This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution
and sharing with colleagues.
Other uses, including reproduction and distribution, or selling or
licensing copies, or posting to personal, institutional or third party
websites are prohibited.
In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website or
institutional repository. Authors requiring further information
regarding Elsevier’s archiving and manuscript policies areencouraged to visit:
http://www.elsevier.com/copyrightAuthor's personal copy
ARTICLE IN PRESS
Continental Shelf Research 28 (2008) 2450–2471

Contents lists available at ScienceDirect

Continental Shelf Research
journal homepage: www.elsevier.com/locate/csr

Wind effects on the lateral structure of density-driven circulation in
Chesapeake Bay
Xinyu Guo a,, Arnoldo Valle-Levinson babCenter for Marine Environmental Studies, Ehime University, 2–5 Bunkyo-Cho, Matsuyama 790-8577, Japan
Department of Civil and Coastal Engineering, University of Florida, 365 Weil Hall, P.O. Box 116580, Gainesville, FL 32611, USAa r t i c l e in f o

a b s t r a c t

Article history:
Received 10 August 2007
Received in revised form
25 March 2008
Accepted 20 June 2008
Available online 27 June 2008

The response of the density-driven circulation in the Chesapeake Bay to wind forcing was studied withnumerical experiments. A model of the bay with realistic bathymetry was ﬁrst applied to produce thedensity-driven ﬂow under average river discharge and tidal forcing. Subsequently, four spatially uniform
wind ﬁelds (northeasterly, northwesterly, southwesterly, and southeasterly) were imposed to examine
the resulting cross-estuary structure of salinity and ﬂow ﬁelds. In general, northeasterly andnorthwesterly winds intensiﬁed the density-driven circulation in the upper and middle reaches ofthe bay, whereas southeasterly and southwesterly winds weakened it. The response was different in thelower bay, where downwind ﬂow from the upper and middle reaches of the bay competed withonshore/offshore coastal ﬂows. Wind remote effects were dominant, over local effects, on volumetransports through the bay entrance. However, local effects were more inﬂuential in establishing thesea-level slopes that drove subtidal ﬂows and salinity ﬁelds in most of the bay. The effect of verticalstratiﬁcation on wind-induced ﬂows was also investigated by switching it off. The absence ofstratiﬁcation allowed development of Ekman layers that reached depths of the same order as the water
depth. Consequently, bathymetric effects became inﬂuential on the homogeneous ﬂow structurecausing the wind-induced ﬂow inside the bay to show a marked transverse structure: downwind overthe shallow areas and upwind in the channels. In the presence of stratiﬁcation, Ekman layers became
shallower and the wind-induced currents showed weaker transverse structure than those thatdeveloped in the absence of stratiﬁcation. In essence, the wind-driven ﬂows were horizontally sheared
under weak stratiﬁcation and vertically sheared under stratiﬁed conditions.
& 2008 Elsevier Ltd. All rights reserved.

Keywords:
Chesapeake Bay
Estuarine circulation
Wind-driven currents
Wind-induced mixing
Transverse structure

1. Introduction
The inﬂuence of winds on estuarine circulation (gravitational
circulation) has been described for several decades. For example,
the analytical solution of estuarine circulation given by Hansen
and Rattray (1965) included the contribution of winds. According
to their solution, a down-estuary wind intensiﬁed the estuarine
circulation, while an up-estuary wind weakened it. Geyer (1997)
applied this solution to explain observations in Waquoit Bay,
Massachusetts, in terms of wind forcing. In addition, Weisberg(1976), Elliott (1978) and Wang (1979) also observed predominant
wind-driven pulses in currents or sea levels of an estuary.
Recent studies have focused, in addition to the vertical andalong-estuary structure of estuarine ﬂows, on their transverse
structure. Assuming a balance between pressure gradient andvertical stress divergence in an idealized estuary with a triangular Corresponding author. Tel./fax: +8189 927 9824.

E-mail address: guoxinyu@dpc.ehime-u.ac.jp (X. Guo).
0278-4343/$ - see front matter & 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.csr.2008.06.008

cross-section, Wong (1994) and Friedrichs and Hamrick (1996)
obtained an analytical solution for the circulation. The solutions inWong (1994) are for ﬂows driven by along-estuary density
gradients, by local along-estuary winds, and by subtidal sea-level
oscillations at the entrance to an estuary, which represent the
remote effect of winds. His solutions revealed a marked transverse
structure that depended on the bathymetry. In the deep central
part of the triangular section, the net ﬂow was in the opposite
direction of the density gradient or the local winds. Over the two
shallow sides of the cross-section, the net ﬂow was in the
direction of the density gradient or of the local winds. The current
caused by a subtidal sea-level oscillation at the entrance to an
estuary (the remote effect) was in the same direction throughout
the cross-section but strongest in the deep central part.
Kasai et al. (2000) introduced rotation effects to the formulation of Wong (1994) and also looked at the transverse dynamics.
They used the Ekman number to evaluate the relative importanceof friction and rotation in their analytical solution. A large Ekman
number meant that most of the water column was occupied by
the Ekman depth. In that case, friction dominated the dynamics

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

2451

and the current structure approached the solution given by Wong
(1994), i.e., bathymetry causes a strong transverse structure in thecurrents. In the case of a small Ekman number, the solution
approached the traditional two-layer vertical structure of estuarine circulation. Valle-Levinson et al. (2003) extended the solutionof Kasai et al. (2000) to a section with arbitrary bathymetry andapplied the solution to explain the transverse structure ofobserved currents in several estuaries with different Ekman
numbers. Following the same dependence on the Ekman number,
Winant (2004) and Sanay and Valle-Levinson (2005) characterized the wind-driven ﬂows affected by Coriolis under various
bathymetric cross-sections and homogeneous density.
The above theoretical studies have examined current structures inside the estuary and assumed a linear superposition of thewind-induced and density-induced currents. This, of course,
differs in a real estuary because winds can change the density
ﬁeld as well as the turbulence ﬁeld. Winds can change thestrength of estuarine currents, while turbulence, according toKasai et al. (2000) and Valle-Levinson et al. (2003), can change thetransverse structure of the current, regardless of whether it iswind induced or buoyancy induced. Chao (1988) investigated thewind effects on a pre-existing estuarine current in an idealized
estuary using a three-dimensional model, which included theeffects of winds on the density ﬁeld but neglected wind effects on
the turbulence ﬁeld because he used a constant viscosity.
In this study, the work of Guo and Valle-Levinson (2007) is
extended through the inclusion of winds. A uniform wind ﬁeld
from four directions (NW, NE, SE, and SW) as well as thecorresponding sea-level change at the bay mouth were prescribedin a numerical model of the Chesapeake Bay to examine themodiﬁcations to a pre-existing estuarine circulation inside the bay
and at the bay mouth. These modiﬁcations were also assessed bydetermining the wind response in a homogeneous ChesapeakeBay.

