TAMU Coastal Oceanography Modeling Group
1. Introduction
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- A. Background
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- B. Review of Previous Plume Studies
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- C. The Texas-Louisiana Shelf
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- D. Objectives and Hypotheses
A. Background
Buoyancy-driven flow can be a prominent feature for those coastal ocean
regions impacted by river discharge. When buoyant riverine freshwater
is released into a shelf region occupied by saltier and more dense oceanic
water, potential energy becomes available to drive thermohaline currents,
where lateral entrainment and vertical mixing occur. Often the dynamical
structure of the spreading low-salinity water over the shelf is referred
to as a river plume. Many observational and theoretical studies suggest
that, in the absence of strong external forcing, a low-salinity bulge
forms near the estuary mouth when the plume reaches the shelf, and the
surface flow turns anticyclonically (clockwise) within the bulge in the
northern hemisphere due to the Coriolis force. Moreover, a baroclinic
boundary current is developed along the coast in a narrow zone propagating
as a coastal Kelvin-like wave, in which the coastal boundary is to the
right in the northern hemisphere (Wiseman et al., 1976; Wiseman and Dinnel,
1988; Kao et al., 1978; Chao and Boicourt, 1986; Oey and Mellor, 1993;
Brooks, 1994; Chapman and Lentz, 1994).
Studies of the temporal and spatial structures of a river plume are of
considerable interest not only because of its influence on the physical
processes of the shelf circulation but also because of its close relationship
to ecosystem and environmental pollution problems. In particular, a vast
amount of land-drained materials, suspended organic materials, industrial
wastes, and sewage brought onto the continental shelves through river
discharge may significantly affect fishery production and water quality.
Indeed, the ecological and environmental aspects are of greater importance
than the structure of the density-driven current itself. It is, therefore,
important to have a general understanding of the coastal circulation as well
as to trace and to predict the pathways and distributions of river-borne
materials or pollutants in the coastal ocean.
The Texas-Louisiana shelf, a continental shelf in the northwestern Gulf of
Mexico, is one of the primary fishery grounds in the nation and also has many
oil activities offshore. It has been recognized that the coastal circulation
over the inner shelf is affected significantly by the freshwater from the
Mississippi-Atchafalaya River system, the largest in the United States. While
some important studies have been conducted on the seasonal circulation patterns
over the Texas-Louisiana shelf, the development and evolution of the river
plume are not yet well understood. This study attempts to improve our
understanding of the temporal and spatial structures of the river plume and
prediction of the pathways of river-borne materials on the Texas-Louisiana
shelf.
B. Review of Previous Plumes Studies
Several studies show that river plumes have different structures in
different regions. A recent review is given by Wiseman and Garvine (1996).
Generally, river plumes can be characterized by a Kelvin number, the ratio
of the width of the estuary mouth to the baroclinic Rossby radius of
deformation (Garvine, 1987), K = wr / λi, where λi
= (g'H)1/2/f, g' is the reduced gravity, H the water depth
and f the Coriolis parameter. Physically, for a plume with K ≥ 1,
in which the plume spreads onto the shelf in a distance of O(&lambdai),
the effects of the earth rotation or the Coriolis force becomes important.
This kind of large-scale plume is classified as a supercritical flow
(Garvine, 1987). In earlier studies, several investigators such as Kao
(1981), Csanady (1984a) and Chao and Boicourt (1986) implied that the study
of a buoyant river plume is a subject related to baroclinic instabilities
and turbulent mixing processes where the nonlinear interactions are crucial.
Similarly, the meteorological conditions such as surface heating and cooling
will also determine the reponse of the river plume structure; however, in
general, the plume structure is principally determined by the local conditions
like the total volume of freshwater outflow, winds, tides, coastal currents
and bathymetry.
As a river plume spreads offshore, a frontal structure where the density
changes rapidly often is found in the transition zone between the riverine
water and the saltier shelf water(Garvine, 1974; Garvine and Monk, 1974;
M\"{u}nchow and Garvine, 1993). Hydrographic data (Garvine and Monk, 1974)
and numerical model studies (Kao et al., 1977; Chao and Boicourt, 1986)
indicate there exists a strong surface convergence and resultant downwelling
near the frontal zone. When the front achieves equilibrium, the pressure
gradient produced by the lateral buoyancy fluxes is balanced by the Coriolis
force; i.e., geostrophic balance is achieved (Csanady, 1976 and 1984; Ou,
1983; Chapman and Lentz, 1994) and an along-shore coastal current is formed.
Moreover, model results show that a transition region of a surface cyclonic
flow occurs at the downstream edge of the bulge, turning into the right-bounded
coastal current on account of nonlinearity in the governing momentum equations
(Chao and Boicourt, 1986; Garvine, 1987; Oey and Mellor, 1993). This process
or feature is not found in a model with linear dynamics (Ikeda, 1984; Chapman
and Lentz, 1994). With the exclusion of all external forcing except river
discharge, Chao and Boicourt (1986) indicate the width of the right-bounded
coastal current is comparable to the scale of the baroclinic Rossby radius of
deformation, $\lambda_{i}$. The intrusion velocity of the river plume into the
ambient ocean is enhanced by increasing the volumetric inflow of freshwater
(Kao et al., 1978; Oey and Mellor, 1993; Chapman and Lentz, 1994) but retarded
by the bottom friction (Whitehead and Chapman, 1986; Chao and Boicourt, 1986;
Chao, 1988a).
