are imposed on S at surface and bottom. The law of the wall provides a specification for and at the bottom. At the free surface, no-flux conditions are enforced on these variables.

Throughout this study we use 21 unequally-spaced vertical nodes everywhere, with 1 meter resolution at surface and bottom. A smoothly graded vertical mesh is obtained with the transformation

wherein increases linearly with node number, from 0 at bottom to 1 at the free surface. The constant is set to give the desired boundary layer resolution. As in Lynch et al [1995a, b] and Naimie [1995], the bottommost node lies within the logarithmic bottom boundary layer, above the true bottom.

Temporal resolution is sufficient to resolve the sexto-diurnal tide.

The numerical implementation is described in Lynch and Werner [1991] and Lynch et al. [1995].

Procedure

To establish the basin-scale circulation for the two bimonthly periods under investigation, we first compute circulation fields on a mesh with broad geographic coverage (the ``G2S.5B'' mesh as depicted in Figure 3a), including Georges Bank and the Scotian Shelf. Seasonally invariant tidal (M2 only) and seasonally dependent residual elevations (as in Lynch and Naimie (1993) and Naimie et al (1994)) are prescribed at the horizontal open boundaries. At the free surface, the appropriate bimonthly climatological wind stress value from Naimie et al (1994) is specified. The model is initialized with the associated diagnostically computed barotropic pressure and velocity fields from Naimie et al (1994), along with their corresponding optimally estimated climatological temperature and salinity fields [Loder et al (1995)]. During the prognostic simulation, heat and salt are transported in tidal time with the surface temperature nudged toward the climatological mean and no net salt flux at the free surface. Consistent with the geographic scale of this calculation, river sources and net precipitation were ignored.

We examine tidally-averaged circulation and transport fields which were obtained after a spinup period of several days, sufficient to advectively correct local temperature and salinity anomalies associated with the climatological initial conditions, and to establish their intratidal variations. Tidal-time Lagrangian particle trajectories were obtained by Fourier decomposing the 3-D velocity field and storing the residual plus tidal constituents at all nodes. Fourth-order Runge-Kutta integration of individual trajectories was carried out with the reconstructed flow fields, using software provided by B. Blanton and F. Werner [Blanton 1992].

A refined coastal mesh (the ``CSTB.1A'' mesh as depicted in Figure 3b) is introduced to examine the coastal region with increased dynamical and topographic resolution. This mesh provides resolution of order 1 km in the shallow parts of Massachusetts and Cape Cod Bays, and grows to roughly 3 km in the deeper regions of Massachusetts Bay and to 5 km in the Gulf of Maine. The increased near-shore spatial resolution facilitates enhanced topographic realism (e.g. Jeffreys Ledge, Stellwagen Bank) relative to G2S.5B. The off-shore boundary of the CSTB.1A mesh is positioned intuitively to include the MCC as ``defined'' by the basin-scale computations. This boundary placement, however, is fundamentally problematic as we demonstrate below.

Forcing on the mesh was as follows. Initial and boundary conditions for the CSTB.1A simulations were interpolated from the G2S.5B solutions described above. Greater realism was added by a) replacing the nudging boundary condition on surface temperature with climatological heat flux values; and b) activating the river sources. The surface heat flux values in Table 1 are taken from Esbensen and Kushnir [1981], for the horizontal position immediately east of Cape Cod (). River source strengths (see also Table 1) are determined from a 1980s decadal average for the two bimonthly periods [U.S.G.S.ME, 1980-1989,U.S.G.S.MA, 1980-1989,C.W.S.CA, 1980-1989]. The river sources are placed at the mesh boundary nodes indicated in Figure 3b, and are distributed uniformly over the topmost element of the water column. River water is assumed to be devoid of salt; to have a temperature equal to the local climatological oceanic value; and to be neutral relative to the turbulence variables. Net precipitation was ignored, and the uniform seasonal wind stress values were unchanged from the G2S.5B simulations. All sources were constant in time and are summarized in Table 1.

  
Table 1: Forcing Parameters for CSTB.1A

Our analysis of the computed results for the CSTB.1A mesh is similar to that used for the gulf-wide simulations. The tidally-averaged circulation and transport fields are obtained after a nine-day spinup period, which allows for intratidal and short-term adjustment resulting from the differences in forcing for the various simulations.

Results

Gulf-Wide Circulation

The March-April and May-June gulf-wide circulation fields are displayed in Figures 4-6 and Figure 7, respectively. The expected cyclonic circulation in the Gulf of Maine is apparent in both seasons, as is a well defined but inadequately resolved coastal current. Within the confines of the gulf-scale cyclonic circulation, each of the three deep basins exhibits separate but interlinked cyclonic tendencies. The seasonal variations in horizontal and vertical detail of these circulation features have important influences on the MCC, making it evident that the MCC is intimately linked with the Gulf-wide circulation for both seasons.

March-April. In March-April the streamfunction (Figure 4a) reveals a combined recirculation of .125 Sv over Jordan and Georges Basin. Nested inside this is an inner gyre comprising an additional .125 Sv over Georges Basin. A separate .075 Sv cyclonic gyre exists over Wilkinson Basin. Encompassing these circulation features is a Gulf-wide cyclonic gyre which results largely from the .300 Sv of inflow from the Scotian Shelf entering the Gulf of Maine from the Northeast. The coastal current division into eastern and western segments is evident, with a prominent offshore meander at the Penobscot branch point. There is also a branch point at Cape Ann, with significant transport into Massachusetts Bay. Downstream at the SCOPEX branch point, .150 Sv departs the coast toward Georges Bank and .100 Sv continues along the coast toward Nantucket Shoals.

The barotropic pressure distribution (Figure 4b) is largely dynamically consistent with the circulation indicated by the streamfunction (Figure 4a). The most noteworthy large-scale structural differences between the constant elevation lines and streamlines occurs in the southeast part of the gulf, especially along the northern flank of Georges Bank (where tidal rectification (Lynch and Naimie, 1993) and baroclinic effects (Naimie et al, 1994) are known to be important).

The residual velocity patterns at depth (Figure 5) illustrate the importance of the baroclinic structure below the wind-mixed layer. The cyclonic gyres at great depth display the impact of bathymetry and slope water believed to cause the low pressure in the deep basins. Lagrangian trajectories of passive particles ``drogued'' at a depth of 60 m (Figure 6) generally confirm the Eulerian circulation pattern in the upper right panel of Figure 5 and provide information regarding the time-scales related to the various circulation features. For example, particles retained in the Bigelow gyre over Jordan and Georges Basins complete approximately half of the circuit around this feature in 60 days. Of particular interest in the context of the MCC are the particles which depart the coast via the Jordan Segment of the MCC, cross Wilkinson Basin, and are subsequently advected towards the exit segments of the MCC.

May-June. In May-June, the cyclonic Georges Basin gyre is stronger and more localized (Figure 7). The Jordan Basin gyre is significantly weaker and the Wilkinson Basin gyre has moved south toward the SCOPEX region. Like March-April, there is a large gulf-scale cyclonic circulation around the Gulf of Maine which is supplied by upstream conditions on the Scotian Shelf. However, the details of this circulation are different, with the May-June solution having significantly greater transport near the beginning of the Eastern Segment of the MCC. The MCC generally follows the coast past the Penobscot branch point (where there was a significant off-shore meander in March-April). In the western half of Massachusetts Bay, an anticyclonic gyre exists (note the streamline which splits the bay in figure 7) and the coastal current largely bypasses the bay after proceeding past Cape Ann. (In MA a significant portion of the MCC entered Massachusetts Bay here). Like the March-April MCC, there is a bifurcation in the MCC in the SCOPEX region, with similar transports toward Georges Bank and Nantucket Shoals.

The Coastal Current in Detail

As mentioned above, the Gulfwide solutions provided initial and boundary conditions for the CSTB.1A simulations. Of major significance is the residual sea level pattern along the open boundary, shown in figure 8 for both seasons. The overall pressure shift between seasons is the result of an arbitrary offshore elevation datum, and has no dynamical significance herein. However, there are important along-boundary pressure variations of order 5 cm which accompany major features of the Gulfwide circulation described above; and these have significant interseasonal differences.

In both seasons, the exit region pressure signal is similar, with a set-down of about 3cm across Nantucket Shoals. The continuing decrease in elevation along the boundary is associated with the SCOPEX circulation. In MJ, its ``center" has shifted southward and this is reflected in a local rearrangement of the low pressure pattern on that part of the boundary. The pressure variations across Wilkinson Basin are very different in the two seasons, with a local peak associated with the MJ offshore meander which is absent in MA. Upstream, the Penobscot meander is prominently displayed in MA as a high pressure bulge along that part of the boundary. Consistent with the Gulfwide discussion, this feature is significantly weaker in MJ. Over Jordan Basin there is a distinctive low pressure signal in MJ, absent or muted in MA, representing the intensification of the circulation around the perifery of this basin in MJ. The eastern, entrance portion of the boundary pressure is similar in both seasons, approximating a linear setup as the boundary cuts across the topography toward Digby Neck. In MJ the pressure rise is greater than in MA, reflecting the deeper low over eastern Jordan Basin and the stronger inflow visible in the circulation fields. In both seasons there is a local pressure anomaly as the boundary makes shore at the narrow tip of the Digby peninsula, where the topography provokes strong tidal rectification. Overall, the change from MA to MJ is one of deepening low pressure in the northeast part of Jordan Basin, and its westward propagation beyond Penobscot.

These barotropic pressure signals, combined with the initial conditions for T and S, contain essentially all of the information about the large-scale dynamics which is available to the CSTB.1A simulations. It is evident that the mesh boundary cuts across major, seasonally-modulated features of the circulation.

March-April. The detailed MA solution is shown in figure 9a and figure 9b. Relative to the Gulfwide calculation above, there are several interesting differences. The cyclonic flow around Grand Manan Basin, while similar to the Gulfwide solution has increased with more flow closer to the shore. Around the Penobscot branch point the 0 Sv streamline is closer to shore, while the .10 Sv streamline on the eastern side appears consistent with the Gulfwide placement. The western segment of the MCC has approximately twice as much flow, with the .20 Sv streamline looking very similar to the .10 Sv streamline in figure 4a. These differences are attributed to the more realistic local forcings used here (climatological river inflows and atmospheric heat flux). Overall, however, the general structure of the MCC as computed with G2S.5B remains essentially the same. In particular, the boundary conditions are successful in reproducing the complex exchanges between the deep Gulf circulation features and the MCC, including both entering and exiting flows across the CSTB.1A boundary.

In figures 10-12 we inspect the CSTB.1A solution in detail. The St. John outflow region shows a large anti-cyclonic cell, also depicted in Brooks, 1994, generated by the freshwater source. In figure 10, Eulerian velocity patterns at selected depths are shown for this area. The outflow bulges out in both directions along the coast. It then turns right and, after navigating around Grand Manan Island, joins the MCC. The spilling out of lighter fluid on top of heavier fluid causes an acceleration of the light fluid to the right and of the heavy fluid to the left. Therefore as we go down in the water column we see flow moving eastward. Close to the bottom a flow returning to the shore line can be seen, consistent with upwelling-favorable winds.

The Penobscot branch point is illustrated in greater detail in figure 11. The surface flow is influenced by both the northwesterly wind and the freshwater inputs, while at greater depth a nearshore return flow is evident. Return flow is especially strong near the two river sources. When this type of structure is vertically averaged, anti-cyclonic cells appear as shown in the bays and estuaries in figure 9b. In Penobscot Bay, the near-surface flow favors the eastern shore, also seen in Brooks 1994. The outflow continues out among the islands and connects to the MCC, with a portion joining the Jordan segment and exiting the model to the south, and a portion generating additional westward flow closer to shore. The Kennebec and Androscoggin river outflow enters the Gulf through a narrow bay which is dominated by the source flow. The river outflow bulges out, extending in both directions along the coast with most of the fluid turning right and adding to the coastal current. Seaward of the 60m contour, the meander at the Penobscot branch point dominates the entire water column. The Jordan segment exits and re-enters the CSTB.1A domain with no apparent lack of harmony between the imposed boundary conditions and the fine-scale circulation.

At the Cape Ann branch point, there is a significant turning of the MCC into Massachusetts Bay, as shown in Blumberg et al (1993). In figure 12, the Eulerian velocities at depth reveal that this effect prevails throughout the water column. The Merrimack river outflow shows little tendency to spread upstream, being immediately swept into the ambient coastal current and increasing its speed. The Bay circulation is generally cyclonic, with a high-speed exit around the tip of Cape Cod.

In figure 13 we illustrate Lagrangian drifter trajectories computed with the MA CSTB.1A solution. These generally confirm the Eulerian circulation patterns displayed at the 10m section in the previous figures, including the entry and exit points associated with the meander at the Penobscot branch point.

May-June. The MJ solution appears in figures 14 through 17. Again differences and similarities can be seen when comparing this solution (figure 14) to the large scale solution in figure 7. The differences noted above are similar to the differences here. Note the flow around Grand Manan Basin, the Penobscot branch point, and the western Gulf. The differences are again related to the more realistic local forcing included here. In particular, the Massachusetts Bay circulation shows the important effect of the Merrimack river outflow which was absent in the G2S.5B solution. Its inclusion here has removed the anticyclonic gyre in the western part of the Bay, and strengthened the Massachusetts branch of the MCC. As in MA, however, the larger scale structure of the MCC in MJ remains similar in both CSTB.1A and G2S.5B solutions.

The St. John river outflow region is depicted in figure 15. Similar to the MA season, the outflow spreads and moves to the right, and joins the MCC after circuiting Grand Manan Island. However, in this season the river discharge has decreased and the wind is southwesterly. These two influences combined do not push the flow offshore as far. The resulting 3-D circulation in the middle of the Bay of Fundy is extremely complex.

The meander at the Penobscot branch point is reduced in this season with most of the flow continuing along the coast and only a small amount farther offshore diverting into the Gulf (figure 16). The surface velocities show the effect of the southwesterly wind in the bays without rivers, while the estuaries are still influenced by the smaller freshwater sources. The Kennebec and Androscoggin outflow bulges out in both directions, as in MA. Seaward of the 60 m isobath, the MCC largely follows the along-coast topography throughout the water column.

In Massachusetts Bay (figure 17), the surface water along the coast is pushed in an eastward direction by the wind. However, further away from the coast the flow is dominated by the MCC and the Merrimack river. As in MA, the MCC branches into the Bay at Cape Ann, but remains somewhat offshore and its penetration of the southern portion of the Bay is significantly reduced.

Dynamical Influences on the Coastal Current

To investigate the role of various physical influences on the March-April circulation, simulations with selected forcing ``turned off'' were computed on the CSTB.1A mesh. By ``turning off'' a mechanism we discover its effect on the composite solution. For example if we turn off the wind: the heat flux, baroclinicity, barotropic boundary pressure, tide, initial conditions, and river sources remain active. The added influence of the wind then is the difference between the ``no wind" simulation and the full seasonal composite, figures 9-13. This strategy preserves most of the nonlinearities in the system, especially the mixing processes which are stratification- and motion-dependent. The exception to this procedure is the influence of tides, which we compute alone with all other forcing removed, in order to identify the isolated influence of barotropic tidal rectification.

Tide. This solution, displayed in figure 18, has only M2 tidal forcing. All other forcing is turned off including the residual pressure along the open boundary, and the initial conditions are uniform . Tidal resonance in the Bay of Fundy sets up a strong velocity gradient from east to west. Accordingly, tidal rectification on the coastline topography contributes significantly to the MCC in the eastern Gulf. The cyclonic flow around Grand Manan Basin is dominated by this process, and its influence extends decreasingly down the coast. The Penobscot meander is present in this simulation, steered only by the topography. However, it has been shifted westward and returns more sharply towards the shore relative to the composite MA solution. Along the western boundary of the Gulf this process contributes little. From Jeffreys Ledge south, the tidal rectification is largely offshore between the 60 and 100 m isobaths. In Massachusetts Bay there is little tidal rectification except in the vicinity of the exit point at the northern tip of Cape Cod. Generally, we expect barotropic tidal rectification to contribute a westward tendency in the eastern Gulf throughout the year, fixed to the topography, with the spatial pattern displayed here.

Wind. Removing the wind creates a small impact, primarily near shore as expected (figure 19). It is evident that the anti-cyclonic cells seen in the composite solution do not appear in the bays without sources, confirming their origin in wind-driven return flow. Recirculation still occurs in the estuaries, although it is weakened relative to the complete solution in figure 9a,b. The seaward transport of salt entrained in the upper layers evidently drives a portion of the recirculation in these features. The transport into southern Massachusetts Bay is slightly reduced by the cancellation of the Ekman transport. Generally, it appears that no important structures at the scale of the MCC originate in response to the local climatological mean wind.

Rivers. In this solution (figure 20) no sources have been included. It is a natural extension of the Gulfwide solution(figure 4) with increased resolution and a slightly different atmospheric heat flux. The river outflow regions show notable differences when compared to the composite(figure 9b). In general, the sources create a local high pressure anomaly near shore and thereby increase and steer the flow along shore. The flow around Cape Ann shows this clearly -- the amount of flow into Massachusetts Bay greatly decreases without the sources, related to the lack of a high pressure near the Merrimack steering the flow around the Cape and into the Bay. The river sources are the principal local buoyancy sources in MA and provide complex 3-D steering mechanisms nearshore. The detailed local response demands further scrutiny and finer resolution at the estuarine scale.

Baroclinicity. Figure 21 illustrates the impact of excluding all baroclinic effects -- including both the baroclinic pressure gradient and the impact of stratification on vertical mixing. Atmospheric heat flux is removed. River outflows are included, but have the same salinity and temperature as the ambient fluid, which is held uniform. All other forcing is active, including the barotropic boundary pressure.

Relative to the complete solution (figure 9a, b), there are two principal effects: a) the coastal current has been shifted offshore; and b) the exchanges across the boundary have been generally rearranged. The eastern MCC segment appears similar to the full MA solution, although shifted offshore; tidal rectification and the barotropic signature of the Gulf-wide circulation are important here. At the Penobscot branch point, the complex balance between the barotropic boundary pressure and the baroclinicity, which was successfully achieved in the composite run (figure 9a, b), is upset and a disorganized exchange between Gulf and MCC results. This is amplified downstream. An exaggerated coastal current reenters the mesh north of Wilkinson Basin and generally turns south with little or no flow returning to the coast. As a result, the coastal region is generally quiescent in the western Gulf, and the apparent MCC is well offshore from its ``correct" position in figure 9aand b.

Barotropic Boundary Pressure. Finally, we investigate the importance of the barotropic boundary pressure (figure 22). In this simulation the residual elevation boundary conditions were set to zero, while all other influences were retained. Like the previous case, this creates a fatal mismatch between the MCC and the Gulf. However, it also illustrates that the nearshore features of the MCC remain mostly intact.

The eastern MCC segment looks very similar to the composite (figure 9a, b) within roughly the 100 m isobath, beyond which it loses validity. The meander at the Penobscot branch point is present, but is incorrectly reflected from the boundary, a classic mathematical outcome.

In the western Gulf, the flow beyond the 100m isobath is seriously misdirected. There are false exchanges between Wilkinson Basin and the MCC, and a cyclonic gyre at the exit region due to the clamped cross-shelf boundary. The nearshore portion of the western MCC is realistic, as is the circulation in Massachusetts Bay and in the vicinity of Cape Ann. However, the waters entering the Bay appear to originate at least partly in the false offshore gyre(s) to the east.

In the large, these errors appear to be offsetting the errors in the previous (no baroclinicity) calculation: moving the MCC shoreward and rerouting the exchange pathways with the Gulf. It is apparent from these two simulations that baroclinicity and barotropic boundary pressure must be carefully balanced if a successful dynamic composite is to emerge.

Discussion

The solutions reported here show many realistic large-scale features of the Gulf of Maine circulation. In addition, the principal observed features of the MCC -- the segments and branch points -- are evident. While there are many aspects which demand further scrutiny, we conclude that these solutions are dynamically representative and, within limits, a valid testing ground for hypotheses about how the MCC works and how to model it.

The dynamical blend of local influences in the MCC is complex and spatially varying. Tidal rectification plus barotropic inflow from the Scotian Shelf are important in the Eastern gulf. Wind driven return flow is a prominent nearshore feature. Local baroclinicity has the effect of moving the barotropic influences shoreward. The barotropic pressure signature of the Gulf-wide circulation is critical beyond 100m and in establishing the proper exchanges with the Gulf, and in establishing the the overall MCC structure.

The Gulfwide solutions show important seasonal variability which directly impacts the MCC. Limited-area analyses of the coastal circulation that ignore this fact will not be realistic. In particular, the interplay among barotropic and baroclinic features seaward of the MCC must be carefully balanced in any representation of the large-scale influence. The branching structure of the MCC involves significant cross-shelf transport in both directions, with seasonal variability. There is, therefore, no easy way to determine a priori any simple coupling rules, or even where to draw a boundary for a limited-area analysis. All of this suggests that Gulfwide analysis with proper resolution in the MCC area is the only general way to avoid a mismatch between local and remote forcing of the MCC. This can be done seamlessly, with a single model, or by carefully nesting models.

In this study we have demonstrated successful use of nested models, with boundary conditions from the large, coarser model driving the local, refined model without artifact. This appears to be a workable general strategy for the climatological circulation. As shown here, the detailed barotropic pressure distribution along the interface boundary, combined with the accompanying mass field, was a suitable surrogate for the Gulfwide influence. It remains to be seen how successful such a strategy will be when one begins to study variability in the MCC features. It is possible that detailed variability in the MCC domain could be studied with the boundaries clamped at climatological values, on the argument that these evolve more slowly; a further refinement would be to radiate departures from the climatology along the boundary. We look forward to studies along these lines, and of course to full-Gulf simulation with a single model which resolves the MCC.

Acknowledgements

John Loder and Peter Smith provided the climatological wind and fields; David Greenberg provided the original finite element bathymetry and tidal boundary conditions; and Francisco Werner and Brian Blanton provided the Lagrangian particle tracking software. Their continuing collegial support and interest has been essential and is greatly appreciated. We also thank Wendell Brown for several important insights relative to the Gulf and coastal circulation. Financial support from the Gulf of Maine Regional Marine Research Program and the New Hampshire Sea Grant College Program is gratefully acknowledged.

Appendix I: Source terms

We illustrate the derivation of the source term configuration in the nonconservative form of the transport equations. For a Boussinesq fluid, we have conservation of volume:

and conservation of a representative dissolved substance -- e.g. salt:

Differentiating the convective term by parts gives

Consolidating the material derivative , and invoking (I.1) leads directly to the nonconservative form used herein:

The application to the momentum equation follows analogously.

Appendix II: Streamfunction and Potential

We briefly elaborate the definition of the stream- and potential functions used herein, and their relation to the tidally- averaged velocity field. The vertically integrated continuity equation is the starting point:

The average of this equation over time is, for periodic conditions (or for very long times),

where T is the period of the motion. We define the transport vector :

and the vertically integrated source strength :

in terms of which (II.2) becomes

is then expressed in terms of the two scalar functions and :

The divergence and curl of (II.6) then lead respectively to

Substitution of the definitions (II.3, II.4) produces

which are as recited in the text. These equations allow computation of and from the velocity solution and its sources.

On landward boundaries, we set as in Lynch and Naimie [1993]. (The cut across the Bay of Fundy is treated as impermeable for this calculation.) The normal component of (II.6) then reduces to

In these calculations, river discharges are treated as sources immediately adjacent to land boundaries. Hence there and this condition on is the natural or homogeneous Neuman condition:

On seaward boundaries we enforce . The tangential () component of (II.6) then gives

which is the natural homogeneous boundary condition for as described in Lynch and Naimie [1993]. These boundary conditions guarantee everywhere in the absence of sources.

References

Bigelow, 1927

Bigelow, H.B., ``Physical Oceanography of the Gulf of Maine'', Bull. U.S. Bur. Fish., 40, 511-1027, 1927.

Beardsley et al, 1993

Beardsley, R., R. Limeburner, P. Cornillon, A. Durbin, E. Durbin, R. Kenney, H. Winn, K. Wishar, M. Macaulay, ``SCOPEX, a multidisciplinary study of right whale - ecosystem interactions'', U.S. GLOBEC News, 3 (May 1993).

Bisagni et al, 1994

Bisagni, J.J., D.J. Gifford, C.M. Rushman, ``The spatial and temporal distribution of the Maine coastal current during 1982'', Continental Shelf Research, (submitted 1994).

Blanton, 1992

Blanton, B.O., DROG3D.f - User's Manual for 3-Dimensional Drogue Tracking on a Finite Element Grid with Linear Finite Elements. Skidaway Institute of Oceanography, Savannah, Georgia, U.S.A., July 1992.

Blumberg et al., 1992

Blumberg, A. F., B. Galperin, and D. J. O'Connor, ``Modeling vertical structure of open-channel flows'', ASCE, J. Hydraulic Engg., 118, 1119--1134, 1992.

Blumberg et al, 1993

Blumberg, A.F., R.P. Signell, H.L. Jenter, ``Modeling transport processes in the coastal ocean'', J. Marine Env. Engg., 1, 31-52 (1993).

Brooks, 1985

Brooks, D.A., ``The vernal circulation in the Gulf of Maine", J. Geophys. Resch. 90, C5, 4687-4705, 1985.

Brooks, 1994

Brooks, D.A., ``A model study of the buoyancy-driven circulation in the Gulf of Maine", J. Phys. Oceanogr. 24, 1994.

Brooks and Townsend, 1989

Brooks, D.A. and D.W. Townsend, ``Variability of the coastal current and nutrient pathways in the Gulf of Maine", J. Mar. Res. 47, 303-321, 1989.

Brown and Irish, 1992

Brown, W.S. and J.D. Irish, ``The annual evolution of geostrophic flow in the Gulf of Maine: 1986-1987", J. Phys. Oceanogr. 22, 445-473, 1992.

Brown and Irish, 1993

Brown, W.S. and J.D. Irish, ``The annual variation of water mass structure in the Gulf of Maine: 1986-1987", J. Marine Resch. 51, 53-107, 1993.

Bumpus and Lauzier, 1965

Bumpus, D.F. and L.M. Lauzier, ``Surface circulation on the continental shelf of eastern North America between Newfoundland and Florida'', Am. Geograph. Soc., Serial Atlas of the Marine Environment, Folio 7, 1965.

Chen, 1992

Chen, C, ``Variability of currents in Great South Channel and over Georges Bank: Observation and Modeling", PhD. Thesis, Woods Hole Oceanographic Institution, June 1992, 283 pp. (Report WHOI-92-20).

Chen et al, 1995

Chen, C, R.C. Beardlsey, R. Limeburner, ``Variability of currents in late spring in the northern Great South Channel", Continental Shelf Research 4/5, 451-473, 1995.

Esbensen and Kushnir, 1981

Esbensen, S.K. and Y. Kushnir. The Heat Budget of the Global Ocean: An Atlas Based on Estimates from Surface Marine Observations. Technical Report 29, Climatic Research Institute and Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331, December 1981.

Franks and Anderson, 1992a

Franks, P.J.S. and D.M. Anderson, ``Along shore transport of a toxic phytoplankton bloom in a buoyancy current: Alexandrium tamarense in the Gulf of Maine", Marine Biology 112, 153-164, 1992a.

Franks and Anderson, 1992b

Franks, P.J.S. and D.M. Anderson, ``Toxic phytoplankton blooms in the southwestern Gulf of Maine: testing hypotheses of physical control using historical data", Marine Biology 112, 165-174, 1992b.

Galperin et al., 1988

Galperin, B., L.H. Kantha, S. Hassid, and A. Rosati, ``A quasi-equilibrium turbulent energy model for geophysical flows'', J. Atmos. Sci., 45, 55--62, 1988.

Geyer et al, 1992

Geyer, W.R., G.B. Gardner, W.S. Brown, J. Irish, B. Butman, T. Loder, R.P. Signell, ``Physical oceanographic investigation of Massachusetts and Cape Cod Bays" Massachusetts Bays Program Report MBP-92-03, 497 pp (October 1992).

Gill, 1982

Gill, A.E., Atmosphere-Ocean Dynamics, Academic Press, 599--603, 1982.

Hopkins and Garfield, 1979

Hopkins, T.S. and N. Garfield III, ``Gulf of Maine intermediate water'', J. Mar. Resch., 37, 1, 103-139, 1979.

Loder et al, 1995

Loder, J.W., G. Han, C.G. Hannah, D.A. Greenberg and P.C. Smith ``Hydrography and baroclinic circulation in the Scotian Shelf Region: winter vs summer", Canadian Journal of Fisheries and Aquatic Sciences Supplement, submitted, 1995.

Lynch, 1982

Lynch, D.R., ``Unified Approach to Simulation on Deforming Elements, with Application to Phase Change," J. Comput. Phys. 47, 3, 387-411 (1982).

Lynch, 1986

Lynch, D.R., ``Basic Hydrodynamic Equations for Lakes'', Physics-Based Modeling of Lakes, Reservoirs, and Impoundments, Chapter 2. W.G. Gray, ed. ASCE, New York 1986.