2. Numerical model and experiments
The model used in this study is the same as in Guo and ValleLevinson (2007), the Princeton Ocean Model (POM). The POM is athree-dimensional primitive equation ocean model that includes
full thermodynamics and a Mellor-Yamada level 2.5 turbulence
closure model (Mellor, 2004). The model domain and bathymetry
are shown in Fig. 1. The horizontal resolution was 1/2401 in both
the zonal and meridional directions, which gave 744 grids in themeridional direction and 420 grids in the zonal direction. In thevertical, 11 sigma-levels were evenly distributed. Calculations
with 21 sigma-levels showed qualitatively the same results as
those with 11 sigma-levels. The minimum water depth in themodel domain was set to 3 m. The time step was 3 s for theexternal mode and 120 s for the internal mode. During calculations, the vertical eddy viscosity and diffusivity were determinedby the Mellor-Yamada turbulence closure model with a background value of 105 m2/s. At the bottom, a common quadratic
friction law was used to calculate bottom stress (see Guo andValle-Levinson, 2007 for the parameters used). The horizontal
eddy viscosity was calculated by the embedded Smagorinsky
formula with a proportionality parameter of 0.1, and thehorizontal eddy diffusivity was obtained using an inverse Prandtl
number of 0.5.
The model was ﬁrst forced with river discharge, an ambient
coastal current and tides to produce the estuarine currents in the
Chesapeake Bay. The water temperature was set as a constant(15 1C) throughout all the calculations and only the evolution ofsalinity was calculated. The contribution of temperature to thedensity gradient in the horizontal and vertical directions has beenFig. 1. Model bathymetry: the boxes denote river locations and the numbers inside
the parentheses denote the percentage of each river discharge, relative to the total(2200 m3/s), as given by Hargis (1980). The longitudinal cross-section (A–A0 ) andtwo lateral cross-sections (B–B0 and C–C0 ) are referenced in subsequent ﬁgures.

suggested to be less than 1/4 relative to salinity (Seitz, 1971;
Goodrich et al., 1987). Referring to Hargis (1980), a total of2200 m3/s of fresh water was introduced to the model domainfrom the Susquehanna (51% of total), Potomac (18%), James (14%),
Rappahannock (4%), York (2%), and other small rivers (11%) (seeFig. 1 for the position of the rivers and see Guo and Valle-Levinson,
2007 for the method of introducing river discharge).
Prescription of the southward ambient current in the shelf was
motivated by previous studies. Beardsley and Boicourt (1981)
reported a southward coastal current in the Middle Atlantic Bight.
Epifanio and Garvine (2001) inferred the existence of a southward
coastal current outside the Chesapeake Bay. In our simulations, anAuthor's personal copy
ARTICLE IN PRESS
2452

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

ambient coastal current was imposed with a speed of 10 cm/salong the eastern boundary from 37.71N to 381N. Furthermore, it
has been shown that the inclusion of an ambient current isessential for a realistic representation of the buoyant plumeoutside the bay (Guo and Valle-Levinson, 2007). The prescriptionof tidal currents is crucial to emulate the transverse structureof subtidal currents inside the bay and to represent the outﬂow plume path outside the bay (Guo and Valle-Levinson, 2007).
Every simulation was forced with semidiurnal tides. In all the
calculations, the results were saved hourly and the intratidal
variability was removed with a low-pass tide killer ﬁlter (Hanawa
and Mitsudera, 1985). The calculated tide and tidal currents
are given by Guo and Valle-Levinson (2007). The open boundary
conditions are speciﬁed in the same way as in the subroutine
BCOND in POM (see Mellor, 2004 for a detailed descriptionof this subroutine), which can directly include tidal currents,
ambient current and sea-level change. Along the eastern open
boundary, the tidal currents and ambient current are linearlysuperposed.
With the above conﬁgurations, the model was started with aconstant salinity (32) in the entire domain and run for 246 days toobtain the estuarine circulation in the bay. Then a spatially
uniform wind was imposed to the fundamental estuarine
circulation to examine its response. Winds from four directions(northeasterly or 451T, northwesterly or 3151T, southwesterly or
2251T, and southeasterly or 1351T) were imposed to the modelfrom day 247 to 249. After that the winds stopped but the model
simulation continued to day 265. During the 3 days of windblowing, the magnitude of wind stresses was ramped-up fromzero to the maximum during the ﬁrst 12 h and was ramped-downfrom the maximum to zero in the ﬁnal 12 h. Consequently,
the magnitude of wind stress was kept maximum for 2 days,
from day 247.5 to 249.5. The sea-level change due to the winds
was calculated by the formula given in Fig. 4d of Paraso andValle-Levinson (1996) and the calculated values were prescribedalong the open boundary to examine the remote effects ofwinds. Essentially, a total of nine different cases were calculated as shown in Table 1, where case 0 is a control experimentwith no winds; cases 1–4 are designed to examine the local
wind effects and cases 5–8 are designed to examine the remotewind effects. Additional experiments 1H–4H were to examine
the local wind effects in the absence of stratiﬁcation and 1C–4C
were to examine the combination of local and remotewind effects. The maximum magnitude of the wind stress incases 1–8 was the same, 0.14 Pa. The calculations with halfof this magnitude did not show essential difference in the
results. The magnitude, direction, and duration of winds usedhere were determined from the analysis by Paraso and ValleLevinson (1996) in Chesapeake Bay and from wind records duringobservations of the currents at the bay entrance (Valle-Levinson
et al., 2001).

3. Results
3.1. Estuarine circulation
The salinity and subtidal currents obtained for the control casehave been reported in Guo and Valle-Levinson (2007). Those
results are described again, brieﬂy, for a comparison with theresults of the cases with winds. Surface salinity shows a typical
distribution in an estuary (Fig. 2a). The along-estuary salinity
gradient is greatest between the head of the bay and theintersection between the Potomac River and the main axis of
the bay, and also at the bay entrance. In the transverse direction,salinity is relatively low along the western side and high along theeastern side, which is explained by the position of the rivers andthe effects of Earth’s rotation. Over the shelf outside the bay, thesalinity is approximately 32, which is the same as the initialsalinity and that prescribed along the open boundary. The only
low salinity area outside the bay is near the bay entrance and isrelated to the outﬂow plume.
In general, the surface subtidal currents inside the bay are
toward the ocean (Fig. 2b). Their speed is 20 cm/s in the upperand middle bay, where the transverse salinity difference acrossthe narrow sections is 2–3. Surface subtidal ﬂow is 10 cm/s inthe lower bay and increases again at the bay entrance. Outside thebay, two southward currents can be found. One is the imposedambient current, north of the bay entrance, and the other is theoutﬂow plume.
The transverse salinity gradient displayed at the surface (Fig.
2a) extends throughout the water column, as shown in a mid-bay
section (Fig. 3c) and the bay entrance (Fig. 3e). The subtidal ﬂow
normal to the mid-bay section concentrates in the central part,with outﬂow in the upper layer and inﬂow underneath, both ofwhich exceed 15 cm/s (Fig. 3d). The interface between opposite
currents is almost ﬂat. At the bay entrance (Fig. 3e), the lower
salinity area at the southern side of the section corresponds to theoutﬂow plume (Fig. 2a). The subtidal ﬂow normal to the section
concentrates in the Chesapeake Channel, with an outﬂow in theupper layer and an inﬂow in the lower layer (Fig. 3f). There is also
an outﬂow in the upper layer and an inﬂow underneath in the
North Channel but weaker than the exchange ﬂows in the
Chesapeake Channel. These subtidal ﬂow features in the Chesapeake and North channels at the bay entrance are remarkably
similar to the observations described in Valle-Levinson et al.
(1998, 2001).
Transverse variability in subtidal ﬂows is more apparent at thebay entrance (Fig. 3f) than in the mid-bay (Fig. 3d). This isindicated by the interface between opposite ﬂows, which slopes
downward to the south in the Chesapeake Channel. Such interface
slope and transverse variability are attributed to tidal forcing,which produces stronger mixing in the lower bay than in the
middle of the bay (Guo and Valle-Levinson, 2007).

Table 1Wind stress and sea level applied at the model’s open boundary
Case

Eastward component (Pa)Northward component (Pa)Sea level (cm)

Eastward component (Pa)Northward component (Pa)Sea level (cm)

0

1

2

3

0
0
0

0.1
0.1
0

0.1
0.1
0

5

6

7

0
0
26.9

0
0
5.3

0
0
26.9

0.1
0.1
0

4

1H

2H

0.1
0.1
0

0.1
0.1
0

0.1
0.1
0

8

1C

2C

3C

4C

0.1
0.1
26.9

0.1
0.1
5.3

0.1
0.1
26.9

0.1
0.1
5.3

0
0
5.3

3H

4H
0.1
0.1
0

0.1
0.1
0

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

a

2453

b

Fig. 2. Horizontal distribution of surface: (a) salinity and (b) velocity calculated for the control case (case 0).

3.2. Response of density-driven circulation to winds: surface layer
after 2 days
As described in Section 2, a spatially uniform wind was
imposed to the pre-existing estuarine circulation in the Chesapeake Bay to examine its effects on the salinity, subtidal currents,
and turbulence ﬁelds. In this and the following sections, results
are reported at the mature state (day 249.5), i.e., after the winds
have blown at maximum speed for 2 days. Section 3.4 describes
the response of the pre-existing estuarine circulation to sea-levelchange at bay mouth, i.e., remote wind effects. Section 3.5
describes the temporal response of water exchange through thebay entrance during the duration of the wind pulses in cases 1–6(local or remote effects separately) and in cases 1C–2C (combination of local and remote effects).
The wind-induced changes in subtidal sea level are shown ﬁrst
(Fig. 4) because they have been extensively studied (e.g., Wang,
1979; Valle-Levinson et al., 2001, 2002). Under northeasterly
winds (case 1; Fig. 4a), the sea level tilts upward from the upper
bay to the lower bay by 0.2 m. Also, sea level shows negative
slopes across the lower bay, i.e., sea level decreases from thesouthwest to the northeast in the lower bay. This is a consequenceof water piling up on the southwestern corner of the lower bay, as
observed by Valle-Levinson et al. (2001, their Fig. 3) undernortheasterly winds. Under northwesterly winds (case 2; Fig. 4b),the sea level also slopes upward from the upper to the lower bay
by 0.2 m. This feature is also consistent with the northwesterly
wind pulse caused by Hurricane Floyd in 1999 (see Fig. 3 in ValleLevinson et al., 2002). Under southwesterly winds (case 3; Fig. 4c),the sea level tilts upward from the southwestern corner of the bay
toward the upper bay, as observed in Valle-Levinson et al. (2001).
Finally, under southeasterly winds (case 4; Fig. 4d), the sea
level slopes upward from the bay entrance to the upper bay,
showing an inverse response to northwesterly winds. This isalso in agreement with observations of Salas-Monreal andValle-Levinson (2008). The sea-level responses produced by themodel are qualitatively the same as those observed. The
magnitude of the slopes is underestimated in the model by
5–30%, relative to observations with comparable winds, becauseof the remote effects as will be shown in Section 3.4 and theinverse barometer effect (Salas-Monreal and Valle-Levinson,2008). Nonetheless, the shape and approximate magnitude of
the sea-level slopes is consistent with observations for all winddirections.
The general features in the salinity ﬁeld (Fig. 5) such as low
salinity in the upper bay and high salinity in the lower bay are
maintained for all wind cases. This suggests that the observed
decrease of salinity in the entire bay during the passage of the
Hurricane Floyd (Valle-Levinson et al., 2002) resulted not only
from winds but also from the increased freshwater supply.

Author's personal copy
ARTICLE IN PRESS
2454

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

a

b

c

d

e

f

Fig. 3. Vertical distribution of salinity (left panels) and velocity (right panels) along Section A (top panels), Section B (middle panels) and Section C (lower panels). The
velocity in (b) is the along-estuary component (parallel to Section A). Positive values denote currents toward the mouth of the bay. The velocity in (d) is the component
normal to Section B and negative values denote current toward the mouth of the bay. The velocity in (f) is the component normal to Section C and negative values denote
outﬂow from the bay entrance. The units shown on the abscissa represent the model grid number.

Northeasterly winds cause a decrease of salinity along the western
coast and an increase along the eastern coast in the upper andmiddle bays (Fig. 5a). This response is seen by an elongation of
isohalines in the north–south direction because of downwelling
along the western coast and upwelling along the eastern coast.
Hence, advective effects seem to dominate the wind response overdiffusive effects (vertical mixing) in this part of the bay. Verticalmixing, were to dominate, would increase the surface salinity

along both western and eastern coasts. Northeasterly winds seemto cause small changes in surface salinity in the lower bay but
they do change the salinity distribution outside the bay. The
downwind transport associated with the northeasterly winddrives low salinity water southward of the bay entrance, along
the coast, consequently narrowing the outﬂow plume. Northwesterly winds drive water out of the bay and consequently thesalinity inside the bay must decrease. However, the salinity inAuthor's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

a

b

c

2455

d

Fig. 4. Anomaly of sea level between cases 1–4 and case 0.

a

b

c

d

Fig. 5. Horizontal distribution of surface salinity calculated for cases 1–4.

the upper and middle bay decreases only slightly and that in thelower bay has no apparent change (Fig. 5b). This is likely caused
by upwelling on the eastern coast and downwelling on thewestern coast in the upper bay plus the rebound of water outside

the bay. Details on the responses of exchange ﬂux through the bay
entrance to the winds will be presented in Section 3.5. Outside thebay, the low-salinity area has a similar distribution to that in thecase of northeasterly winds.

Author's personal copy
ARTICLE IN PRESS
2456

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

Southwesterly winds tend to reverse the sign of the east–west
salinity gradient in the upper and middle bay (Fig. 5c). In this case,the salinity becomes higher along the western coast than along
the eastern coast because of downwelling along the eastern coast
and upwelling along the western coast. As in other cases, thesalinity in the lower bay shows little change but outside the bay itshows a marked change in the structure of the plume (Fig. 5c). The
outﬂow plume is detached from the coast to the south of the bay
entrance and moves eastward and slightly northward. Southeasterly winds tend to weaken, relative to the control case, theeast–west salinity gradient in the upper and middle bays but
preserve the sign (Fig. 5d). Again, the salinity in the lower bay
changes little but outside the bay it is noticeably modiﬁed.
The subtidal currents in the surface layer are sensitive to thewind direction (Fig. 6). In the upper and middle bay, northeasterly
winds strengthen the surface outﬂow along the western coast(Fig. 6a). Outside the bay, northeasterly winds drive a coherent
current structure by combining the ambient ﬂow with thebuoyant coastal current from the plume (Fig. 6a). Northwesterly
winds intensify the outﬂow inside the bay and the outﬂow plumeoutside the bay (Fig. 6b). This intensiﬁcation of the plume ﬂow iscaused by the convergence of the southward ambient ﬂow at theoutﬂow plume (Fig. 6b). Southwesterly winds dramatically hinder
the surface outﬂow inside the bay but enhance the outﬂows fromthe Potomac and James Rivers to the main stem of Chesapeake Bay(Fig. 6c). Outside the bay, the outﬂow plume detaches from thecoast to the south of the bay entrance while eastward outﬂow
emanates from the bay entrance (Fig. 6c). Southeasterly winds
hamper the surface outﬂow inside the bay and even produce
opposite currents in the eastern portion at mid-bay (Fig. 6d).
Outside the bay, a northward current appears offshore of the bay
entrance, which collides with the ambient southward current at
approximately 37.51N (Fig. 6d).
Qualitatively, the response to wind of the subtidal surface
currents (Fig. 6) can be interpreted as the combination of theabcurrents following the wind direction (Hansen and Rattray, 1965;
Geyer, 1997), and that normal to the wind direction (Chao, 1988;
Fong and Geyer, 2001). The former is apparent in the upper andmiddle bay, where northwesterly winds reinforce the surface
outﬂow while southeasterly winds weaken it. The latter isapparent outside the bay. Through the combination of onshore
Ekman transport and sea-level setup near the coast, northeasterly
winds produce a coherent southwestward current along the coast.
Consequently, part of the coastal water is pushed into the bay andthe outﬂow plume from the bay entrance is slenderized. Southwesterly winds, in contrast, cause a withdrawal of water out of thebay and a detachment of the outﬂow plume from the coast to thesouth of the bay entrance.
The lower bay shows a relatively insensitive response to wind
forcing when compared to the bay as a whole. This is because thecurrents following the wind direction and those normal to thewind direction compete with each other there. For example,
northeasterly winds drive water from the upper to the lower bay
while they also drive coastal water into the lower bay, opposing
the southward ﬂows from the upper bay. As will be shown in
Section 3.5, the initial response to northwesterly winds, forinstance, is that the water inside the bay ﬂows out. However, as
the sea-level distribution shown in Fig. 4b is established, theﬂushing slows down and coastal water begins to enter the bay.
Then the lower bay goes back to the state prior to wind forcing.

3.3. Response of density-driven circulation to winds: verticalstructure after 2 days
The effect of winds on the vertical structure of salinity andsubtidal currents under bathymetric variations is illustrated at a
cross-section in the middle of the bay (Fig. 7) and at the bay
entrance (Fig. 8). In the middle of the bay, northeasterly winds
cause a westward migration and straightening of isohalines in thecFig. 6. Horizontal distribution of surface velocity calculated for cases 1–4.

dAuthor's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

2457

a

b

c

d

e

f

g

h

Fig. 7. Vertical distribution of salinity and along-estuary velocity along Section B calculated in cases 1–4. Negative values denote ﬂow toward the bay entrance. The units on
the abscissa represent the model grid number.

upper 10 m (Fig. 7a). The wind strengthens the landward inﬂow,
which extends further up to the surface, relative to no-winds,causing transverse shears in the subtidal currents (Fig. 7b).
Northwesterly winds change the salinity ﬁeld the least whencompared to the other wind directions (Fig. 7c). On the other
hand, these winds strengthen the two-layer circulation (Fig. 7d).
Southwesterly winds tend to mix the water column (Fig. 7e) andto reverse the pre-existing estuarine circulation (Fig. 7f). The
response consists of downwind ﬂows along the shallow coastalsides and upwind ﬂow along the deep channel of the bay. In otherwords, southwesterly winds change the pre-existing verticallysheared circulation to a horizontally sheared circulation in the
middle and upper bay. Southeasterly winds cause a similar but
stronger impact than southwesterly winds on the salinity andsubtidal ﬁelds (Fig. 7g and h).
At the bay entrance, the effect of winds on the verticalstructure of salinity and subtidal currents under bathymetricvariations (Fig. 8) seems more complex than in the middle andupper bay (Fig. 7). Northeasterly winds drive coastal waters into
the bay and cause near-surface salinity increments, particularly inthe northern portion of the bay entrance (Fig. 8a). North of
Chesapeake Channel (412 in the abscissa of Fig. 8a) watercolumn stratiﬁcation is rather weak. It is noteworthy that thesalinity in the deepest part of Chesapeake Channel decreases
relative to the no-wind case (Fig. 3e). This salinity drop illustrates
the effects of vertical mixing with the low salinity outﬂow of thesurface layer. The subtidal currents show more transverse
variability under northeasterly winds (Fig. 8b) than under nowinds (Fig. 3f). The inﬂow area extends up to the surface while theoutﬂow along the southern coast is maintained. The outﬂow in
the North Channel is slightly weakened by the onshore transportof coastal water.
Northwesterly winds slightly weaken the stratiﬁcation of thesurface layer at the bay entrance (Fig. 8c) relative to the control(no wind) case (Fig. 3e). At the same time, these winds produce a
decrease in the salinity below 10 m depth in the ChesapeakeAuthor's personal copy
ARTICLE IN PRESS
2458

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

a

b

c

d

e

f

g

h

Fig. 8. Vertical distribution of salinity and along-estuary velocity along Section C calculated in cases 1–4. Negative values denote outﬂow from the bay entrance. The units
on the abscissa represent the model grid number.

Channel. They also intensify the outﬂow in the upper layer andinﬂow in the lower layer of the Chesapeake Channel (Fig. 8d). The
ﬂow in the North Channel does not change appreciably (Fig. 8d).
Southwesterly winds show a marked inﬂuence of coastal wateron the salinity and subtidal current ﬁelds at the bay entrance (Fig.
8e and f). The slope of isohalines is reversed in such a way that thesalinity is high in the southern part and low in the northern part(Fig. 8e). This is caused by the wind-induced upwelled waters thatappear most prominently off Cape Henry, at the southern end of
the transect, and in the deepest part (410 m depth) of Chesapeake
Channel. The two-layer structure of the subtidal currents is
intensiﬁed by the upwelling-type exchange ﬂow, i.e., downwind
ﬂow at the surface and upwind ﬂow underneath (Fig. 8f).
Southeasterly winds drive coastal water with higher salinity
into the bay, which can be found in the entire water column at
the bay entrance (Fig. 8g). However, volume outﬂow, and notinﬂow, dominates the entire section. This is, in fact, caused

by a rebounding ﬂux of water inside the bay as explained in
Section 3.5.
3.4. Response of density-driven circulation to sea-level change at bay
entrance
On the basis of observations, Paraso and Valle-Levinson (1996)
proposed that sea level at the bay entrance (Zmouth) can bepredicted from eastward (tx) and northward (ty) components ofwind stresses, as well as barometric pressure (Pa) through therelationship:

Zmouth ¼ 10:58  ½1:06ty þ 1:63tx þ 10:42  105 Pa.

(1)

Here, the effect of barometric pressure changes is not considered and a value of pressure at equilibrium (1.0153  105 Pa) isused. The maximum values of sea-level setup corresponding toAuthor's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

northeasterly, northwesterly, southwesterly, southeasterly winds
are 26.9, 5.3, 26.9, and 5.3 cm, respectively. During the periodof 3 days of a wind pulse, the sea level is ramped up (or down) to
its extreme value in the ﬁrst 12 h; then it is maintained for 2 days;
and then it drops (or increases) to zero in the ﬁnal 12 h. Such sealevel change was added along the open boundary to examine theresponse of the pre-existing estuarine circulation.
The imposed sea-level changes in cases 5–8 differ only in theirmagnitude or in the order of rising or dropping. Hence, the resultsof one case are easily applicable to the other cases. Only the
results of case 5, a sea-level change presumed from a north-2459

easterly wind but without direct wind stress prescription, arepresented. A rapid response occurred in the sea level inside thebay as shown in Fig. 9a, which is the difference in sea level along
the thalweg of the bay between case 5 and case 0. As expected, thesea level at the bay entrance (540 in the abscissa of Fig. 9a)
rapidly rose to a large value in the ﬁrst 12 h, kept a high sea levelwith a maximum value larger than 25 cm in the following 2 days,
and ﬁnally dropped to zero.
Dynamically, the gradient of sea level rather than sea level
itself affects ﬂow ﬁelds (Fig. 9b). At the stage of sea-level rising,
the sea level is higher at bay entrance than in the upper bay by

a

b

c

d

e

f

Fig. 9. (a) Anomaly of sea level between case 5 and case 0 along Section A; (b) difference of sea level between each grid point along Section A and the upper bay (gridnumber ¼ 1) at the same time as in panel (a); (c) the same as (a) but for case 1C and case 0; (d) the same as (b) but for panel (c); (e) the same as (a) but for case 1C and case5; (f) same as (b) but for panel (e). The number in the contours is in centimeter, the units on the abscissa represent the model grid number along section A.

Author's personal copy
ARTICLE IN PRESS
2460

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

410 cm. At the mature stage of the wind, the sea-level difference
between bay entrance and upper bay is small (o5 cm). Finally, atthe stage of sea-level drop, the situation reverses from the stage ofsea-level rising. Spatially, the gradient in sea level caused byremote wind effects is large (maximum of 15 cm) in the lower bay
and decreases toward the upper bay.
The inclusion of wind stresses and sea-level setup (aspredicted by Eq. (1); case 1C) causes the sea level inside the bay(Fig. 9c) to be less uniform than case 5 (Fig. 9a). A maximum sealevel difference between bay entrance and upper bay reached
430 cm (Fig. 9d). The difference between case 1C (both windstresses and remote effects) and case 5 (only remote effects)

shows that wind stress contributes more to the sea level inside
the bay (Fig. 9e) and to the sea-level gradient along the bay(Fig. 9f) than the remote effect. The sign of the sea-level gradientinside the bay caused by wind stress does not depend on thepresence (Fig. 9f) or absence (Fig. 4a) of remote effects. Fig. 9 also
indicates that wind stress contributes roughly two thirds (420 cm
out of 430 cm) of sea-level difference between the bay entrance
and the upper bay. Remote effects contribute the remaining one
third. This ratio is kept in the case of southwesterly winds, but
drops to a lower value in the cases of northwesterly andsoutheasterly winds when a lower sea-level change (5.3 cm) wasprescribed along the open boundary of model domain.

a

b

c

d

e

f

Fig. 10. Horizontal distribution of surface velocity (a–c) and salinity (d–f) calculated for case 5, at 6 h of day 248, 12 h of day 249, and 18 h of day 250.

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

Fig. 9b shows that remote effects on subtidal ﬂow are strongest
at 6 h of day 248 and 18 h of day 250. The seaward pressure
gradient at 6 h of day 248 acted against the seaward surface ﬂow
and weakened it in the lower bay (Fig. 10a). Analogously, thelandward pressure gradient at 18 h of day 250 enhanced theseaward surface ﬂow in the lower bay (Fig. 10c). Between those
two days (Fig. 10b), the subtidal ﬂow was very similar to its
original state (Fig. 2b), which indicates that the perturbation on
subtidal ﬂow due to sea-level change at the bay entrance canvanish in a day or so. The remote effects on surface salinity
are generally small and restricted only to near the bay entrance(Fig. 10d–f). Compared with Fig. 2a, the salinity contours at 6 h on
day 248 slightly shifted into the bay because of the weakening ofseaward surface ﬂow. As the seaward surface ﬂow increased on
day 250, the lowest salinity water appeared at southern side of thebay entrance (see position of isohaline 24 in Fig. 10f).
According to the solution by Wong (1994), the current caused
by a subtidal sea-level oscillation at the entrance to an estuary isin the same direction throughout the cross-section. Therefore, thesurface salinity change near the bay entrance (Fig. 10d–f) is
expected to be consistent throughout the entire water column.
This is conﬁrmed in Fig. 11 where the surface outﬂow and thebottom inﬂow of Fig. 3f were weakened and enhanced, respectively, by the rising of sea level at 6 h of day 248 (Fig. 11d) whilesalinity increased at the entire transect (Fig. 11a). At 12 h of day
249, salinity kept increasing but the cross-section ﬂow approached the original state (Fig. 3f). At 18 h of day 250, thesalinity nearly returned to its initial state (Fig. 3e) while surface

2461

outﬂow and bottom inﬂow were enhanced and weakened,
respectively, by the sea-level drop. The difference in the crosssection ﬂow between the case with remote effects and the control
case presents a unidirectional ﬂow through the bay entrance withlargest speed above the deepest channel (Fig. 11g–i). All of thesefeatures are consistent to the solution given by Wong (1994).

3.5. Volume transport through the bay entrance due to winds
The inﬂuence of wind forcing on water exchange in Chesapeake
Bay is illustrated by hourly volume transports through the section
at the bay entrance (Figs. 12 and 13). The volume transports
shown in Figs. 12 and 13 actually represent the difference between
cases with winds and the case without winds, i.e., the volumetransport due to winds. Volume inﬂows and outﬂows respondquickly to the onset of wind forcing on day 247 (Fig. 12) and sealevel change at 12 h of day 247 (Fig. 13a and b), regardless of thewind direction. After the wind stops, it takes 3 days for theinﬂow and outﬂow to return to their original state.
For local wind responses, northeasterly winds produce6000–8000 m3/s of volume outﬂow in the ﬁrst 12 h andmaintain it for 2 days (Fig. 12a). Inﬂows develop simultaneously
but their magnitude is lower than the outﬂows. Consequently, net
outﬂows appear on day 249. This response seems to beinconsistent with onshore Ekman transport but is consistent withsea level decreasing in the upper and middle bays (Fig. 4a) as
explained with observations by Valle-Levinson et al. (2001). After

a

d

g

b

e

h

c

f

i

Fig. 11. Vertical distribution of salinity (left panels) and along-estuary velocity (middle panels) calculated by case 5, and difference of along-estuary velocity between case 5
and case 0 (right panels) along Section C, at 6 h of day 248, 12 h of day 249 and 18 h of day 250. Negative values in middle and right panels denote outﬂow from the bay
entrance. The units on the abscissa represent the model grid number.

Author's personal copy
ARTICLE IN PRESS
2462

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

a

b

c

d

Fig. 12. Temporal variation of volume inﬂow (negative values), volume outﬂow (positive values) and net water ﬂuxes through the bay entrance (Section C) between cases
1–4 and case 0.

day 249, the volume in the bay ‘bounces back’ as inﬂows exceed
outﬂows. The net volume inﬂow increases until the windcompletely stops and the maximum inﬂow of 3000 m3/s isreached. After the wind stops, inﬂows and outﬂows decrease
simultaneously while net inﬂows gradually approach zero.
Southwesterly winds produce the opposite response to northeasterly winds (Fig. 12c). The volume inﬂow in this case reaches
10,000–12,000 m3/s in the ﬁrst 12 h but soon begins to decrease.
The inﬂow exceeds the outﬂow during most of the wind pulse,
being consistent with the sea level increasing in the middle andupper bays (Fig. 4c). After day 249, the outﬂow exceeds the inﬂow
and results in net outﬂow that reaches a maximum of 4000 m3/s
at the end of the wind pulse. After that, like in the case ofnortheasterly winds, both the inﬂow and outﬂow decrease and thenet ﬂux approaches zero.
Northwesterly (Fig. 12b) and southeasterly (Fig. 12d) winds
cause the largest volume ﬂuxes in the cases for local wind effects.
This is likely because northwesterly and southeasterly winds act
concurrently inside and outside the bay whereas northeasterly
and southwesterly winds act in opposing directions inside andoutside the bay. For example, northeasterly winds drive water outof the bay within the estuary but at the same time they drive
water toward the lower bay from the ocean. Northwesterly winds
cause a net outﬂow of 16,000 m3/s in only 1 day. After that theoutﬂow weakens and inﬂow increases greatly. As the winds stop,
the inﬂow reaches a value of 16,000 m3/s and the outﬂow

vanishes. After that the inﬂow approaches gradually to zero. The
response to southeasterly winds is opposite to that of northwesterly winds but the features are similar.
Volume ﬂows indicate that the wind response during transition periods (ﬁrst and ﬁnal 12 h) depends on the wind direction(Fig. 12). Northeasterly and southwesterly winds produce bidirectional exchange ﬂows, while northwesterly and southeasterly
winds tend to produce only volume inﬂow or outﬂow in the entire
section. During the periods of mature state of the wind (between
the two transition periods), bidirectional ﬂows can be found in allcases. For northeasterly and southwesterly winds, the bidirectional volume ﬂows are maintained throughout the mature wind
period. For northwesterly and southeasterly winds, the bidirectional volume exchange develops gradually. The sea-level slopes
induced by northwesterly winds (Fig. 4b) cause a gradualdevelopment of volume inﬂow. Similarly, the gradual development of volume outﬂow in the case of southeasterly winds iscaused by the sea-level slopes (set up toward the upper bay,
Fig. 4d).
The remote effect due to northeasterly winds produces
20,000 m3/s of volume inﬂow and practically no volume outﬂow
in the ﬁrst 18 h (Fig. 13a). The volume inﬂow reaches its maximum
value at 6 h on day 248, when the seaward sea-level gradient at
the bay entrance is greatest (Fig. 9b). After the maximum volume
inﬂow, the transport starts to drop gradually with the reduction of
the seaward sea-level gradient at the bay entrance (Fig. 9b). The

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

2463

a

b

c

d

Fig. 13. Same as Fig. 12 but for those between case 5 and case 0 (a), between case 6 and case 0 (b), between case 1C and case 0 (c), and between case 2C and case 0 (d).

volume inﬂow becomes zero as the sea level at bay entrance
reaches its maximum at 0 h of day 250, corresponding to nearlyzero sea-level gradient (Fig. 9a). Subsequently, volume outﬂow
appeared along with landward sea-level gradient at the bay
entrance, reaching 20,000 m3/s at 18 h of day 250, and thengradually drops to zero (Fig. 13a).
The remote effects due to northwesterly winds cause a volume
outﬂow ﬁrst and then a volume inﬂow (Fig. 13b). The maximum
volume ﬂuxes (4000 m3/s) are one-ﬁfth of those produced bynortheasterly winds. This is because the sea-level changeprescribed at the open boundary is 5.3 cm for northwesterly
winds compared to 26.9 cm for northeasterly winds.
The analytical solution of Wong (1994) suggests that the local
response to winds consists of bidirectional currents while theremote effect causes unidirectional currents. Following thatsolution, volume inﬂows and outﬂows are of the same order ofmagnitude and both of them are larger than the net volume ﬂow if
the local effect dominates. If the remote effect dominates, either
the volume inﬂow or the outﬂow is much larger than the otherand is comparable to the net ﬂux. In the middle and upper bay, thelateral distribution of current caused by local wind stresses (Fig. 7)
and the landward reduction of response in ﬂow ﬁelds to sea-levelchange prescribed at the open boundary of the model domain(Fig. 10) suggest that the local effect of wind dominates. At the bay
entrance, the remote effect given by a sea-level change at the open
boundary produces only volume inﬂows or outﬂows (Fig. 13a andb), and therefore dominates the volume ﬂuxes there.

In his estimate for remote effects of wind, Wong (1994) usedsea-level setup or set-down at a constant rate as the only forcing.
This formulation suggests that the remote effects are proportional
to the rate of change of subtidal sea-level change at the bay
entrance. Therefore, the relation between volume inﬂow or
outﬂow and the rate of sea-level rise or drop at the open
boundary (Fig. 13a and b) is actually controlled by the rate of sealevel rise or drop at the bay entrance. In the calculations presented
here, all wind events span the same period and therefore the rateof sea-level change is proportional to the values given in Table 1.
In a limiting case such as at steady state, the remote effectapproaches zero (Wong and Valle-Levinson, 2002). This also
occurs in the model results as the sea level at the bay entrance
reaches the highest level while the landward sea-level gradientdisappears (Fig. 9a and b).
The combination of local and remote wind effects suggests thateither of these two dominate at different periods of a wind pulse.
For northeasterly winds (Fig. 13c), because of the lag between sealevel change and local winds (Paraso and Valle-Levinson, 1996),
the initial response is the appearance of bidirectional volume
ﬂows due to local effects. The remote effects gradually increase
and soon overcome the local effects. At the end stage of anortheasterly wind pulse, the local effects dominate again. As thewind stresses completely stop and the sea level at the bay
entrance drops, the remote effects become dominant again. For
northwesterly winds (Fig. 13d), except for the end stage whenbidirectional volume ﬂows overcome the net volume transport,

Author's personal copy
ARTICLE IN PRESS
2464

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

NE

NE

NE

a1

b1

NW

NW

NW

a2

c1

b2

c2

a3

SW

SW

b3

SW

c3

a4

SE

SE

b4

SE

c4

Fig. 14. Vertical distribution of along-estuary velocity, parallel to Section A (left panels), normal to Section B (middle panels) and normal to Section C (right panels)
calculated by the winds given in cases 1–4 but with a constant density throughout the model domain. The units on the abscissa represent the model grid number.

unidirectional volume transports are dominant role of remote
effects under northwesterly winds appears even in the calculation
for local wind forcing (Fig. 12b). This is evident during thetransition periods, as the wind stress increases in the ﬁrst 12 h or
decreases in the last 12 h.

4. Discussion
4.1. Wind-induced currents under homogeneous conditions
The linear superposition of wind-induced currents underhomogeneous conditions and estuarine currents has been usedin several studies (e.g., Hansen and Rattray, 1965; Wong, 1994;
Geyer, 1997). Following this approach, wind-induced currents
were obtained under homogeneous conditions (constant water

density) throughout the bay and without tide. These calculations
are denoted as case 1H to case 4H, hereafter. It should be notedthat the wind-induced currents under homogenous condition in
an idealized bathymetry with or without Earth’s rotation havebeen studied extensively (e.g., Csanady, 1982; Hunter and Hearn,
1987; Hearn et al., 1987; Wong, 1994; Friedrichs and Hamrick,
1996; Mathieu et al., 2002; Winant, 2004; Sanay and ValleLevinson, 2005).
Under homogeneous conditions, the wind-induced currents
inside the bay are affected by bathymetry. Bathymetric effects on
ﬂows are best illustrated in cross-sections (Fig. 14). Along thethalweg of the bay, the currents are persistently upwind(Fig. 14a1–a4). This feature is consistent with analytical solutions(e.g., Wong, 1994; Winant, 2004) in the sense that the current in
the deep portions of a transverse section is upwind and that overthe shallow portions is downwind. In addition to this transverse

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

structure, analytical solutions also indicate that the upwind
current is bottom-intensiﬁed while the downwind current issurface-intensiﬁed. All these features can be observed at thesection in middle bay (Fig. 14b1–b4) and at the bay entrance inthe cases of northwesterly and southeasterly winds (Fig. 14c2 andc4). In the cases of northeasterly and southwesterly winds, thewater at the bay entrance responds not only to the wind stressinside the bay but also to the onshore or offshore transport
outside the bay. The vertical structure shows that the inﬂow or
outﬂow in the northern part of bay entrance (410 in the abscissaof Fig. 14c1 and c3) is not limited to the surface layer but occurs in
the entire water column. At the same time, an opposite ﬂow
develops in the entire water column in Chesapeake Channel,
resulting in appreciable lateral variability in this section (Fig. 14c1
and c3).

NE

NE

c1

NW

NW

a2

a4

The differences in the subtidal currents between cases 1–4 andcase 0 represent the response of estuarine circulation to winds(Fig. 15). Comparison of such differences with the wind-induced
currents in the homogeneous condition (Fig. 14) clearly illustrates
the inﬂuence of density gradients (both horizontal and verticalgradients) on the response of the subtidal ﬂow to winds. The
density gradients cause the wind-induced currents to show morevertical structure (Fig. 15) than under homogeneous conditions.
For northwesterly and southeasterly winds, the currents along thethalweg are downwind at the surface and upwind underneath(Fig. 15a2 and a4). Under northeasterly and southwesterly winds,
the ﬂow shows a two-layer or even three-layer structure (Fig. 15a1
and a3).

b1

NW

a3

4.2. Effects of density gradients on the response of the bay to winds

NE

a1

2465

b2

SW

SE

SW

SE

b3

b4

Fig. 15. Same as Fig. 14 but for the difference between cases 1–4 and case 0.

c2

SW

c3

SE

c4

Author's personal copy
ARTICLE IN PRESS
2466

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

a0

b0

b1

c1

NW

NW

NW

a2

NE

NE

NE

a1

c0

b2

c2

a3

SW

b3

SW

c3

SW

a4

SE

b4

SE

c4

SE

Fig. 16. Distribution of eddy viscosity along Section A (left panels), along Section B (middle panels) and along Section C (right panels) calculated for case 0 (top panels) andcases 1–4.

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

The vertical structure of the wind-induced currents in thepresence of stratiﬁcation is also illustrated in the mid-bay
section (Fig. 15b1–b4). For northeasterly winds, a relatively weak(o5 cm/s) down-estuary current on the shoals separates astronger (410 cm/s) up-estuary current in the channel (Fig.
15b1). Also, a three-layer structure develops over the western
shoal. Northwesterly winds produce a similar ﬂow pattern as forthe homogeneous condition but the upwind surface current is
weaker (Fig. 15b2). Southwesterly and southeasterly winds
produce a well-developed two-layer structure of wind-induced
currents, which is downwind at the surface and upwind underneath (Fig. 15b3 and b4).
In the presence of stratiﬁcation, the wind-driven ﬂow is
conﬁned to a surface layer at the bay mouth (Fig. 15c1 and c3).

NE

a1

Northeasterly winds drive water into the bay within the upper
5 m, while southwesterly winds drive water out of the bay. In the
Chesapeake Channel, these winds produce bidirectional exchange
ﬂows that differ from the unidirectional ﬂows arising underhomogeneous conditions (Fig. 14c1 and c3). Northwesterly
and southeasterly winds also produce a two-layer structurethat differs from the one-layer response under homogeneousconditions.
As shown above, wind-driven currents over laterally variable
bathymetry are signiﬁcantly different from stratiﬁed to homogeneous conditions. Wind-induced currents under stratiﬁed
conditions tend to be vertically sheared while those in homogeneous conditions tend to be horizontally sheared. This isconsistent with the ﬁndings of Lentz (2001) on the continental

b1

a2

NE

NE

c1

NW

NW

NW

2467

b2

c2

a3

SW

b3

SW

c3

SW

a4

SE

b4

SE

c4

SE

Fig. 17. Same as Fig. 16 but for cases 1H–4H, in which the density is constant throughout the model domain.

Author's personal copy
ARTICLE IN PRESS
2468

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

a

b

c

d

e

Fig. 18. Vertically averaged vertical eddy viscosity coefﬁcients (ordinate, in units of cm2/s1) versus water depth (abscissa, in units of meter) in case 0 (top panel), cases 1–4(black symbols in the middle and bottom panels), and cases 1H–4H (red symbols in the middle and bottom panels). Note: (a) No Wind, (b) NE Wind, (c) NW Wind, (d) SW
Wind and (e) SE Wind.

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

2469

a

b

c

d

e

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Fig. 19. Ratio of Ekman depth ( 2K v =f , Kv ¼ vertically averaged eddy viscosity, f ¼ Coriolis parameter) to water depth (ordinate) versus water depth (abscissa, in units ofmeter) for case 0 (top panel), cases 1–4 (black symbols in the middle and bottom panels), and cases 1H–4H (red symbols in the middle and bottom panels). Note: (a) No
Wind, (b) NE Wind, (c) NW Wind, (d) SW Wind and (e) SE Wind.

Author's personal copy
ARTICLE IN PRESS
2470

X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

shelf. Two causes should be responsible for this different responsein the model experiments. The ﬁrst cause is the change in thedensity ﬁeld, namely the horizontal density gradient, caused bywinds. A change in horizontal density gradients would modify the
pre-existing estuarine circulation. However, the horizontal distribution of salinity (Fig. 5) suggests that wind-induced modiﬁcations are localized but are small at the scales of the entire bay andcannot explain the different current structures shown in Figs. 14
and 15. The second cause is the wind-induced structure of the
turbulence ﬁeld. As shown by Kasai et al. (2000) and ValleLevinson et al. (2003), increased internal friction tends to enhance
the transverse structure of the subtidal currents. Examination of
the vertical eddy viscosity coefﬁcients for cases 0–5 and 1H–4H
illustrates the different structure of the wind-induced currents forthe homogeneous and stratiﬁed conditions driven by the samewind condition.

4.3. Wind-induced mixing and Ekman depth
In the cases that included wind forcing, the vertical eddy
viscosity coefﬁcient calculated by the Mellor-Yamada turbulent
closure model increases signiﬁcantly at mid-depth (Fig. 16).
Without winds (Fig. 16a0–c0), the eddy viscosity coefﬁcients arelarge only near the bottom, particularly at the bay entrance,
resulting from tidal currents (Guo and Valle-Levinson, 2007). As
winds are imposed, the eddy viscosity coefﬁcients increasesigniﬁcantly at mid-depth and maximum values reach
10–200 cm2/s. The vertical eddy viscosities increase the least in
the case of northwesterly winds, which cause the least destratiﬁcation (Figs. 7 and 8). Interestingly, without stratiﬁcation, thevertical eddy viscosities depend little on the wind direction(Fig. 17). The eddy viscosities are larger in the homogeneous cases
than in the corresponding stratiﬁed cases and the areas with
coefﬁcients 4100 cm2/s are widespread. Because the vertical
proﬁle of eddy viscosity in neutral conditions (destratiﬁed, nobuoyancy forcing) from the Mellor-Yamada level 2.5 turbulence
closure is parabolic (see Fig. 6 in Lentz, 2001), the largest values
appear at mid-depth and over the deepest places of a crosssection. When plotting the vertically averaged eddy viscosity
versus the water depth for the grids inside the bay, a quasi-linear
relation is obtained (red symbols in Fig. 18). This is consistent withthe depth-dependent formulation used in other studies (e.g.,Friedrichs and Hamrick, 1996).
A linear relationship between eddy viscosity and water depth
does not hold, however, in the presence of stratiﬁcation,
regardless of the presence or absence of winds (Fig. 18). In thecase of no wind, an eddy viscosity near 0 cm2/s can be found for all
depths. The tidal currents around the bay mouth contribute to therelatively large values for depths of 5–20 m. The prescription ofwinds causes an increase of the minimum eddy viscosity to
5–10 cm2/s and also a signiﬁcant increase for all depths. It isnoteworthy that the maximum eddy viscosities for depths
between 5 and 20 m exceed those for the homogeneous cases,
most clearly for the cases of northeasterly and southeasterly
winds.
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
The ratio of Ekman layer depth ( 2K v =f , Kv ¼ verticallyaveraged eddy viscosity, f ¼ Coriolis parameter) versus the water
depth is plotted for cases 0–4 and 1H–4H in Fig. 19. The ratio of
0.6–1.6 in the homogeneous cases (red symbols in Fig. 19)
indicates that bathymetry molds the wind-driven current inside
the bay. This is because the Ekman layer occupies all or most of
the water column. The presence of stratiﬁcation reduces the
Ekman layer depth and in the deep channel (20–40 m) the ratio
becomes typically o0.2 (no wind in Fig. 19). Wind forcing
increases the ratio (typically 40.2) for all depths and also theminimum ratio over the shallow places increases markedly. The
presence of stratiﬁcation limits the Ekman layer depth andreduces bathymetric effects. For all depths, the ratio decreases
relative to homogeneous conditions. Therefore, the wind-induced
variations in the ﬂow ﬁeld tend to have a vertically sheared twolayer structure (Fig. 15). In the homogeneous cases, the Ekman
layer depth reaches the same order as the water depth (Fig. 19)
and therefore bathymetric effects appear clearly in the laterally
sheared wind-driven ﬂow (Fig. 14).