In some coastal oceans, tide-induced currents are one source for enhancing
turbulent mixing and entrainment. Theoretical and numerical studies indicate
that tide-induced residual currents have significant impact on the vertical
mixing over variable bottom topography (see, e.g., Chen, 1992). The residual
current can be generated by the nonlinear interactions between tides and
bottom or lateral friction (Tee, 1976, 1977; Zimmerman, 1978, 1981;
Ridderinkhof and Zimmerman, 1982; Signell and Geyer, 1991). Chao (1990) studied
the tidal modulation of estuarine plumes, using a three-dimensional,
primitive-equation, numerical model. The model predicts that there are two
counter-rotating tidal eddies near the estuary mouth. The scale of the estuarine
plume is increased because freshwater is trapped by the eddies, but the
development of the coastal current is retarded. Brooks (1994) studied the
influence of river runoff and tides over the shelf in the Gulf of Maine using
a quasi-linear numerical model, in which the linear momuntum equations are coupled
with the nonlinear advective-diffusion transport equation for the denisty field,
representing river inflow by point sources. In his model results, the
tide-induced residual currents do not show a tendency to form two counter-rotating
tidal eddies near the river mouth; instead, they show an anticyclonic turning
current.
In general, wind-driven currents principally dominate the main circulation
patterns and mixing processes over the continental shelf. The pioneering work on
wind-driven currents is obtained mathematically by Ekman (1905) under the
assumptions of no lateral boundaries, infinitely deep water (no bottom friction),
constant eddy viscosity ($A_{z}$), steady-state condition, homogeneous water and no
pressure gradient. Thus, the Ekman's equations can be expressed as the balance
of the Coriolis force and wind friction. The analytical model predicts that
the surface current flows at $45^{o}$ to the right of the wind direction in the
northern hemisphere, and the effective depth of the wind-driven current, the
Ekman layer, can be estimated by the equation, $D_{e} = \pi\left(2A_{z}/|f|\right)^{1/2}$,
where $|f|$ is the magnitude of $f$. However, to study wind-driven currents over
a continental shelf such as the Texas-Louisiana shelf, the bottom friction becomes
important in the shallow water region (Csanady, 1978; Hsueh and Cushman-Roisin,
1982; Gill, 1982). The Csanady's (1978) analytical model indicates the alongshore
velocity is in phase with the wind stress at the shore, but an angle between the
alongshore velocity and the wind stress far from the coast. In terms of physical
interpretation, in the shallow water the wind stress is primarily balanced by the
bottom friction, and the Coriolis force is negligible. In contrast, far from the
coast, the wind stress is balanced by the Coriolis force, which the bottom friction
is less influence to the surface current. Therefore, the Ekman layer exists at the
offshore, but not in a very shallow inner shelf.
Observations from many locations show that the alongshore component of current is
strongly coherent with the alongshore component of wind stress. According to the
physical theme, the upper layer Ekman transport, normal to the coast, is induced
by the component of wind stress parallel to the coast and leads upwelling or
downwelling near the coast. Analytical studies (e.g., Stommel and Leetmaa, 1972;
Csanady, 1984b) do not demonstrate clearly the possible interactions between wind
stresses and river plumes. However, model studies such as Chao (1987, 1988b)
and Kourafalou et al. (1996) display that the plume expands seaward and the
right-bounded coastal current is almost eliminated in the upwelling-favorable
wind case, in which wind stress generates Ekman transport toward the offshore.
Downwelling-favorable wind causes the plume to be narrower and enhances the
right-bounded coastal current. In contrast to the studies by a comprehensive
model (Chao, 1987,1988b), observations from the Mid-Atlantic Bight (Beardsley
et al., 1976) and the shelf off the Delaware Bay (M\"{u}nchow and Garvine, 1993)
show that density-driven coastal currents flow, opposing the mean wind, toward
the downstream.
C. The Texas-Louisiana Shelf
The Texas-Louisiana shelf is defined as the shelf region from the
Mississippi Delta to the Rio Grande, bounded by the coast to the north and
northwest (Fig. 1).
The geometry of the Texas-Louisiana shelf is in a concave shape, which is narrow
off the Rio Grande, wider and flat in the central portion, and which nearly
vanishes at the Mississippi Delta. The shelf break is in depths of about 100 m.
Near the delta there is a narrow submarine canyon, the Mississippi Canyon,
impinging onto the shelf with steep bottom topography. The Mississippi and
Atchafalaya Rivers flow onto the east Texas-Louisiana shelf and are the main
contributors of freshwater to the shelf, although Texas rivers add significant
amounts of freshwater during floods.
The circulation on the Texas-Louisiana shelf is basically affected by several
factors including river discharge, weak tides, winds, and eddies detached from
the Loop Current in the eastern Gulf of Mexico. Based on a theoretical
calculation of shelf freshwater content using a hydrographic data set, Dinnel
and Wiseman (1986) estimated that approximately 53\% of the total Mississippi
River flux discharges consistently onto the Texas-Louisiana shelf.
Fig. 2 shows the daily volume transports of the Mississippi and the
Atchafalaya Rivers for the historical mean, maximum, minimum (U. S. Geological
Survey, 1994), and also for the Mississippi flood of 1993 (U. S. