Subtidal flow structure at the turning region of a wide outflow plume
Arnoldo Valle-Levinson*
Civil and Coastal Engineering Department
University of Florida
365 Weil Hall
Gainesville FL 32611
arnoldo@ufl.edu
Tel. 353-392-9537 ext. 1479
*corresponding author
Kris Holderied
NOAA Kasitsna Bay Laboratory, Homer Office
2181 Kachemak Drive
Homer, Alaska 99603
Chunyan Li
Coastal Studies Institute
Louisiana State University
Baton Rouge, LA
Robert J. Chant
Institute of Marine and Coastal Sciences
Rutgers University
New Brunswick, NJ 08904
Abstract
A series of underway current velocity profiles and near-surface temperature and salinity
measurements were combined with temperature and salinity profiles to characterize the
subtidal flow structure at the turning region of a wide plume, the Chesapeake Bay
outflow plume. In this context, “wide” refers to the ratio of lateral plume expansion to
internal radius of deformation being greater than one. Observations were obtained in
September and November of 1996 and in February and May of 1997 with the idea of
capturing the variability in forcing conditions typically associated with these seasons.
However, regional precipitation patterns yielded similar buoyancy forcing conditions for
the 4 surveys and among the wettest years on record. This buoyancy forcing produced a
well-delineated outflow plume that separated from the coast on its way out the estuary.
The plume separation acted in conjunction with frictional effects to delineate an inshore
front, in addition to the customarily described offshore front. The outflow plume was
markedly constrained by the Chesapeake Channel, which was also the main conduit of
shelf waters toward the estuary. The bathymetric influence was also evident in the
surface salinity field, the mean flows and the volume fluxes. The offshore extent of the
plume was found between the scale predicted by geostrophic dynamics (internal Rossby
radius) and that predicted by cyclostrophic dynamics. Such offshore extent was most
likely linked to the plume interactions with the bathymetrically steered up-estuary flow.
This was corroborated by an analytical solution that explored the dynamical balance
among pressure gradient, Coriolis accelerations and friction. In addition to being
influenced by bathymetry, the Chesapeake Bay outflow plume was modified by local and
remote effects related to atmospheric forcing.
1
Introduction
The study of buoyant outflow plumes has produced an extensive body of
literature. Many studies have used numerical approaches (e.g. Chao, 1988; Kourafalou et
al., 1996; Oey and Mellor, 1993; Ruddick et al., 1995; Garvine, 2001) and others have
used observational approaches (Boicourt, 1981; Münchow and Garvine, 1993; Simpson
and Souza, 1995; O’Donnell et al., 1998) and laboratory experiments (e.g. Stern et al.,
1982; Whitehead and Chapman, 1986; Avicola and Huq, 2002; Lentz and Helfrich,
2002). There is an inherent difficulty in studying outflow plumes observationally
because of their relatively large extensions, high horizontal and vertical gradients, and
very large temporal variability (e.g. Hickey et al., 2005; Fong et al., 1997). Outflow
plumes tend to be characterized by an inertial, or turning, region where the buoyant
outflow forms a bulge before it turns into a coastal current that propagates downstream in
the Kelvin wave sense (Garvine, 1995; Chao and Boicourt, 1986). Several modeling
studies have characterized the inertial bulge of the plume, but few observational efforts
have concentrated on this region. The main objective of this study is to characterize the
spatial structure of the Chesapeake Bay outflow plume at its turning region and under
different forcing conditions of winds, tides and river discharge. This objective was
addressed with underway measurements of current velocity profiles and surface
hydrography, combined with hydrographic profiles recorded at different times of the
year. Because bathymetry plays a crucial role in shaping exchange flows at an estuarine
entrance (e.g. Wong, 1994), it was hypothesized that bathymetry also influenced the
lateral structure of the outflow plume. It was found that the main channel that connects
2
Chesapeake Bay with the adjacent inner shelf indeed constrains the expansion of the
plume and contains most of its outflow volume.
The Chesapeake Bay Outflow Plume Experiment (COPE) investigated several
aspects of the buoyant outflow from 1996 to 1998 using state-of-the-art in-situ and
remote sensors. This experiment produced the first synoptic maps of surface salinity
(Miller et al., 1998) and radar-derived surface tidal currents (Marmorino et al, 1999; Shay
et al., 2001) in the outflow region. The study also produced an analysis of the Chesapeake
Bay plume response to upwelling winds (Hallock and Marmorino, 2002) and
distributions of tidal elevation and currents (Hallock et al., 2003). Observations with real
aperture radar and sideways pointing current profilers showed that the offshore edge of
the plume was linked to the offshore limit of the Chesapeake Channel and that another
front marked the onshore edge of the plume (Sletten et al., 1999; Marmorino and Trump,
2004). In addition, in-situ observations depicted the gravity-current aspects associated
with the plume (Marmorino and Trump, 2000). The above studies have revealed
valuable characteristics of the plume but none has investigated its overall spatial structure
(both horizontal and vertical) with enough horizontal resolution (< 500 m), which is the
topic of this study.
Study Area
The Chesapeake Bay is the largest estuary of the United States, with a length of
~300 km. The lower estuary has typical widths of ~20-30 km (Fig. 1), which are at least
twice the ~5-10 km dimension of the internal radius of deformation (Valle-Levinson and
Lwiza, 1997). The lower bay bathymetry is characterized by channels and shoals (Fig.
3
1). It features a relatively wide (~4 km) and deep (maximum depth of 30 m) Chesapeake
Channel that curves to the south around Cape Henry, the southern cape at the bay
entrance. This channel is the main conduit of oceanic waters to the estuary (ValleLevinson et al. 1998) and its delineation is appreciable in the inner shelf for ~7 km to the
south of Cape Henry (Fig.1). Offshore of the bay entrance and outside Chesapeake
Channel, i.e., in the area influenced by the outflow plume, the bathymetry slopes gently
downward.
The Chesapeake Bay is influenced by a mean annual river discharge of ~2,500
m3/s derived from various tributaries (Goodrich, 1988). A 30-year record shows that
mean daily river discharge into the bay is greatest in March and April and reaches a
minimum in August (Fig. 2). As a result, the plume outflow is expected to be strongest
and have the lowest salinities in the April-May period (roughly one month after the river
discharge peak). Similarly, the plume is expected to be weakest and have the highest
salinities in September-November. The low-discharge period is coincident with
increased wind-induced vertical mixing associated with cold air outbreaks and extratropical storms. However, tropical and extra-tropical storms may produce anomalously
high runoff during seasons of normally low runoff (Fig. 2) and cause extremely reduced
salinities throughout the bay. The combination of wind forcing and river discharge
typically results in strongly stratified (top to bottom differences in salinity of order 10)
conditions in April-May, and nearly homogeneous (maximum top to bottom salinity
difference of less than 2) conditions in October-November (Valle-Levinson and Lwiza,
1997). The anomalously high precipitation in the fall of 1996 meant that there was less
variation in buoyancy forcing than expected between our fall and spring surveys.
4
The Chesapeake Bay is also forced by seasonal wind patterns (Paraso and ValleLevinson, 1996). In the lower bay, northeasterly and northwesterly winds dominate from
late summer to early spring, while southwesterly winds dominate during the summer.
The most energetic wind events are usually northeasterly or northwesterly during late fall
and winter, although southwesterly winds can occasionally be very energetic. Owing to
the orientation of the bay entrance, northeasterly and southwesterly winds cause the
greatest effects on the subtidal sea level and current variability in the area (ValleLevinson, 1995).
Tidal forcing affecting the lower bay is predominantly semidiurnal (Browne and
Fisher, 1988). The interaction among the three semidiurnal tidal constituents (M2, N2 and
S2) generates fortnightly and monthly variability in the tidal currents. Owing to the
elliptical moon orbit, the N2 constituent dominates over the S2 in this part of the world.
This causes a marked asymmetry between consecutive spring (or neap) tides, which
results in a spring (or neap) tide of perigee and a spring (or neap) tide of apogee during
one month. During spring tides, the currents in the lower bay may exceed 1 m/s,
resulting in reduced stratification and weaker subtidal flows than during neap tides
(Valle-Levinson, 1995). Thus, bathymetric variations, freshwater discharge, wind
velocity, and tidal forcing are expected to influence the flow and water density at the
Chesapeake Bay entrance and in its adjacent coastal ocean. This study was carried out
through ship surveys at different times of the year in an attempt to assess the influence of
those forcing mechanisms on the turning region of the Chesapeake Bay outflow plume.
Data Collection and Processing
5
A total of four surveys were conducted onboard NOAA’s ship Ferrel with the
purpose of collecting data on the flow and density fields in the turning region of the
Chesapeake Bay outflow plume. In each survey, three ~16-17 km long transects
(Transects 1, 2 and 3 in Fig. 1) were sampled during the periods of September 23-26,
1996, November 12-15, 1996 and May 12-15, 1997. In the period February 18-21, 1997
two transects (Transects 1 and 3 in Fig. 1), instead of three, were sampled because wind
conditions and sea state hindered data collection during the first day of scheduled
sampling. In May 1997, Transect 2 had a different orientation than in the other surveys
in order to coordinate data sets of that survey with those of COPE II experiments (e.g.
Sletten et al., 1999; Hallock and Marmorino, 2002).
At each transect, underway measurements of current velocity profiles and of nearsurface temperature and salinity were obtained repeatedly for at least 24 hours of cruising
at speeds of ~2.5 m/s. Transect repetitions had to be delayed or interrupted periodically
because of heavy ship traffic through the Chesapeake Channel. Despite those difficulties,
each transect was occupied for at least 10 times during the sampling period.
Complementing the underway measurements were profiles of temperature and salinity
obtained typically at the ends of each transect repetition and roughly in the middle or at
the deepest point of the transect.
Underway current velocity profiles were obtained with a Broadband RD
Instruments 600-kHz acoustic Doppler current profiler (ADCP) mounted on a ~1.4 mlong catamaran. The catamaran was towed mid-ship with a three-point bridle so the
catamaran traveled off the starboard side in water undisturbed by the ship’s wake. The
ADCP pointed downward and collected current and bottom track velocities. The
6
velocities were recorded every 4 seconds in 0.5 m bins and averaged into 30 second
ensembles. This represented a spatial resolution of ~75 m in the horizontal. The first
ADCP bin was centered at ~2 m for every survey. Navigation data were obtained with a
Trimble 2000 Differential Global Positioning System (DGPS) and were used for ADCP
compass calibration and current velocity data correction as in Joyce (1989). This data set
corresponds to a total of 11 experiments, each spanning at least 24 hours, or more than
110 transect realizations. As such, this is the most comprehensive data set available for
current velocity profiles with high horizontal resolution in the turning region of the
Chesapeake Bay outflow plume.
The values of current velocity obtained at each transect repetition were rotated to
their axis of maximum variance. Then they were interpolated, for each component, onto
a uniform grid with horizontal and vertical resolutions of 200 m and 0.5 m, respectively.
The time series of current velocity components for each separate cruise was least-squares
fitted to a periodic function with semidiurnal (period of 12.42 hrs) and diurnal (period of
23.93 hrs) constituents (e.g. Valle-Levinson et al., 1998). This procedure yielded five
parameters related to the flow at the entrance to Chesapeake Bay: the subtidal flow
during the period of observation, the amplitude and phase of the semidiurnal constituent,
and the amplitude and phase of the diurnal constituent. At the bay entrance (Transect 1),
the least-squares fit explained an average of 92% of the variability observed in the
principal-axis component of the flow at every grid point. The fit yielded root-meansquared errors between the fit and the observations that in general remained below 0.15
m/s. The percent of variability explained by the fits (or goodness of fit) decreased from
Transect 1 to Transect 2 and 3.
7
Underway near-surface (~1.5 m depth) temperature and salinity values were
obtained with a SeaBird SBE 21 thermosalinograph. The instrument was connected to
the flow-through seawater system of the Ferrel. Temperature and salinity data were
combined with the DGPS signal and recorded every 10 seconds, yielding a spatial
resolution of ~25 m. These data were used to construct profiles of mean surface salinity
along each transect. Mean surface salinities were used to characterize the hydrography of
the outflow plume at each transect sampled.
Profiles of temperature and salinity were obtained at fixed stations of each
transect with a conductivity-temperature-depth (CTD) recorder. An Applied
Microsystems EMP-2000 CTD was used in the 1996 surveys and a Seabird SBE25 was
used in the 1997 surveys. CTD use was dictated by instrument availability. During the
four surveys, profiles of temperature and salinity were customarily collected at each end
of the transect repetition and in the middle or at the deepest part of the transect. This
approach was adopted to best characterize the hydrography data without compromising
the quality of the towed ADCP data, because the ADCP data collection deteriorates every
time the ship stops. The main purpose of the CTD data collection was to help discern the
vertical structure of the plume.
Forcing Agents - Ancillary data.
Ancillary data were used to characterize the forcing at the lower Chesapeake Bay
and outflow plume during the survey periods. Ancillary data consisted of river discharge
(Fig.2), wind velocity (Fig. 3) and subtidal sea level variability (Fig. 3). River discharge
data were obtained from the United States Geological Survey National Water Information
8
System (waterdata.usgs.gov/nwis/discharge). Daily data were retrieved for the
Susquehanna River at Conowingo MD (01578310), for the Potomac River near
Washington DC at Little Falls Pump Station (01646500), and for the James River at
Cartersville, VA (02035000). The river discharge values portrayed in Figure 2 represent
the combination of those three rivers, which account for ~82% of the river input into the
bay, for the common period 1967-1997. Hourly wind velocity and sea level observations
were obtained from NOAA’s Chesapeake Bay Bridge Tunnel station (8638863). This
was the closest station to the sampling region with data available during the study period.
The surveys were conducted at times of the year (vertical arrows on Fig. 2) to
capture the expected seasonal variability in river discharge and wind conditions. Weak
river discharge was expected in September on the basis of daily averages across the year
from the 30-year record (Fig. 2). Strong wind forcing was expected in November and
February, and strong freshwater influence was anticipated in May (Fig. 2). However,
1996 was the wettest year on record for the Chesapeake Bay (black continuous line on
Fig. 2), with daily discharge maxima records established several times that year. The
September and November surveys actually took place during anomalously high river
discharges for those months (>3000 m3/s) and after discharge peaks >10,000 m3/s (Fig.
2). The observations in February 1997 and May 1997 occurred during river discharges
close to their respective monthly means and to the annual mean of 2500 m3/s (Fig. 2).
Because of this sustained buoyancy forcing, a well-defined outflow plume was identified
in every survey. The plume itself was noticeably influenced by tides and winds.
The September 1996 survey took place two days before and during spring tides,
with variable winds (southwesterly to northwesterly) and subtidal sea level (Fig. 3a). The
9
November 1996 survey was carried out following spring tides with northwesterly and
northeasterly winds that kept subtidal sea level down (by driving water out of the bay),
but allowed it to set-up during sampling of Transect 1 (Fig. 3b). The February 1997
survey took place at the transition from neap to spring tides and had southwesterly,
northeasterly and southeasterly winds that first caused weak set-down and then weak setup of the subtidal sea level (Fig. 3c). Finally, the May 1997 survey was conducted during
the three days leading to neap tides under variable winds. Winds caused sea level setdown followed by set-up in Transect 1 sampling and weak subtidal sea level oscillations
during sampling of the other 2 transects (Fig. 3d). The response time of the flow to wind
forcing from the northeast and southwest in the lower bay is less than 10 hours.
Northeasterly winds cause unidirectional, laterally varying exchange flows at the bay
entrance (Valle-Levinson et al., 2001). Northwesterly winds cause the greatest flushing
of water out of the bay and southwesterly winds induce the strongest bidirectional
(vertically varying) exchange flows (Valle-Levinson et al., 2001). The variability in
these forcing agents will be discussed in the context of similarities and differences in the
subtidal flows observed at each transect.
Data Description
The description of the data set derived from these surveys begins with the
distributions of mean surface hydrography along each transect. It continues with the
portrayal of mean vertical profiles of salinity at different locations along the transects. It
then presents survey-to-survey similarities and differences exhibited by the subtidal flow
at each transect sampled. Throughout these descriptions “downstream” refers to the
10
preferred direction of coastal current produced by the plume (Kelvin-wave sense) and
“upstream” indicates toward the estuary’s mouth.
Mean Surface Salinity
In the 3 transects sampled, the lowest overall salinity should have been observed
at Transect 1, which was closest to the source of fresh water. This was clearly the case in
May 1997, but not in the other surveys (Fig. 4) because of dissimilar atmospheric
influences during sampling of different transects. For instance, the streamwise salinity
gradients in May 1997 (Fig. 4d) were produced by wind-induced advection of high
salinity water toward the bay entrance during Transect 3 sampling. Overall, for all
transects, the lowest salinities were observed immediately off Cape Henry in Transect 1,
i.e., right against the coast (distances <500 m in Fig. 4). As the plume moved
downstream it seemed to have separated from the coast because the lowest salinity of
Transects 2 and 3 was typically found at distances >1 km (Fig. 4). This location
corresponded to that of the Chesapeake Channel and suggested that, downstream of the
point of separation at Cape Henry, the core of the plume was largely constrained by the
channel.
The plume separation from shore was also observed in the offshore, or
streamnormal, gradients of the mean surface salinity ∂S/∂n, where n is the streamnormal
direction. The distributions of ∂S/∂n showed portions with negative values at distances
<6-8 km on Transects 2 and 3 (Fig. 4). This indicated that salinity decreased offshore at
those transects and that the lowest salinities were observed detached from the coast. On
Transect 1, at the bay entrance, the gradient was weak or positive near Cape Henry as the
11
lowest salinity was found against the coast. These distributions around the turning region
of the Chesapeake Bay outflow were consistent with observations in Delaware Bay
(Sanders and Garvine, 1996). The offshore hydrographic edge of the plume could be
identified as the location where the gradient decreased markedly, after having attained
high values. Such location was somewhat ambiguous in Figure 4 and is plausible to be
found between 10 and 14 km. The offshore edge of the plume as suggested by ∂S/∂n was
less ambiguous in November for transects 2 and 3 (~12 km), in February for transect 3
(~13.5 km) and in May for transect 3 (~13 km). This edge could have been related to the
internal radius of deformation Ri, which equals (g’ H)½ / f, where g’ is the reduced gravity
(in m/s2), H is the outflow plume depth (in m) and f is the Coriolis parameter (8.8×10-5 s-1
for the Chesapeake Bay entrance). To compare Ri to the observed location of the plume’s
edge, g’ and H were derived from mean salinity profiles.
Mean Salinity profiles
Mean salinity profiles are only shown for February 1997, when the lowest salinity
of the four surveys was observed. The vertical patterns remained consistent from survey
to survey when comparing transect to transect and location to location. The mean salinity
profiles at the bay entrance (Transect 1) showed increasing salinity away from Cape
Henry (Fig. 5), consistent with the surface salinity distributions. The greatest range of
surface to bottom values was observed in Chesapeake Channel, the deepest location
sampled. Downstream of the bay entrance, the lowest salinity in Transects 2 and 3 was
observed in the channel, away from the coast (Transect 2 not available in February as
portrayed in Fig. 5). This location of the lowest salinity was consistent with the mean
12
surface distributions and also indicated the separation of the plume from the coast.
Otherwise the lowest salinity should have been against the coast. The vertical gradients
of the salinity profiles showed a well-defined structure associated with the outflow plume
and suggested plume depths H of 5-10 m. Typical top-to-bottom salinity differences of 6
to10 indicated g’ values between 0.05 and 0.08 m/s2. The self-advecting speeds of the
outflow plume cp, as derived from the long internal wave speed (g’H)½ were then 0.5 to
0.9 m/s, which yielded a Ri of 7-10 km. These Ri values are conservative overestimates
(they are likely to be ~7 km) on the basis of Figure 5 results and are smaller than the
offshore plume edge suggested by hydrography. These Ri estimates will also be
compared later to plume locations indicated by subtidal flows.
Another noteworthy hydrographic feature observed in the surveys was that the
highest salinities (>29) were observed in Chesapeake Channel (Fig. 5) and offshore. This
distribution suggested that offshore dense waters make their way into Chesapeake Bay by
plunging into Chesapeake Channel and following the deepest channels. So it is likely
that a substantial source of salty water to the Chesapeake Bay has downstream origins,
drawn by the gravitational circulation associated with the plume.
Subtidal flows
The mean flows observed during ~24 hours of sampling at each transect (Figs. 6
and 7) illustrated the transverse structure of the outflow plume. The patterns observed at
Transect 1 have already been described in detail by Valle-Levinson et al. (1998) and will
not be repeated here. Here we focus on the patterns of subtidal flow associated with the
containment of the plume and the withdrawal of salty waters from a downstream source,
13
as well as the outflow plume separating from Cape Henry. The outflow plume itself
showed transverse structure similarities and differences from transect to transect and
from survey to survey. Consistent patterns across all the Transect 2 and 3 surveys
included the development of depth-independent upstream flows throughout a 2 to 3 kmwide region next to the coast. Other similarities were found in the area of Chesapeake
Channel, as the channel: a) mostly constrained exchange flows; b) contained the strongest
downstream and upstream flows; and c) enclosed most of the outflow plume volume.
Differences were distinguished in the depth at which the outflow plume felt the bottom at
each transect and survey, although there were some similarities in this aspect, too. More
differences were noted in instances when the outflow plume remained detached from the
bottom, as suggested by the patterns of downstream flow. Similarities and differences
among subtidal flows in different transects are now explored further, with the mean
streamwise and streamnormal flows illustrated in Figures 6 and 7.
A revealing pattern that arouse from the surveys was the upstream flow in the
nearshore 2-3 km of Transects 2 and 3. This pattern was consistent with separation of the
plume noted in the mean surface and profile salinity distributions (Figs. 4 and 5) and
indicated a recirculation of bay plume waters likely caused by flow separation at Cape
Henry. At this northern hemisphere location, Coriolis accelerations fU, where U is a
typical outflow speed, would try to keep the outflow plume constrained against the coast.
In contrast, centrifugal accelerations U 2/ R , where R is the radius of curvature of the
bathymetry off Cape Henry (~6-7 km), would try to separate the outflow from the coast.
The value of U at which Coriolis and centrifugal accelerations become the same, or when
the Rossby number equals 1, is the product f R or 0.5 to 0.6 m/s. The outflow was
14
occasionally >0.5 m/s and therefore could have separated from Cape Henry. Another
possible explanation for this separation was the asymmetric nature of tidal flows at the
bay mouth, i.e., tidal rectification. During ebb, the flow is like a source potential and
during flood it is like a radial sink (e.g. Chadwick and Largier, 1999). The ebb-flood
asymmetry translates into a tidal mean recirculation around the cape. Whether the flow
separation results from tidal rectification or from seasonal pulses of strong plume outflow
remains to be determined. Regardless of the cause, the flow separation should generate
the recirculation pattern observed in all four surveys, with nearshore upstream flow (Figs.
6 and 7). The recirculation around Cape Henry can be illustrated more clearly in a vector
representation (Fig. 8) that showed large lateral shears in the outflow near the coast. In
general, surface downstream flow developed in the channel while upstream flow
appeared at every depth close to the shore. The vector representation also illustrated
bathymetric influences on exchange flows.
Consistent exchange flows were also mostly found in Chesapeake Channel during
every survey at each of the three transects sampled (Figs. 6 to 8). These exchange flows
followed the typical estuarine circulation consisting of buoyant, downstream flow in
upper layers and denser, upstream flow underneath. This vertically sheared pattern,
preferentially observed in the deepest part of each transect, contrasted to the laterally
sheared pattern in which upstream flows develop throughout the channel and downstream
flows appear over adjacent shallow areas (e.g. Wong, 1994). The observed vertically
sheared pattern has been attributed to non-negligible Earth’s rotation effects relative to
frictional influences as characterized by the vertical Ekman number E (Kasai et al., 2000;
Valle-Levinson et al., 2003). Earth’s rotation effects were quantified by Coriolis
15
accelerations fU and frictional influences could be represented by AzU/h 2, where Az is a
typical kinematic eddy viscosity (1×10-3 m2/s) and h is a typical depth that scales U (10
m). The Ekman number was then Az / fh 2 or 0.1, which suggested that both Coriolis and
frictional accelerations played a role in shaping the observed exchange flows. Friction
was less influential in the deepest areas (E depends inversely on h2) and that is why
exchange flows appeared there. In Chesapeake Channel, the asymmetric cross-channel
distribution of net flows indicated that Coriolis accelerations must have deflected net
upstream and downstream flows to their right, respectively (Figs. 6 to 8). These
bathymetric influences are explored with an analytical solution further described in the
Discussion.
The strongest downstream flows of each transect sampled were observed near the
surface in the Chesapeake Channel (Fig. 6 and 7). Net plume flows were as strong as 0.7
m/s (Transect 3 in November 1996 and February 1997) but also as weak as 0.05 m/s
(Transects 2 and 3 in May 1997) and 0.15 m/s at the bay entrance (Transect 1).
Similarly, the strongest upstream flows preferentially appeared in the channel at depths
between 10 and 20 m. Maximum inflows of 0.3 m/s were observed at the bay entrance in
February 1997 (Fig. 7). Another interesting aspect that was similar from survey to survey
was that most of the outflow plume was constrained by the channel. Even though the low
salinity signal may have extended beyond both edges of the channel, the mean volume
outflow was largely delimited by those edges. The net downstream volume fluxes in
Chesapeake Channel oscillated between ~200 and 18,000 m3/s and were determined, in
some measure, by wind forcing (Fig. 9).
16
Wind forcing, both local and remote, caused some variability in the net flow
patterns. For instance, the strongest downstream flow and transports in Transect 3
occurred in November 1996 and February 1997 (Figs. 6 to 9). These flows developed
with ~10 m/s northwesterly and southwesterly winds, respectively, with very little
variability in their speed and direction (Fig. 9). Northwesterly winds are the most
efficient for flushing waters out of Chesapeake Bay and southwesterly winds are the most
efficient in favoring exchange (surface outflow and inflow underneath) at the bay
entrance (Valle-Levinson et al., 2001). Even though the resultant wind was southwesterly
during the period of observations of Transect 1 in May 1997, the downstream flow and
transport were very weak (Fig. 9c). This was attributed to the periods of southeasterly
winds before and during transect sampling and also, perhaps more prominently, to the
fact that subtidal sea level was increasing (Fig. 3d). This sea level response was not
directly linked to local wind forcing and points to the importance of remote effects in
modifying both the volume exchange at the bay entrance and the behavior of the plume.
The importance of remote forcing on the outflow plume was also evident during
sampling of Transect 3 in September 1996. Although winds were predominantly from
the north (Fig. 3a and 9a), their magnitude changed markedly and their direction switched
from northwesterly to northeasterly. In addition, sea level increased during sampling and
caused very weak downstream transports.
The pattern in Transect 2 changed from a robust downstream transport in
September and November of 1996 to a very weak transport in May 1997. In September
1996 the downstream transport was not likely driven by the observed onshore winds (Fig.
3a and 9a) but rather by a subtidal sea level drop (Fig. 3a). In November 1996, the
17
downstream transport was likely driven by the combination of northwesterly winds and
depressed subtidal sea level (Fig. 3b). The weak transport of May 1997 in Transect 2 was
likely the result of a rebounding stage of the plume after the influence of southwesterly
winds the day before. The cessation of southwesterly winds caused an increase in subtidal
sea level 0.5 days before sampling. This subtidal sea level increase, together with strong
southeasterly winds during the second half of sampling, opposed the downstream
progression of the plume. The joint effects of subtidal sea level increase and
southeasterly winds could have caused the plume to expand offshore (e.g. Hallock and
Marmorino, 2002). Finally, the pattern in Transect 1 was that of a relatively well
developed outflow plume, except in February 1997, when northeasterly and southeasterly
winds combined with a subtidal sea level that was trending up to markedly weaken the
outflow plume. One of the main findings from these surveys was that both the local
winds and remote wind effects, as represented by subtidal sea level changes, modified the
structure of the outflow plume.
Discussion
This section centers on the a) temporal variability of the subtidal flow structure, b)
bathymetric constraints to the plume and c) recirculation characteristics at the turning
region of the Chesapeake Bay plume. The effects of river discharge in modulating the
subtidal flow structure of the plume were not discernible in the surveys because there was
always enough freshwater input to produce a marked plume. For these surveys,
atmospheric forcing played the most important role in modifying the outflow plume. The
effects of downwelling- and upwelling-favorable winds have been relatively well
18
documented (e.g. Hickey et al., 2005; Chao, 1987; Fong and Geyer, 2001; Xing and
Davies, 1999). Remote atmospheric forcing, in the form of subtidal fluctuations in sea
level <∂η/∂t>, should also be crucial for the fate of the plume by modulating it at its
source (e.g. Garvine, 1985; 1991). Remote effects are proportional to <∂η/∂t> and are
most effective when the subtidal fluctuations in sea level are relatively fast (~ 1 day) or
when water column stratification is relatively weak (e.g. Wong and Valle-Levinson,
2002). Similarly, Wong and Valle-Levinson (2002) found that local effects are effective
when stratification is strong.
It has been proposed by Yankovsky and Chapman (1997) that when stratification
is strong, the plume is detached from the bottom and is ‘surface-advected’ allowing it to
react easily to local wind forcing. According to them, on the basis of cyclostrophic
dynamics, the plume will be constrained within a distance Ls, given by:
Ls = 2 (3 g’ H + up2 ) / f (2 g’ H + up2)½ ,
(1)
where up is a typical speed of the outflow plume and H is the plume depth as it enters the
coastal ocean. For the observations at the turning region of the Chesapeake Bay outflow
plume up attained values between 0.15 and 0.7 m/s, H was between 10 and 15 m, and g’
between 0.05 and 0.08 m/s2. Thus, predicted Ls would be between 30 and 55 km, which
is more than twice the various limits observed, and the Chesapeake Bay outflow plume
was unlikely ‘surface advected’ during the periods observed.
In contrast to the surface-advected plume, the plume could remain attached to the
bottom until reaching a critical depth hc. If hc > H and the distance at which hc is found is
farther offshore than Ls then the offshore extent of the plume would be determined by
19
advection in the bottom boundary layer. Following Yankovsky and Chapman (1997), the
critical depth is given by:
hc = (2 L up H f /g’)½
(2)
where L is the width of the estuary mouth (16 km). Taking the range of values observed,
the critical depth hc was between 7 and 24 m. This suggested that the Chesapeake Bay
plume may sometimes be bottom-advected (for high values of hc ). It is essential to note,
however, that in some instances hc < H and the bottom-advected approach to estimate the
offshore plume extent (Yankovsky and Chapman, 1997) would not apply. This issue was
addressed by Lentz and Helfrich (2002), who included bottom slope γ effects. They
proposed that the typical scale of the internal radius of deformation Ri, as defined in the
Mean Salinity Profiles subsection, is modified by the ratio of cp, the long internal wave
speed, to cγ, the propagation speed over small bottom slope and equals γg’ / f. The
offshore extent of the plume is then Ri (1 + cp /cγ). In the Chesapeake Bay outflow
region, however, the bottom slope is not constant (see for instance Fig. 6 and 7) and
changes sign in Chesapeake Channel. Even so, taking values of γ between 0.001 and
0.003, cp between 0.5 and 0.9 m/s (Mean Salinity Profiles subsection), and cγ between 0.6
and 2.7 m/s, yields ratios of cp /cγ between 0.2 and 1.5. This means that the plume is
contained within distances between 1.2 Ri and 2.5 Ri. The observations showed a smaller
range of plume containment than those proposed by the above theories. Clearly, the
plume core and its main outer edge were constrained by Chesapeake Channel, as also
suggested by Sletten et al. (1999). It can then be proposed that the bathymetrically
steered upstream flow contributes to restrain the main volume of the outflow plume.
20
Through both friction and advection, such upstream flow should influence the dynamics
and the offshore extent of the plume.
The effects of advection on the Chesapeake Bay plume were discerned by
comparing mean advective effects to mean Coriolis accelerations for each transect and
survey (Figs. 10 and 11). Mean advective effects were approximated with the only
advective term that could be reliably determined. This term was calculated from lateral
flows v reconstructed from the harmonic analysis results through <v∂v/∂n>, where
brackets denote tidal averages and n indicates streamnormal direction. Mean Coriolis
effects were calculated with the streamwise flow u and were represented as <fu>. The
comparisons consistently showed the importance of advective effects in Transects 1 and
2, at the turning region of the plume. In those transects, the absolute value of the ratio
<v∂v/∂n> / <fu> was mostly > 1, which suggested that Coriolis accelerations may not
have been dominant in that region. Further downstream, at Transect 3, Coriolis
accelerations became clearly prevalent. This difference can also be seen in the increasing
importance of Coriolis accelerations when Transect 2 was reoriented further downstream
in the May 1997 survey. It was also seen that the outflow plume could separate from
Cape Henry when the velocity exceeded the product of the Coriolis parameter and the
radius of curvature f R, i.e., when centrifugal accelerations exceeded Coriolis
accelerations. By Transect 3, R becomes large (relatively straight isobaths) and therefore
a much larger velocity is required before advection becomes important.
The influence of bathymetry, and the friction related to its variability, on the
plume structure could be explored with a linear solution (e.g. Kasai et al., 2000; ValleLevinson et al., 2003). The solution arises from a simplified dynamic balance among
21
pressure gradient (both barotropic and baroclinic), Coriolis acceleration and friction. The
shape of the solution describing exchange flows (given in the Appendix) depends on the
prescription a) of a sea level slope, b) of a space-independent eddy viscosity Az, and c) of
net transports through the section. The exchange patterns arising from solution A3
showed very good agreement with those observed in Transect 3 (Fig. 12). The
resemblance was striking at distances >3.5 km, which indicated that the main dynamics
in most of the transect was well captured by a linear approach. In transect 3 (Fig. 12),
advective accelerations were weakest and that is why the comparison is so favorable. At
the other 2 transects, where advective effects were more prominent, comparable
exchange flow patterns can still be reproduced (e.g. Valle-Levinson et al., 2003).
Solutions over flat-bottom bathymetry, with the same forcing as that used to produce the
results of Figure 12, showed a markedly different plume and upstream flow structure.
The model-observations agreement underlined the importance of bathymetry in
constraining the upstream flow and the outflow plume. It is noteworthy that the
Delaware River plume, for instance, shows analogous bathymetric steering (e.g.
Münchow and Garvine, 1993) whereas the Hudson River plume is unconstrained by
bathymetry in the vicinity of the outflow (Chant et al in prep). Both the Chesapeake and
Delaware channels tend to steer the estuarine outflow along the coast and may favor
coastal current formation. In contrast, the lack of bathymetric steerage of the Hudson’s
outflow may play a role in the tendency for its discharge to form a large unsteady bulge
(Choi and Wilkin, submitted; Chant et al; in prep). In general, it can be postulated that
plumes constrained by channels will produce coastal currents (in the Kelvin-wave sense),
22
while unconstrained plumes will be more reactive to wind forcing and prone to bulge
formation.
The recirculation (upstream flow) observed in the Chesapeake Bay outflow within
the 3.5 km closest to the coast was not explained by solution A3 (Fig.12). This was
because of the non-linear character of the recirculation, which was associated with flow
separation at Cape Henry. The flow separation caused the formation of two boundaries
for the plume waters, one offshore and one inshore, during ebb periods. This was
analogous to observations in Delaware Bay (Sanders and Garvine, 1996) and from radar
measurements in the Chesapeake Bay (Sletten et al. 1999) and ADCPs (Marmorino et al.,
2000; Marmorino and Trump, 2004). During flood periods, the flow is like a potential
sink (e.g. Chadwick and Largier, 1999) and moves in roughly the same direction as in
ebb (toward the bay mouth) in the region inshore of the Chesapeake Channel. This
resulted in net flows moving downstream in the channel and upstream inshore of the
channel. The mean anticyclonic recirculation was clearly illustrated by forming surface
maps from interpolated values of each transect (Fig. 13). Even though these
representations could not provide a truly synoptic picture of the surface flow field
because of the rapidly changing forcing conditions, even from day to day, they did show
a recirculation. This is owing to the persistent and coherent flow toward the bay mouth
in the region inshore of the channel. Whether the observed anticyclonic recirculation
around Cape Henry develops under much weaker riverine input than those observed in
this study remains a question to be explored. Nonetheless, it is hypothesized that the
recirculation is most likely caused by tidal rectification as also suggested by Johnson
(1976), Marmorino et al. (2000) and Marmorino and Trump (2004). The persistent
23
observations of this anticyclonic recirculation in different studies suggests additional
observational or modeling studies to explore whether it functions as a retention
mechanism for transport of larvae that require re-entrance into Chesapeake Bay for their
survival.
Conclusion
This observational study at the turning region of the Chesapeake Bay outflow
plume has produced revealing results. Centrifugal accelerations combine with frictional
influences to produce an anticyclonic recirculation off Cape Henry and also, through
bathymetric variations, to limit the offshore extent of the plume. The mean downstream
flow related to the plume is mostly constrained by the edges of Chesapeake Channel.
This channel provides and important pathway for coastal ocean water to enter into
Chesapeake Bay underneath the plume.
24
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29
Appendix. Model
The model that generated the results of Figure 12 solves for the non-tidal or mean
along-isobath u and transverse v flows produced by pressure gradients and modified by
Coriolis and frictional influences. In a right-handed coordinate system (x, y, z), where x
points downstream, y offshore and z upward, the non-tidal (or steady) momentum balance
to be solved becomes a set of two differential equations:
 g 
 2u

z  Az 2
 x  x
z
 g 
 2v
f u  g

z  Az 2
y  y
z
 f v  g
(A1)
where f, g, o, , , Az are the Coriolis parameter, the gravity acceleration (9.8 m/s2),
reference water density, variable water density (kg/m3), surface elevation (m), and
vertical eddy viscosity homogeneous in z and y (m2/s), respectively. The set of equations
(A1) may be represented in terms of a complex velocity w = u + iv, where i 2 = 1 is the
imaginary number:
g N  D z  Az
2w
z2
 i f w.
(A2)
In (A2), N and D represent the barotropic and baroclinic pressure gradients, respectively:


i
x
y
g  
 
D   i 
 x  y 
N
and are assumed independent of depth. Then, the flow w has contributions from the sea
level slope and from the horizontal density gradients, i.e.,
w(z) = gNF1 (z) + F2 (z)
30
(A3)
and F1 and F2 represent functions that depict the vertical structure of the barotropic (from
sea level slope) and baroclinic (from density gradient) contributions to the flow. Using
equation (A3), then equation (A2) can be rewritten as:
 2 F1
z
 F2
2
2
z2

if
1
F1 
Az
Az
if
Dz

F2  
Az
Az
.
(A4)
Assuming, as boundary conditions, no stress at the surface (F1 /z = F2 /z = 0 at z
= 0), and no-slip at the bottom (F1 and F2 = 0 at z = Hy), and that the horizontal density
gradient is independent of depth, the solution of (A4) is:
F1 
iD
F2 
f
cosh  z  
i 
1 

f  cosh  H y 
 



 z
cosh  z 
H y
 H y
 e  z  e
cosh  H y






(A5)

In this solution, the parameter  equals (1 + i)/DE, where DE is the Ekman layer depth
[2Az / f ]½. Solutions (A5) and (A3) require prescription of the sea level slope N and the
eddy viscosity Az and a density gradient D that is dynamically consistent with N. In order
to derive the value of D we use a boundary condition that assumes a prescribed net
volume flux R (m3/s) along or across a cross-section (Kasai et al., 2000), i.e.,
B 0
  w dz dy  R
0 H y
where B is the estuary’s width. The value of D that satisfies a prescribed N is:
31
(A6)
B
R f 2  i g I1  N ( y ) dy
D

0
iI2
B

R f 2  i g  N ( y ) ( e
H y
 H y ) tanh( H y )  (1  e
H y

  2 H y2 2) dy
(A7)
0
B


i  tanh( H y )  H y dy
0
Prescribing N (= 110-6 {1+ i exp[-(y/B-1)2]}), Az (order 10-4 to 10-3 m2/s), R, and Hy (as
any function of y), the solution to (A3) is obtained with (A5) and (A7) and portrayed in
Figure 12. The shape of N was justified by observations as described by Valle-Levinson
et al. (2003).
32
Acknowledgments
This work was funded by the U.S. Mineral Management Service under
Cooperative Agreement No. 14-35-001-30807 and by the NOAA Office of Sea Grant,
under Grant No. R/CF-47 to the Virginia Graduate Marine Science Consortium and
Virginia Sea Grant College Program. Ship time on the NOAA ship Ferrel was provided
by the National Sea Grant College Program. We greatly appreciate the professional
support and cooperation from the crew of the Ferrel under the able command of LCDR
S.D. McKay. We also appreciate the technical support of R.C. Kidd and L. Brasseur plus
the participation of T. Royer, J. Klinck, R. Ellison, E. Haskell, G. Jiang, J. Koziana, T.
McCarthy, M. Moore, S. Paraso, B. Parsons, C. Reiss, C. Reyes, D. Ruble, S.
Wathanaprida, and B. Wheless, M. Gruber, S. East, S. Kibler on various surveys. We
appreciate the comments of A. Yankovsky and one anonymous reviewer who helped
improve the presentation of the paper.
33
List of Figures.
Figure 1. Study area in the lower Chesapeake Bay showing transect locations. CC and
CBBT indicate Chesapeake Channel and Chesapeake Bay Bridge Tunnel,
respectively. Insert shows Chesapeake Bay in the Mid-Atlantic Bight region of
eastern United States. CBBT is the location of wind and sea level measurements.
