ARTICLE IN PRESS

Continental Shelf Research 27 (2007) 20–42
www.elsevier.com/locate/csr

Tidal effects on estuarine circulation and outﬂow plume in the
Chesapeake Bay
Xinyu Guoa,, Arnoldo Valle-LevinsonbaCenter 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, USAb

Received 10 January 2006; received in revised form 17 August 2006; accepted 30 August 2006
Available online 1 November 2006

Abstract
The response of the Chesapeake Bay to river discharge under the inﬂuence and absence of tide is simulated with anumerical model. Four numerical experiments are examined: (1) response to river discharge only; (2) response to riverdischarge plus an ambient coastal current along the shelf outside the bay; (3) response to river discharge and tidal forcing;and (4) response to river discharge, tidal forcing, and ambient coastal current. The general salinity distribution in the fourcases is similar to observations inside the bay. Observed features, such as low salinity in the western side of the bay, areconsistent in model results. Also, a typical estuarine circulation with seaward current in the upper layer and landward
current in the lower layer is obtained in the four cases. The two cases without tide produce stronger subtidal currents thanthe cases with tide owing to greater frictional effects in the cases with tide. Differences in salinity distributions among thefour cases appear mostly outside the bay in terms of the outﬂow plume structure. The two cases without tide produce an
upstream (as in a Kelvin wave sense) or northward branch of the outﬂow plume, while the cases with tide produce an
expected downstream or southward plume. Increased friction in the cases with tide changes the vertical structure of outﬂow
at the entrance to the bay and induces large horizontal variations in the exchange ﬂow. Consequently, the outﬂow from thebay is more inﬂuenced by the bottom than in the cases without tide. Therefore, a tendency for a bottom-advected plumeappears in the cases with tide, rather than a surface-advected plume, which develops in the cases without tide. Further
analysis shows that the tidal current favors a salt balance between the horizontal and vertical advection of salinity aroundthe plume and hinders the upstream expansion of the plume outside the bay.
r 2006 Elsevier Ltd. All rights reserved.
Keywords: Estuarine dynamics; River plume; Tidal effects; Vertical mixing; Mathematical models; Chesapeake bay

1. Introduction
Studies on the circulation and salinity distributions in Chesapeake Bay have a long history(Pritchard, 1952). Using observations, (Pritchard,
1954, 1956) constructed a two-dimensional (2D)Corresponding author. Tel./fax: +81 89 927 9824.

E-mail address: guoxinyu@dpc.ehime-u.ac.jp (X. Guo).
0278-4343/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.csr.2006.08.009

framework for the dynamics of estuarine circulation, in which the effects of tidal currents on the salt
and momentum balances in an estuary wererecognized. Boicourt (1973) depicted the nature of
the Chesapeake Bay outﬂow plume and the intruding oceanic ﬂow underneath. Goodrich and Blumberg (1991) demonstrated the presence of anestuarine circulation in the Chesapeake Bay basedon 168 current records from 1977 to 1983.

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X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

This consisted of a seaward current in the surface
layer and a landward current in the lower layer.
Observations across the entrance to the Chesapeake
Bay showed that the exchange ﬂow varies largely inthe transverse direction (Valle-Levinson et al.,1998). An analytical solution illustrated that not
only bathymetry variations but also friction is
crucial to determine the transverse structure of
exchange ﬂows across the entrance to any estuary(Valle-Levinson et al., 2003). Following theseobservational and theoretical studies, the circulationin the Chesapeake Bay at any time scale should bestudied in a 3D framework. Such framework should
include a realistic bathymetry and tidal forcing.
Numerical simulations on the estuarine circulationin Chesapeake Bay also have a long history. Using a
3D primitive equation numerical model, Chao andBoicourt (1986) carried out a pioneering simulation of
a plume in an idealized estuary with an adjacent shelfocean. With a very similar model, Chao (1988a, b,1990) investigated the inﬂuences of the bottom slope,
winds and tide on the plume. Concentrating on thewater exchange at the Chesapeake Bay entrance,
Valle-Levinson et al. (1996) studied numerically the
dynamics at the transition between an idealized estuary
and an adjacent shelf. Wheless and Valle-Levinson(1996) investigated intratidal variations of a plume in
an idealized inlet-shelf domain. Several numericalsimulations with bathymetries that resemble those of
Chesapeake Bay have also been carried out. Spitz and
Klinck (1998) simulated the tides in the Chesapeake
Bay by assimilating data from tide gauges. Wang andJohnson (2000) developed a 3D hydrodynamic modelfor the Chesapeake Bay, in which the model was driven
by realistic forcing from 1985 to 1994. Xu et al. (2002)
demonstrated the improvements of model results byassimilating high-resolution salinity data. Recently, Li
et al. (2005) applied Regional Ocean Modeling System(ROMS) to the Chesapeake Bay and examined thesensitivity of model results to turbulence mixing
parameterizations. At present, several other 3D numerical models for this estuary are being developed (http://
ccmp.chesapeake.org/CCMP/workshops.html).
In this study, a 3D numerical model is used to
examine the effects of tidal currents on estuarine
circulation in Chesapeake Bay. Because ofimportant effects of bathymetry in the bay (ValleLevinson et al., 2003), a ﬁne grid size (400 m) is
implemented in the simulations. Fresh water
discharge, tidal forcing, and ambient coastal
current outside the bay are used to drive the model.
By including and excluding tidal forcing and21

ambient coastal currents, their effects on thesubtidal currents are examined inside and outside
the bay.
After a description of the numerical model in
Section 2, the model results for the four cases areshown in Section 3. Analysis of the dynamics of theplume outside the bay is given in Section 4 alongwith a comparison with other studies. Finally, asummary is given in Section 5.
2. Numerical model
One of the community ocean models, thePrinceton Ocean Model (POM), is used as the basicmodel. The POM is a 3D primitive equation ocean
model that includes full thermodynamics and a level
2.5 Mellor–Yamada turbulence closure model(Blumberg and Mellor, 1987; Mellor, 1998). The
model domain and bathymetry are shown in Fig. 1.
The horizontal resolution is 1/2401 in both the zonal
and meridional directions. In the vertical, 11 sigmalevels are evenly arranged. The minimum water
depth in the model domain is set to 3 m. The time
step is 3 s for the external mode and 120 s for theinternal mode. During the calculations, the verticaleddy viscosity and diffusivity are given by the
Mellor–Yamada turbulence closure model with abackground value of 105 m2/s. The horizontal eddy
viscosity is calculated by the embedded Smagorinsky formula with a proportionality parameter of
0.1, and the horizontal eddy diffusivity is obtainedusing an inverse Prandtl number of 0.5.
At the surface, no wind stresses are imposed. The
bottom stresses ðtx ; ty Þ are calculated using aquadratic friction law:ðtx ; ty Þ ¼ rC z ðu; vÞðu2 þ v2 Þ,(1)where r is the water density, u and v are zonal andmeridional components of velocity. The bottom
drag coefﬁcient is calculated by the embedded
formula in POM (Mellor, 1998),
k2
C z ¼ max 0:0025;,(2)½lnð0:05H=z0 Þ2where k ¼ 0:4 is the von Karman constant, H thewater depth, and z0 the roughness parameter that is
set to 0.1 cm.
The model is forced with river discharge, ambient
coastal current and tides. The water temperature isset as a constant ( ¼ 151) and only the salinity issolved. Instead of using the standard central
difference scheme for tracer advection, we used theARTICLE IN PRESS
22

X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

Susquehanna
(51%)

39.5

A

39.0

40
35
30
25
20

38.5

Potomac
(18%)

Other

15

(11%)

10
5

B

0

B

(m)

38.0

Rappa.
(4%)

D

37.5
York
(2%)

James
(14%)

C

37.0

D
C

A

36.5
-77.0

-76.5

-76.0

-75.0

Fig. 1. Model bathymetry. The boxes denote location of rivers and the numbers inside the parentheses denote the ratio of river dischargeof each river to total river discharge, which are given by Hargis (1980). Four red lines denote location of four sections shown in subsequentﬁgures.

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Smolarkiewicz iterative upstream scheme (Smolarkiewicz, 1984). This scheme has been included in thecode of POM. Comparison of results calculated by
the central difference scheme and by the Smolarkiewicz scheme showed that the Smolarkiewicz scheme
produced a sharper river plume outside the Chesapeake Bay than the central difference scheme(ﬁgures not shown here).
Referring to Hargis (1980), a total of 2200 m3/s offresh water is introduced into the model domainfrom the Susquehanna (51% of total), Potomac(18%), James (14%), Rappahannock (4%), York(2%), and the other small rivers (11%)(see Fig. 1 forthe position of the rivers). The river input isdistributed to the corresponding grid points shownin Fig. 1 by specifying the vertical velocity ws ¼
Q=ðNDxDyÞ (Oey, 1996), where Q is river discharge(m3/s), N is the number of grid points covered by theriver head and Dx and Dy are the sizes of grid points
in the east and north directions, respectively. The
salinity of river water is assumed to be 0 psu.
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) presented the horizontal distribution of the coastal current south ofDelaware Bay and inferred the existence of asouthward coastal current outside the Chesapeake
Bay. In our simulations, we impose an ambient
coastal current with a speed of 10 cm/s along theeastern boundary from 37.7 to 38 1N.
The M2 tide is the dominant tidal constituent in
the Chesapeake Bay (Browne and Fisher, 1988;
Shay et al., 2001). It is introduced in the simulations
through oscillation of tidal currents along theeastern and southern boundaries. The harmonic
constants of tidal currents along the eastern andsouthern boundaries are calculated in advance using
a horizontal 2D model in which the oscillation ofsea level is imposed. The amplitude and phase of theM2 tide along the eastern and southern boundaries
are 46 cm and 2101, which produce similar calculated tidal charts to observations in the entire
Chesapeake Bay (Browne and Fisher, 1988).
The open boundary conditions are speciﬁed in thesame way as in the subroutine BCOND in POM. In
the case that includes both tidal currents andambient current, a linear superposition of the twocurrents at the open boundary is used.
In this study, four cases are compared. In the ﬁrst
case (Case 1), only river discharge is introduced; in23

the second case (Case 2), river discharge andambient coastal current are included; in the thirdcase (Case 3), river discharge and the M2 tide areprescribed; and in the fourth case (Case 4), riverdischarge, ambient coastal current, and the M2 tideare introduced. All the simulations start from restwith an initial salinity of 32 psu at all grid points
and run for 360 days. The results of Cases 3 and 4
are saved hourly and the tidal components are
removed with a tide killer ﬁlter (Hanawa and
Mitsudera, 1985).
Before examining subtidal currents, we conﬁrmed
the reproduction of adequate M2 tide and tidal
current distributions by the model. The amplitudeof the M2 tide (Fig. 2a) shows the same features as
those from observations (Fig. 17 in Browne andFisher, 1988) and results of data assimilation(Fig. 10 in Spitz and Klinck, 1998). Its amplitude
is slightly lower along the western coast than along
the eastern coast of the bay, which is attributed to
Earth’s rotation effects (Browne and Fisher, 1988).
Two regions with the lowest amplitude are foundaround 37.61N and 38.81N along the western coast
and are related to virtual amphidromic points. The
phase of the M2 tide (Fig. 2b) varies more than one
tidal cycle from the mouth to the head of the bay,which is consistent with observations (Fig. 15 in
Browne and Fisher, 1988) and results of data
assimilation (Fig. 11 in Spitz and Klinck, 1998).
The M2 tidal current amplitude (Fig. 3a) is largest in
the lower bay and at two other areas: the junction of
the Potomac River and Chesapeake Bay and in theupper bay near Annapolis in the vicinity of the Bay
Bridge. The features shown in these distributions, aswell as the values of the M2 tidal current amplitude,
are consistent with observations (Browne andFisher, 1988; Shay et al., 2001). The phase of theM2 tidal current (Fig. 3b) increases from the mouthto the head of the bay and is similar to the
distribution of the tidal elevation phase. The effectof friction on the tidal current is shown in Fig. 3b. The
smaller value of phase near the coast than in thecentral part of the Chesapeake Bay results from
relatively stronger friction over the shallow water withrespect to deep water. As for the vertical structure oftidal current (not shown here), the modeled tidal
current at the entrance to the bay weakens near thebottom and over shoals, which is consistent withobservations by Valle-Levinson et al. (1998). All ofthese comparisons suggest that the calculated tides
and tidal currents have satisfactory characteristics for
examining tidal effects on estuarine circulation.

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24

(a)

(b)

(cm)

C.I.=3(deg.)

C.I.=20

AmplitudePhase
M2 tideM2 tideFig. 2. Amplitude (a) and phase (b) of tide, calculated by Case 4.

3. Model results
3.1. Horizontal distribution of salinity and mean
velocity
The mean velocity (thick line on Fig. 4a) and themean barotropic velocity (thin line on Fig. 4a),which was calculated by averaging the correspond-ing velocity at all grids of the model domain,indicate that the motion reaches steady state at day
200, although salinity continues to decrease(Fig. 4b). The baroclinic velocity, i.e., the difference
between the two lines (mean and barotropic) for
each case in Fig. 4a, evolves in the ﬁrst 100 days
and reaches an approximate steady state after day
200. Examination of the horizontal and vertical

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X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

(a)

25

(b)

(cm/s)(deg.)

C.I.=6

C.I.=20

AmplitudePhase
M2 tidal current

M2 tidal current

Fig. 3. Amplitude (a) and phase (b) of tidal current, calculated by Case 4.

distributions of velocity and salinity at different
times (ﬁgures not shown here) shows that thevelocity ﬁeld in the entire domain and the salinity
ﬁeld outside the bay have small differences from day
180 to 240 to 300 to 360. The decrease in salinity
portrayed in Fig. 4b occurs mostly inside the bay.
The results of day 240 are chosen here as thesolution to be examined in each case because themean salinity inside the bay on day 240 is close to
the observed value (18 psu, Austin, 2002).
The general distribution of salinity inside the bay
in the four cases (Figs. 5 and 6) is similar toobservations (Pritchard, 1952). Observed features
such as low salinity in the western side of the bay are
consistent in the model results. The most signiﬁcantdifferences in the salinity distributions among theARTICLE IN PRESS
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26

Case3
Mean salinity (psu)

Mean velocity (cm/s)

Case4

Case2

Case2

Case1

Case4
Case1

(a)

Case3

Time (day)(b)

Time (day)Fig. 4. Temporal variation of mean velocity (a) and mean salinity (b) in the entire model domain. The thin line in (a) is calculated byP
1=N i;j ðua2i;j þ va2i;j Þ1=2 , where ua and va are the vertically averaged velocity at grid point (i, j), N is the total number of grid points in thePPhorizontal; the thick line is calculated by 1=N i;j 1=M k ðu2i;j;k þ v2i;j;k Þ1=2 , where u and v are the velocity at grid point (i,j,k), M is the total
number of grid points in the vertical.

four cases appear outside the bay. Case 1 produces aplume reaching 37.5 N, far upstream (in the sense of
Kelvin wave propagation) from the mouth; thesouthward ambient coastal current in Case 2 largely
corrects the northward plume but not completely;
tidal forcing in Case 3 weakens greatly the northward plume; the combination of tidal forcing andambient coastal current in Case 4 produces a plume
similar to that observed by Marmorino et al. (2000).
A typical estuarine circulation with net seaward
current in the upper layer and net landward current
in the lower layer (not shown here) is obtained
inside the bay in the four cases (Figs. 7 and 8). The
inclusion of tide makes the current in the main stemof the bay to concentrate in the deep channel. The
reason for this tidal effect on estuarine circulation is
explained in Section 3.3. As with salinity, the mostsigniﬁcant difference in the current ﬁelds is associated with the outﬂow plume outside the bay. The
cases without tide produce a northward (upstream)
branch of the outﬂow plume (Fig. 7), while the caseswith tide produce an expected southward (downstream) plume (Fig. 8).
The inﬂuence of the ambient coastal current inmodifying the northward plume is clear (Fig. 7), assuggested by previous plume simulations that adownstream ambient current can eliminate theupstream propagation of plume water on the shelf(e.g. Chapman and Lentz, 1994; Yankovsky andChapman, 1997; Fong, 1998; Narayanan andGarvine, 2002). The tidal currents, however, also
constrain the development of an upstream plume asshown in Fig. 8. A dynamical explanation on thisphenomenon is given in Section 4.

3.2. Vertical structure of salinity and mean currents
An axial section along the bay displays a typical
distribution of salinity and current in a partiallymixed estuary (Fig. 9). The results of Cases 1 and 3
are not shown here because the ambient coastal
current has little effects on the results inside the bay.
Fig. 9a shows that salinity increases gradually fromthe head to the mouth of the bay and stratiﬁcation is
maintained in the vertical. The inclusion of tidal
currents slightly decreases the salinity inside the bay
and weakens the stratiﬁcation (Fig. 9b). The salinity
distribution shown in Fig. 9 is similar to observations in autumn and winter (Seitz, 1971). In springand summer, however, the observed vertical stratiﬁcation (Seitz, 1971) is stronger than the model
results (Fig. 9). Surface heating and large fresh
water discharge in spring and summer could cause
the stronger stratiﬁcation portrayed by the observations but remains to be explored further.

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0m

Case 1Case 2

27

Fig. 5. Surface salinity simulated by the two cases without tidal forcing.

The mean currents along the longitudinal axis of
the bay show a typical estuarine circulation with aseaward current in the upper layer and a landward
current in the lower layer (Fig. 9c). The typical
speed of the currents is 10–20 cm/s and the level ofno motion is located roughly at 5 m. The inclusionof tidal forcing slightly weakens the landward
current in the lower layer, deepens the level of no

motion, and intensiﬁes the seaward current in theupper layer (Fig. 9d). It must be noted that theintensiﬁed seaward current in the upper layer inCase 4 (Fig. 9d) is caused by the concentration ofcurrent in the central deep channel (Fig. 10). This
concentration of mean outﬂow in the deep channel
responds to the variation of vertical eddy viscosities
and will be discussed in Section 3.3. In Fig. 10, theARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

28

0m

0m

Case 3

Case 4

Fig. 6. Surface salinity simulated by the two cases with tidal forcing.

landward current is stronger in Case 2 than in Case
4, indicating that the tide weakens the landward
current inside the Chesapeake Bay. The lifting of thelevel of no motion above the channel in Case 2
induces two cores of the seaward current in thesurface layer. As the tide is included, the lifting of
the level of no motion vanishes and the seaward
current concentrates above the channel.

In order to further evaluate the vertical structure of
the mean ﬂow and salinity, a cross-section at theentrance (see Fig. 1 for its position) is chosen tocorrespond with that of observations by ValleLevinson et al. (1998) and Reyes-Hernandez (2001).
There are two channels in the section. The Chesapeake Channel is located in the southern side and theNorth Channel in the northern side. The shallow area

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29

Fig. 7. Surface current simulated by the two cases without tidal forcing.

between these two channels is called Six-Meters Shoal.
Model results show that salinity is lower in thesouthern than in the northern side of the bay entrance(Fig. 11a). Also, stratiﬁcation is stronger in the
Chesapeake Channel than in the North Channel.
These features are consistent with observations (ValleLevinson and Lwiza, 1997; Reyes-Hernandez, 2001)

and are attributed to the competition between Earth’s
rotation and friction (Valle-Levinson et al., 2003). As
tidal forcing is included, strong tidal currents aroundthe entrance to the Chesapeake Bay (Fig. 3a) increase
mixing and weaken stratiﬁcation there (Fig. 11b),
resulting in decreased vertical gradients but increasedtransverse gradients.

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X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

Fig. 8. Surface current simulated by the two cases with tidal forcing.

The vertical structure of the current across thesection corresponds to a two-layered current in themain channel: outﬂow in the upper layer and inﬂow
in the lower layer (Fig. 11c). Inﬂow appears only
near the bottom of the two channels. The inclusionof tidal forcing transforms the level of no motion
from being ﬂat to being sloped (Fig. 11d). This

indicates that tidal forcing produces larger horizontal gradients in the subtidal currents. Consequently,
the outﬂow shifts to the southern part of the
Chesapeake Channel and to the North Channel
and a weak inﬂow appears between the twochannels, i.e., over the Six-Meters Shoal. These
distributions reproduced by the case with tide are

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Head

(a)

(c)

Mouth

31

Head

Salinity
Case 2(b)

Velocity
Case 2(d)

Mouth

Salinity
Case 4Velocity
Case 4

Fig. 9. Vertical distribution of salinity and mean current along the longitudinal axis of the bay (section A–A in Fig. 1), calculated by Cases
2 and 4. The unit of abscissa is grid number. The lines in (c) and (d) show the level of no motion.

West

East

West

Case 4
Northward velocity

Case 2
Northward velocity
(a)

East

(b)

Fig. 10. Mean current across the section at 38.15 N in the middle bay (section B–B in Fig. 1). The unit of abscissa is grid number. Positive
values denote northward current and negative values southward current.

remarkably similar to those observed by ValleLevinson et al. (1998). In turn, the current along thesection (transverse current) at the bay entrance

is southward in the upper layer and northward in
the lower layer (Fig. 11e). The strength ofsouthward and northward currents is sensitive toARTICLE IN PRESS
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32

South

North

South

North

Case 4
Salinity

Case 2
Salinity(b)(a)

Case 2
Velocity across section

Case 4Velocity across section
(d)

(c)

Case 2
Velocity along section(e)Case 4Velocity along section(f)Fig. 11. Vertical distribution of salinity and the velocities across and along the section at the entrance of the bay (section C–C in Fig. 1).
The unit of abscissa is grid number. Positive values in (c) and (d) denote inﬂow and negative values outﬂow. Positive values in (e) and (f)denote northward current and negative values southward current.

tidal forcing. In the case with tide, the northward current in the lower layer weakens largely
and the southward current dominates the section(Fig. 11f).
In addition to river discharge and tidal forcing,wind forcing also inﬂuences the subtidal currents

observed at the entrance. However, the essential
features of the currents observed at the entrance to
the Chesapeake Bay are that the outﬂow in thesurface layer concentrates in the southern part of
the Chesapeake Channel and in the North Channel.
Also, the inﬂow concentrates in the lower layer ofARTICLE IN PRESS
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the two channels. The level of no motion in
Chesapeake Channel slopes steeply, and the current
over the Six-Meters Shoal shows a weak inﬂow(Valle-Levinson et al., 1998). All these features are
consistent with the results of Case 4 (Fig. 11d)
rather than those of Case 2 (Fig. 11c). Furthermore,
the observations show that the southward current in
the surface layer dominates the current along thesection at the entrance (Valle-Levinson et al., 1998).
This is also consistent with the results of Case 4(Fig. 11f) rather than those of Case 2 (Fig. 11e).
Therefore, it can be concluded that tidal forcing isnecessary to produce appropriate frictional inﬂuences that reliably represent the subtidal currents at
the entrance to Chesapeake Bay.
3.3. Tidal effects on the vertical eddy viscosity
According to Kasai et al. (2000), friction plays apreponderant role in the transverse variability of
exchange ﬂows in estuaries. Valle-Levinson et al.
(2003) use this ﬁnding to show that the spatial
structure of exchange ﬂows at the Chesapeake Bay
entrance is explained by the inﬂuence of relatively
large Ekman numbers (ratio of friction to Coriolis
accelerations) with respect to a geostrophic exchange. The numerical results of Case 4 illustratethat the vertical eddy viscosity varies largely withinclusion of tidal forcing (Fig. 12). Compared toCase 2 (Fig. 12a), Case 4 shows that the verticaleddy viscosity increases signiﬁcantly near thebottom throughout the bay and in the area near
the entrance (Fig. 12b). Interestingly, at a transverse
section in the middle of the bay (same as Fig. 10) thevertical eddy viscosity decreases slightly from Case 2(Fig. 12c) to Case 4 (Fig. 12d) near the interface
between seaward and landward currents. This might
result from decreased vertical shears in Case 4
relative to Case 2. At the transverse section in thebay entrance, the vertical eddy viscosity increases
signiﬁcantly in the entire section from Case 2(Fig. 12e) to Case 4 (Fig. 12f).
The weakening of landward ﬂows in Case 4
relative to Case 2 (Figs. 9 and 10) is a natural
response to the increase of vertical eddy viscosity
near the bottom from the inclusion of tidal forcing.
The transverse structure of exchange ﬂows in the
middle bay (Fig. 10) and at the entrance (Fig. 11) is
consistent with the analytical solution given by
Valle-Levinson et al. (2003). The numerical results
were consistent with the analytical in the sense thatinﬂows and outﬂows are concentrated in the33

channel under relatively weak friction but segregate
horizontally as friction increases. In the middle bay,
the apparent larger viscosity in Case 2 lifts theinterface of exchange ﬂows upward, i.e., causes thecore of net outﬂow to shift away from the channel(Fig. 10a). In Case 4, reduced viscosity (friction)
allows the net outﬂow core to appear in the channel(e.g. Valle-Levinson et al., 2003). At the bay
entrance, larger friction in Case 4 increases the tiltof the interface between inﬂows and outﬂows(Fig. 11d). This causes weaker net outﬂows overthe deepest part of the section than in Case 2 andalso induces larger horizontal variations of exchange ﬂows.
4. The plume outside the bay
As shown in Figs. 6 and 7, Case 1 produces anorthward plume outside the Chesapeake Bay. The
ambient coastal current in Case 2 largely corrects
the northward plume but not completely. Tidal
forcing in Case 3 weakens the northward plume but
cannot eliminate it. The combination of ambient
coastal current and tidal forcing in Case 4 produces
a realistic plume outside the Chesapeake Bay. If wefollow the plume classiﬁcation of Yankovsky andChapman (1997), Case 1 seems to represent an
extreme case of surface-advected plume and Case 4
illustrates a bottom-advected plume. These concepts
are explained next.
4.1. Surface-advected plume versus bottom-advectedplume
On the basis of the vertical structure of a plume,
Yankovsky and Chapman (1997) suggested two
extreme cases of river plumes: a bottom-advected
plume and a surface-advected plume (see Figs. 1 and
2 of Yankovsky and Chapman, 1997). In thebottom-advected plume, the plume water occupies
the entire water column and turns right immediately
after it ﬂows out of the estuary mouth. The outﬂow
associated with the bottom-advected plume is incontact with the bottom. In the surface-advected
plume, the plume water stays on the surface layer
forming a thin layer above the ambient denser
water. The plume typically forms a bulge near theestuary mouth within which an anticyclonic ﬂow is
generated. The outﬂow associated with the surfaceadvected plume is limited to the surface layer andessentially remains detached from the bottom.

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34
Head

Mouth

Head

Mouth

Case 2

(a)

-4

-3

West

Case 4
-2

(b)

East

West

H

-4

-3

-2

East

H

Case 2
C.I.=0.5

(c)

South

(d)

North

Case 4
C.I.=0.5

South

North

L
H
H

(e)

Case 2
C.I.=0.5(f)Case 4
C.I.=0.5

Fig. 12. Vertical eddy viscosity coefﬁcients along the section of longitudinal axis of the bay (section A–A in Fig. 1), along the section at
38.15 N in the middle bay (section B–B in Fig. 1), along the section at the entrance of the bay (section C–C in Fig. 1). The unit of abscissa isgrid number. Values are base-10 logarithmic scale of vertical eddy viscosity coefﬁcients (m2/s).

The northward plume outside the Chesapeake
Bay produced by Case 1 resembles the well-known
upstream intrusion of buoyant water from an inlet
into the shelf (Garvine, 2001). Garvine (2001) notedthat the upstream intrusion of buoyant water isoften found in the results of numerical models(Chapman and Lentz, 1994; McCreary et al., 1997;
Fong, 1998; Garvine, 1999, 2001; Yankovsky, 2000;
Narayanan and Garvine, 2002), but it is rarely
observed in the real ocean. In addition to the
upstream intrusion of buoyant water, numericalmodels also tend to produce a type of plume with aARTICLE IN PRESS
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massive anticyclonic bulge near the mouth ofestuary (Pichevin and Nof, 1997; Nof and Pichevin,2001; Garvine, 2001; Nof, 2005), which is also rarely
observed in the real ocean (Garvine, 2001). Moreover, these two types of plumes do not reach asteady state, even for steady forcing (Pichevin andNof, 1997; Garvine, 2001; Nof, 2005).
Garvine (2001) suggests that the unrealistic
aspects in model conﬁguration such as a simple
inlet, a deep coastal wall or a large angle (usually901) between the inlet channel and coastal wall of
shelf are the fundamental causes for producing the
upstream intrusion. Yankovsky(2000) pointed outthat the oversimpliﬁcation of the boundary conditions, such as uniform velocity in the verticalapplied for buoyant discharge at the mouth, blocks
the landward ﬂow in the lower layer and initiates
the upstream spreading of buoyant ﬂow. In ourmodel conﬁguration, the buoyant discharge enters
the shelf through a natural mouth where thelandward current in the lower layer is not blocked.
The only concern is the coastal wall. Because of the
inclusion of tidal forcing, we set the minimum water
depth in the model as 3 m that is larger than the
0.1 m used by Garvine (2001) in an experimentshowing effects of a coastal wall on the upstream
intrusion of buoyant water.
The inclusion of an ambient current ﬂowing in thedownstream direction has been shown to restrain
the upstream intrusion of buoyant water (Chapman
and Lentz, 1994; Yankovsky and Chapman, 1997;
Fong, 1998; Narayanan and Garvine, 2002). Garvine (2001) noted that this method is not a universal
remedy for models reproducing a realistic plume.
With no downstream ﬂowing ambient current, but
improving the model conﬁguration with shallow
depths (0.1 m) at the coast, Garvine (2001) showedthat the upstream intrusion of buoyant water
almost disappears. However, the improvement ofmodel conﬁguration is usually limited in a realistic
application. For example, simulations in Chesapeake Bay with tidal forcing hinder the use of acoastal wall 0.1 m deep as used by Garvine (2001)
because of numerical stability problems.
Therefore, a downstream ambient current wasalso added in Case 2 to correct the northward
intrusion appearing in Case 1. On the other hand, as
noted in Section 2, observations also support asouthward ambient current outside the Chesapeake
Bay (Beardsley and Boicourt, 1981; Epifanio andGarvine, 2001). As shown in Figs. 5 and 7, thedownstream ambient current largely corrects the35northward plume but not completely. This can beunderstood as follows. In the simulation, thereproduced current structure at the bay entrance
acts as a boundary condition to the plume outside
Chesapeake Bay. The current structure at the bay
entrance without tide is favorable to form an
upstream intrusion of buoyant water along the shelf
in Case 1. Although the ambient current can
restrain the northward plume by advecting thebuoyant water southward, it cannot eliminate thedrive of the northward plume. This is because
the ambient coastal current has a minor, apparently
negligible, effect on the subtidal circulation inside
Chesapeake Bay.
As shown later, the inclusion of tidal current is anecessary condition to produce a correct plume
structure at the mouth, which in turn affects the
upstream intrusion of buoyant water in the shelf.
Chao (1990) emphasized the effects of tide-induced
residual eddies on the plume in a coupled plume–
shelf system but did not mention the change ofvertical structure of the subtidal current at theestuary mouth. (The cyclic condition used in his
model conﬁguration is questionable because thebuoyancy-driven coastal current is stronger in thedownstream area than in the upstream area and acyclic condition implicitly imposes an unrealistic
downstream ambient current in the shelf.) Garvine(1999) examined the tidal effects on the downstream
penetration of buoyant water and concluded thatshelf tides have a detectable but moderate inﬂuenceon plume downstream penetration. In the same
paper, he also mentioned that the upstream
penetration is reduced with tides but did not analyze
its details. Garvine (2001) showed that a sinusoidally varying alongshelf wind can reduce the upstream penetration speed from 2.08 to 1.54 cm/s andmentioned that the effects of shelf tides are similar
with a varying wind but did not present the resultswith shelf tides. By introducing a variable discharge
at the estuary mouth at tidal frequencies, Yankovsky et al. (2001) concluded that tidal ﬂuctuations in
the inﬂow of buoyant discharge has minor effects on
the buoyant plume along the shelf. Recently, Isobe(2005) demonstrated that the alongshore component of tidal currents effectively stabilizes theoffshore growth of a river-plume bulge.
In addition to the above explicit results on the
tidal effects on the plume, Yankovsky (2000) andGarvine (2001) also studied the effects of verticalviscosity and vertical mixing on the upstream
intrusion of buoyant water. In particular, Garvine

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36(2001) presented an analytic solution to demonstrate that reduced vertical mixing and increased
vertical viscosity tend to reduce the upstream
intrusion speed. Because tidal currents tend tosimultaneously increase vertical mixing and verticalviscosity, the tidal effects on the upstream intrusionof the plume are not easily interpreted from theanalytic solution given by Garvine (2001).
In a coupled estuary–shelf system, tidal effects on
the plume outside the estuary include two aspects.
The ﬁrst is the direct effect on the buoyancy-driven
coastal current. This issue has been studied by theuse of an artiﬁcial estuary mouth and shelf domain(Garvine, 1999, 2001; Yankovsky, 2000). The otheraspect is the inﬂuence of tidal currents on thesubtidal current structure inside the estuary and inturn the outﬂow at the mouth of estuary. This
aspect is identical to how the tide affects theboundary condition given at the artiﬁcial estuary
mouth in the simulation with only shelf domain(Garvine, 1999, 2001; Yankovsky, 2000). Since thisissue has not been fully addressed in the previous
studies, Case 1 through 4 are interpreted in terms ofthe vertical structure of the plume for each case.
In the cases without tide (Fig. 5), the plume issimilar to a surface-advected plume, while in thecases with tide (Fig. 6) the plume emulates abottom-advected plume. Obviously, the tide makes
the river plume shift from a surface-advected plume
to a bottom-advected plume and this change should
relate to the variation in the vertical structure ofplume. The vertical distribution of salinity along asection that crosses the plume outside the bay
conﬁrms this inference (Fig. 13). In the cases
without tide (Figs. 13a and b), the isohalines lean
toward the plume front (Fig. 13a), similarly to thesurface-advected plume shown by Yankovsky andChapman (1997). The inclusion of ambient coastal
current cannot change this basic structure(Fig. 13b). In the cases with tide (Figs. 13c and d),the salinity becomes vertically well mixed and thisvertical structure is consistent with the isohalines(a)Case 1salinity(psu)(b)
Case 2salinity(psu)(c)
Case 3salinity(psu)(d)
Case 4salinity(psu)

Fig. 13. Vertical distribution of salinity in four cases along the section across the plume outside the bay (section D–D in Fig. 1).

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structure of the bottom-advected plume shown by
Yankovsky and Chapman (1997). Returning to thevertical distribution of exchange ﬂows at the bay
entrance (Fig. 11), the outﬂow in the region o8 km
is more in contact with the bottom in Case 4 than inCase 2. This again conﬁrms the inference that tidal
forcing transforms the outﬂow of Chesapeake Bay
water from a surface-advected plume to a bottomadvected plume by altering the vertical structure ofoutﬂow of buoyant discharge. Because the tidal
current has a spring–neap cycle and the fresh water
discharge also changes temporally, the bay plume
can also behave as a surface-advected plume,
especially when high fresh water outﬂow occurs ina neap tide period.
Garvine (1999) showed that the simulated plumeis sensitive to the background eddy viscosity or
diffusivity in the Mellor–Yamada turbulent closure
model used to avoid zero viscosity or diffusivity
when the local Richardson number exceeds about
0.2. However, the results presented here are not as
sensitive to the background viscosity as Garvine’s
results. Fig. 12 indicates that the vertical eddy
viscosity given by the turbulence model is larger
than the background value used, in particular in thecase with tide.
Chapman and Lentz (1994) explain the upstream
movement of a plume along the shelf as a selfadvected process. Applying their explanation to thenorthward movement of the plume outside the bay,
a positive acceleration of northward velocity and anegative temporal variation of salinity are necessary
near the plume front. To conﬁrm these two points,
the terms in the momentum equation are analyzed
for the northward velocity and the terms in theconservation equation for salinity are evaluated.
4.2. Dynamics of northward velocity
The momentum equation for the northward
velocity v can be expressed asqv
þ ADV ¼ PRE þ COR þ VDIF ,(3)
qt
where ADV denotes advection terms, PRE denotes
pressure gradient, COR denotes Coriolis force,
VDIF denotes the internal stress divergence related
to vertical eddy viscosity. The stresses related to thehorizontal viscosity are small enough to be negligible. All these terms are calculated by POM andthe tidal components are removed with a tide killer
ﬁlter (Hanawa and Mitsudera, 1985).

37

In Figs. 14 and 15, surface distributions of eachterm in Eq. (3) are presented for all of the four cases,
plus the isohaline of 31.5, which approximately
represents the plume front (Fig. 13). The dynamics
terms are shown on day 100 and the salinity contours
on days 90, 120, and 150. The plume front in Case 1
moves northward with a speed of 0.7 km/day(0.8 cm/s). Behind the plume front, i.e., south ofthe plume front, there is an area with positive
acceleration close to the coast (Fig. 14a). The plume
front in Case 3 also moves northward. Its speed issmaller than that in Case 1. The positive accelerationof northward velocity behind the plume is weaker inCase 3 than in Case 1. In Cases 2 and 4, positive
acceleration of northward velocity behind the plume
weakens greatly because of the ambient ﬂow andtidal forcing (Figs. 14b and d).
The advection terms (Figs. 14e–h) are generally
small except for the bay entrance in the cases withtide and the northeastern corner where the ambient
coastal current is imposed. In the cases with tide,
tidally averaged advection terms correspond to thegeneration of tide-induced residual current, which isappreciable around the entrance to the bay.
The combination of pressure gradient and Coriolis force (Figs. 14i–l) is responsible for the positive
acceleration of northward velocity behind the plume
front. This is particularly clear in Case 1 (Fig. 14i).
Fig. 15 indicates that the positive acceleration ofnorthward velocity is caused by the pressure
gradient. In Case 1 (Fig. 15e), an area with positive
pressure gradient exists from the bay entrance to theplume. The ambient coastal current in Case 2 brings
negative pressure gradient ahead of the plume front,i.e., north of the plume front. Tidal forcing in Case 3
weakens the positive pressure gradient behind theplume front.
Internal stresses (Figs. 15a–d) vary greatly with
the inclusion of tidal forcing. Behind the plume
front, internal stresses show negative values andtherefore act to prevent the northward movement of
the plume. In Case 1 (Fig. 15a), negative internal
stresses are very weak and allow northward
propagation. In Case 3 (Fig. 15c), stresses increase
greatly. Therefore, tidal forcing increases internal
stresses in the plume front area and hinders northward plume propagation.
Further analysis may be derived from the salinity
equation, which can be expressed asqS
þ ADVS ¼ VDIFS,
qt(4)

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X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

Fig. 14. Local acceleration (top panels), advection (middle panels), and combination of pressure gradient and Coriolis force (bottom
panels) in the momentum equation for northward velocity at surface layer on day 100. The contours show the position of 31.5 psu on days
90, 120, and 150 that moves northward. The values of qv=qt, ADV, and PRE+COR have been multiplied by a factor of 24  3600  50.

where S denotes salinity, ADVS denotes advection,
and VDIFS denotes vertical diffusivity. Similarly tothe momentum Eq. (3), horizontal diffusivity is
negligible.
The temporal variation of salinity around theplume front is negative in all the four cases (Fig. 16),
indicating a decrease of salinity. The magnitude of
the negative temporal variation of salinity aroundthe plume front in Cases 1 and 2 is large while thatin Cases 3 and 4 is small. Fig. 16 indicates that theimbalance between advection and vertical diffusivity
causes the decrease of salinity.
The advection of salinity in Fig. 16 is thenseparated into two components: horizontal andvertical (Fig. 17). Around the plume front, horizontal
advection is positive and vertical advection isnegative. This suggests that vertical advection
compensates the salinity loss caused by horizontal
advection. In Cases 1 and 2, horizontal advection is
not balanced by vertical advection. However, inARTICLE IN PRESS
X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

39

Fig. 15. Vertical viscosity (top panels), pressure gradient (middle panels), and Coriolis force (bottom panels) in the momentum equation
for northward velocity at surface layer on day 100. The contours show the position of 31.5 psu on days 90, 120, and 150 that moves
northward. The values of VDIF, PRE, and COR have been multiplied by a factor of 24  3600  50.

Cases 3 and 4, advection in the two directions isnearly balanced. Therefore, the self-advected processof an upstream intrusion of a plume along the shelf,
as suggested by Chapman and Lentz (1994), is
conﬁrmed in the cases without tide. In Case 1, thenorthward pressure gradient behind the plume front
is not balanced by the other terms and produces apositive acceleration of northward velocity along thecoast north of the entrance. Meanwhile, horizontal
advection of salinity is not balanced by the otherprocesses and causes the decrease of salinity. These
two effects make the plume propagate northward.
On the other hand, the inclusion of tidal forcing
increases friction, decreases the northward pressure
gradient around the plume, and makes the horizontal
and vertical advection of salinity to be balanced.

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40

X. Guo, A. Valle-Levinson / Continental Shelf Research 27 (2007) 20–42

Fig. 16. Temporal variation (top panels), advection (middle panels), and vertical diffusion (bottom panels) in the salinity equation at thesurface layer on day 100. The contours show the position of 31.5 psu on days 90, 120, and 150 that moves northward. The values of qS=qt
have been multiplied by a factor of 24  3600  10, those of ADVS and VDIFS by a factor of 24  3600  100.

Therefore, the northward plume outside the bay isseverely hampered by these processes.
5. Conclusions
Tidal forcing affects not only estuarine circulation and the salinity distribution inside the Chesapeake Bay but also the river plume outside the bay.
Increased mixing by tidal currents weakens stratiﬁ-

cation. Inside the bay, the seaward ﬂow in thesurface layer concentrates in the deep channel andthe landward ﬂow in the bottom layer weakens.
Additionally, tidal forcing induces large horizontal
variation of exchange ﬂows at the bay entrance andmakes the outﬂow plume to be in contact with thebottom. Consequently, a bottom-advected plume isformed in the presence of tidal forcing. Within theplume outside the bay, tidal currents increase

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41

Fig. 17. Horizontal advection (top panels) and vertical advection (bottom panels) in the salinity equation at the surface layer on day 100.
The contours show the position of 31.5 psu on days 90, 120, and 150 that moves northward. The values of HADVS and VADVS have been
multiplied by a factor of 24  3600  10.

friction, and make horizontal and vertical advectionof salinity to be balanced. These two effects, favoredby tidal forcing, hinder the upstream movement of
the plume. In general, because the transverse
structure of exchange ﬂows in estuaries is sensitive
to friction (Valle-Levinson et al., 2003), which isgreatly affected by tidal forcing, inclusion of tidal
forcing is necessary to simulate estuarine circulation
properly. This is not only true in the Chesapeake
Bay, but should also be the case in many estuaries.

Acknowledgements
This work was carried out while X. Guo wasvisiting the Center for Coastal Physical Oceanography at Old Dominion University. He thanks
support from Ministry of Education, Culture,
Sports, Science and Technology, Japan. AVL
acknowledges support from NSF project 9983685.

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