Lynch and Naimie, 1993

Lynch, D.R., and C.E. Naimie, ``The M2 tide and its residual on the outer banks of the Gulf of Maine'', J. Phys. Oceanogr., 23, 2222-2253, 1993.

Lynch and Werner, 1991

Lynch, D.R., and F.E. Werner, ``Three-dimensional hydrodynamics on finite elements. Part II: Non-linear time-stepping model'', Intl. J. Numer. Meths. Fluids, 12, 507--533, 1991.

Lynch et al., 1995a

Lynch, D.R., J.T.C. Ip, C.E. Naimie, F.E. Werner, ``Convergence studies of tidally rectified circulation on Georges Bank", Quantitative Skill Assessment for Coastal Ocean Models, D.R. Lynch and A.M. Davies, eds. American Geophysical Union, Coastal and Estuarine Studies Volume 47, 1995.

Lynch et al., 1995b

Lynch, D.R., J.T.C. Ip, C.E. Naimie, and F.E. Werner, ``Comprehensive coastal circulation model with application to the Gulf of Maine'', Continental Shelf Research, in press 1995.

Mellor and Yamada, 1982

Mellor, G. L., and T. Yamada, ``Development of a turbulence closure model for geophysical fluid problems'', Reviews of Geophys. Space Phys., 20, 851--875, 1982.

Naimie, 1995

Naimie, C.E., ``On the modeling of the seasonal variation of the three-dimensional circulation near Georges Bank'', PhD Thesis, Dartmouth College, Hanover, New Hampshire, 1995.

Naimie et al., 1994

Naimie, C.E., J.W. Loder, and D.R. Lynch, ``Seasonal variation of the 3-D residual circulation on Georges Bank'', J. Geophys. Res., 99, C8, 15967-15989, 1994.

Signell et al., 1994

Signell, R.P., H.L. Jenter, A.F. Blumberg, ``Circulation hindcasting in Massachusetts Bay'', Gulf of Maine Circulation Modeling: Workshop Proceedings, E. Braasch, ed. Regional Association for Research on the Gulf of Maine, Report no. 94-1, pp 68-77. Dartmouth College, Hanover NH, 1994.

Pettigrew, 1994

Pettigrew, N.R., ``The observational basis for subtidal circulation in the Gulf of Maine'', Gulf of Maine Circulation Modeling: Workshop Proceedings, E. Braasch, ed. Regional Association for Research on the Gulf of Maine, Report no. 94-1, pp 3-19. Dartmouth College, Hanover NH, 1994.

Smagorinsky, 1963

Smagorinsky, J., ``General circulation experiments with the primitive equations I. The basic experiment'', Monthly Weather Review, 91, 99--164, 1963. (1993)

Townsend, 1991

Townsend, D.W., ``Influences of oceanographic processes on the biological productivity of the Gulf of Maine", Reviews in Aquatic Sciences 5, 3-4, 211-230, 1991.

Townsend et al, 1987

Townsend, D.W., J.P. Christensen, D.K. Stevenson, J.J. Graham, S.B. Chenoweth, ``The importance of a plume of tidally-mixed water to the biological oceanography of the Gulf of Maine", J. Marine Research 45, 699, 1987.

U.S.G.S.ME, 1980-1989

United States Geological Survey, Water Resources Division. Water Resources Data - Maine Water Year 1980, through ... 1989. Technical Reports ME-80-1 through ME-89-1, 1980-1989.

U.S.G.S.MA, 1980-1989

United States Geological Survey, Water Resources Division. Water Resources Data - Massachusetts and Rhode Island Water Year 1980, through ... 1989. Technical Reports MA-RI-80-1 through MA-RI-89-1, 1980-1989.

C.W.S.CA, 1980-1989

Water Resources Branch, Water Survey of Canada. Surface Water Data - Atlantic Provinces 1980 through .. 1989. Technical Report EN 36-405/1980 through 1989, 1980-1989.

...boundaries.

In the Gulf-wide simulations, T and S were clamped at the climatological values on wet boundaries.

...variables.

The surface conditions on and represent a departure from that used in Lynch et al. 1995; it has no practical consequence herein.

...19).

Here and throughout it is important to keep in mind that the boundary pressure signal, when ``on", incorporates the full-physics interaction of local and Gulfwide influences. Turning off the local wind stress does not affect the total barotropic pressure enforced on the boundary.