Figure 2. River discharge into Chesapeake Bay as derived from the Susquehanna,
Potomac and James Rivers. Range of daily discharges (shaded) throughout a year.
The white line indicates the 30-year average. Darkest line indicates daily values for
1996 and dark line shows daily values for 1997. Periods of observation are marked
with vertical arrows on top of the figure.
Figure 3. Wind velocity vectors (indicating direction toward which the wind blows),
subtidal sea level, and high-pass sea level during each experiment. Shaded periods
indicate measurement of a transect.
Figure 4. Temporal mean surface salinity (upper subpanel) and streamnormal salinity
gradient (lower subpanel) drawn along each transect for all surveys. All dotted
lines represent Transect 1, dark lines relate to Transect 2 and gray lines represent
Transect 3.
Figure 5. Profiles of mean salinity and vertical gradient at each location of the two
transects sampled in February 1997.
Figure 6. Mean streamwise (contours) and streamnormal (vectors) flows at each section
measured in September and November 1996. Looking upstream. Shaded areas
indicate upstream flow.
34
Figure 7. Mean streamwise (contours) and streamnormal (vectors) flows at each section
measured in February and May 1997. Looking upstream. Shaded areas indicate
upstream flow.
Figure 8. Mean vectors for each survey, plotted at different depths. The figure suggests
anticyclonic circulation off Cape Henry and exchange flows in Chesapeake
Channel.
Figure 9. a) Resultant and variability of wind velocity during the period of each section
measured. Positive arrows indicate northward and eastward winds. b) Maximum
net flow for each section. c) Volume flows integrated in Chesapeake Channel.
Figure 10. Absolute value of the tidal average ratio between advective and Coriolis
accelerations as estimated from observations. Shaded areas denote ratios < 1
(Coriolis > advective). Looking upstream. Transects measured in September and
November 1996.
Figure 11. Same as Figure 10 but for February and May 1997.
Figure 12. Observed along-isobath flows (a through d in cm/s) in Transect 3 compared to
model results with observed bathymetry (e through h in cm/s) and flat bottom (i through
l, at transect’s mean depth). Model results were obtained by prescribing the following
parameters: e) and i) Az = 0.0014 m2/s, R = 7000 m3/s upstream; f) and j) Az = 0.001 m2/s,
R = 16000 m3/s downstream; g) and k) Az = 0.0006 m2/s, R = 11000 m3/s downstream; h)
and l) Az = 0.0017 m2/s, R = 12000 m3/s upstream. Prescribed transports were within 10%
of the net transports calculated from observations for each case.. Sea level slopes were N
= 110-6 {1+ i exp[-(y/B-1)2]} (see appendix).
35
Figure 13. Surface vectors interpolated onto a uniform grid. Even though this figure
does not portray a synoptic picture because of the changing winds from one day to
another, all representations depict anticyclonic circulation over the shallow area off
Cape Henry.
36
Figure 1. Study area in the lower Chesapeake Bay showing transect locations. CC and CBBT
indicate Chesapeake Channel and Chesapeake Bay Bridge Tunnel, respectively. Insert shows
Chesapeake Bay in the Mid-Atlantic Bight region of eastern United States. CBBT is the location
of wind and sea level measurements.
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Figure 2. River discharge into Chesapeake Bay as derived from the Susquehanna, Potomac and
James Rivers. Range of daily discharges (shaded) throughout a year. The white line indicates the
30-year average. Darkest line indicates daily values for 1996 and dark line shows daily values for
1997. Periods of observation are marked with vertical arrows on top of the figure.
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Figure 3. Wind velocity vectors (indicating direction toward which the wind blows), subtidal sea
level, and high-pass sea level during each experiment. Shaded periods indicate measurement of a
transect.
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Figure 4. Temporal mean surface salinity (upper subpanel) and streamnormal salinity gradient
(lower subpanel) drawn along each transect for all surveys. All dotted lines represent Transect 1,
dark lines relate to Transect 2 and gray lines represent Transect 3.
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Figure 5. Profiles of mean salinity and vertical gradient at each location of the two transects
sampled in February 1997.
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Figure 6. Mean streamwise (contours) and streamnormal (vectors) flows at each section
measured in September and November 1996. Looking upstream. Shaded areas indicate upstream
flow.
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Figure 7. Mean streamwise (contours) and streamnormal (vectors) flows at each section
measured in February and May 1997. Looking upstream. Shaded areas indicate upstream flow.
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Figure 8. Mean vectors for each survey, plotted at different depths. The figure suggests
anticyclonic circulation off Cape Henry and exchange flows in Chesapeake Channel.
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Figure 9. a) Resultant and variability of wind velocity during the period of each section
measured. Positive arrows indicate northward and eastward winds. b) Maximum net flow for
each section. c) Volume flows integrated in Chesapeake Channel.
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Figure 10. Absolute value of the tidal average ratio between advective and Coriolis accelerations
as estimated from observations. Shaded areas denote ratios < 1 (Coriolis > advective). Looking
upstream. Transects measured in September and November 1996.
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Figure 11. Same as Figure 10 but for February and May 1997.
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Figure 12. Observed along-isobath flows (a through d in cm/s) in Transect 3 compared to model results with
observed bathymetry (e through h in cm/s) and flat bottom (i through l, at transect’s mean depth). Model results
were obtained by prescribing the following parameters: e) and i) Az = 0.0014 m2/s, R = 7000 m3/s upstream; f) and
j) Az = 0.001 m2/s, R = 16000 m3/s downstream; g) and k) Az = 0.0006 m2/s, R = 11000 m3/s downstream; h) and l)
Az = 0.0017 m2/s, R = 12000 m3/s upstream. Prescribed transports were within 10% of the net transports calculated
from observations for each case. Sea level slopes were N = 110-6 {1+ i exp[-(y/B-1)2]} (see appendix).
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Figure 13. Surface vectors interpolated onto a uniform grid. Even though this figure does not
portray a synoptic picture because of the changing winds from one day to another, all
representations depict anticyclonic circulation over the shallow area off Cape Henry.
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