5. Summary
In this study, the response of the density-driven (estuarine)
circulation in Chesapeake Bay to winds from four directions andthe induced sea-level changes outside the bay is investigated. In
general, northeasterly and northwesterly winds enhance theestuarine circulation inside the bay while southeasterly andsouthwesterly winds weaken it. In the lower bay, the response
is different because the wind-driven onshore transport (fornortheasterly winds) or offshore transport (for southwesterly
winds) outside the bay competes with the downwind transport
within the bay. Remote wind effects dominate volume transports
through the bay entrance. However, the local effect is the main
responsible for sea-level slopes that drive the ﬂows and salinity
ﬁelds in most of the bay under stratiﬁed conditions.
The response of the bay to wind depends on whether the watercolumn is stratiﬁed or not. The absence of stratiﬁcation allows thedevelopment of Ekman layers that attain depths of the same orderas the water depth. Consequently, bathymetric effects become
prominent on the ﬂow structure and the wind-induced ﬂow inside
the bay is laterally sheared because of the appearance ofdownwind ﬂow over the ﬂanks and upwind ﬂow in the channel.
In the presence of stratiﬁcation, Ekman layers attain shallower
depths than in the absence of stratiﬁcation. Therefore, the windinduced currents are less inﬂuenced by bathymetry and become
vertically, rather than laterally, sheared with downwind ﬂow at
the surface and upwind ﬂow underneath.
The change of orientation of the Chesapeake Bay axis in thelower bay is crucial to cause different responses to winds fromthe upper-mid bay to the lower bay. It should be noted that thestratiﬁcation that develops in the control case is produced by theannual river discharge and it is usually weaker than the real
springtime situation. The imposed winds are also idealized. In the
future, the inﬂuence of variations in river discharge and thetemporal and spatial variations in the wind ﬁeld need to beaddressed.

Acknowledgments
X. Guo acknowledges support by Grant-in-Aid for Global COE
Program from the Ministry of Education, Culture, Sports, Science,
and Technology, Japan (MEXT); and the Japan Society for the
Promotion of Science (JSPS). A.V.L. acknowledges support fromNSF Projects 0551923 and 0603540.
References
Beardsley, R.C., Boicourt, W.C., 1981. On estuarine and continental shelf circulationin the Middle Atlantic Bight. In: Warren, B.A., Wunsch, C. (Eds.), Evolution of
Physical Oceanography. The MIT Press, pp. 198–233.
Chao, S.-Y., 1988. Wind-driven motion of estuarine plumes. Journal of Physical
Oceanography 18, 1144–1166.
Csanady, G.T., 1982. Circulation in the Coastal Ocean. D. Reidel, 279pp.
Elliott, A.J., 1978. Observations of the meteorologically induced circulation in the
Potomac estuary. Estuarine, Coastal and Shelf Science 6, 285–300.

Author's personal copy
ARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 28 (2008) 2450–2471

Epifanio, C.E., Garvine, R.W., 2001. Larval transport on the Atlantic continental shelfof North America: a review. Estuarine, Coastal and Shelf Science 52, 51–77.
Friedrichs, C.T., Hamrick, J.M., 1996. Effects of channel geometry on cross sectionalvariations in along channel velocity in partially stratiﬁed estuaries. In: Aubrey,
D. (Ed.), Buoyancy Effects on Coastal and Estuarine Dynamics, Coastal andEstuarine Studies, 53. American Geophysical Union, pp. 283–300.
Geyer, W.R., 1997. Inﬂuence of wind on dynamics and ﬂushing of shallow estuaries.
Estuarine, Coastal and Shelf Science 44, 713–722.
Goodrich, D.M., Boicourt, W.C., Hamilton, P., Pritchard, D.W., 1987. Wind-induced
destratiﬁcation in Chesapeake Bay. Journal of Physical Oceanography 17,
2232–2240.
Guo, X., Valle-Levinson, A., 2007. Tidal effects on estuarine circulation and outﬂow
plume in the Chesapeake Bay. Continental Shelf Research 27, 20–42.
Fong, D.A., Geyer, W.R., 2001. Response of a river plume during an upwellingfavorable wind event. Journal of Geophysical Research 106, 1067–1084.
Hanawa, K., Mitsudera, H., 1985. On daily average of oceanographic data. Coastal
Oceanographic Bulletin 23, 79–87 (in Japanese).
Hansen, D.V., Rattray Jr., M., 1965. Gravitational circulation in straits and estuaries.
Journal of Marine Research 23, 104–122.
Hargis, W.J., 1980. A Benchmark Multi-Disciplinary Study of the Interaction
Between the Chesapeake Bay and Adjacent Waters. Chesapeake Bay Plume
Study Superﬂux 1980. NASA Conference Publication 2188, Williamsburg, VA,
pp. 1–14.
Hearn, C.J., Hunter, J.R., Heron, M., 1987. The effects of a deep channel on the windinduced ﬂushing of a shallow bay or harbor. Journal of Geophysical Research
92, 3913–3924.
Hunter, J.R., Hearn, C.J., 1987. Lateral and vertical variations in the wind-driven
circulation in long, shallow lakes. Journal of Geophysical Research 92,
13106–13114.
Kasai, A., Hill, A.E., Fujiwara, T., Simpson, J.H., 2000. Effect of the earth’s rotation on
the circulation in regions of freshwater inﬂuence. Journal of GeophysicalResearch 105, 16961–16969.
Lentz, S.J., 2001. The inﬂuence of stratiﬁcation on the wind-driven cross-shelfcirculation over the North Carolina shelf. Journal of Physical Oceanography 31,
2749–2760.
Mathieu, P.P., Deleersnijder, E., Cushman-Roisin, B., Beckers, J.M., Bolding, K., 2002.
The role of topography in small well mixed bays, with application to the lagoonof Mururoa. Continental Shelf Research 22, 1379–1395.

2471

Mellor, G.L., 2004. Users guide for a three-dimensional, primitive equation,
numerical ocean model, 53pp. Program in Atmosphere and Ocean. Science,Princeton University.
Paraso, M.C., Valle-Levinson, A., 1996. Meteorological inﬂuences on sea level andwater temperature in the lower Chesapeake Bay: 1992. Estuaries 19, 548–561.
Salas-Monreal, D., Valle-Levinson, A., 2008. Sea level slopes and volume ﬂuxes
produced by atmospheric forcing in estuaries: Chesapeake Bay case study.
Journal of Coastal Research 24, 208–217.
Sanay, R., Valle-Levinson, A., 2005. Wind-induced circulation in semienclosed
homogeneous, rotating basins. Journal of Physical Oceanography 35,
2520–2531.
Seitz, R.C., 1971. Temperature and salinity distributions in vertical sections along
the longitudinal axis and across the entrance of the Chesapeake Bay (April
1968 to March 1969). Chesapeake Bay Institute, The Johns Hopkins University,
99pp.
Valle-Levinson, A., Li, C., Royer, T.C., Atkinson, L.P., 1998. Flow patterns at the
Chesapeake Bay entrance. Continental Shelf Research 18, 1157–1177.
Valle-Levinson, A., Wong, K.-C., Bosley, K.T., 2001. Observations of the windinduced exchange at the entrance to Chesapeake Bay. Journal of Marine
Research 59, 391–416.
Valle-Levinson, A., Wong, K.-C., Bosley, K.T., 2002. Response of the lower
Chesapeake Bay to forcing from Hurricane Floyd. Continental Shelf Research
22, 1715–1729.
Valle-Levinson, A., Reyes, C., Sanay, R., 2003. Effects of bathymetry, friction, androtation on estuary–ocean exchange. Journal of Physical Oceanography 33,
2375–2393.
Wang, D.P., 1979. Wind-induced circulation in the Chesapeake Bay, winter 1975.
Journal of Physical Oceanography 9, 564–572.
Weisberg, R.H., 1976. The nontidal ﬂow in the Providence River of Narragansett
Bay: a stochastic approach to estuarine circulation. Journal of Physical
Oceanography 6, 721–734.
Winant, C.D., 2004. Three-dimensional wind-driven ﬂow in an elongated, rotatingbasin. Journal of Physical Oceanography 34, 462–476.
Wong, K.-C., 1994. On the nature of transverse variability in a coastal plain estuary.
Journal of Geophysical Research 99, 14209–14222.
Wong, K.-C., Valle-Levinson, A., 2002. On the relative importance of the remote andlocal wind effects on the subtidal exchange at the entrance to the Chesapeake
Bay. Journal of Marine Research 60, 477–498.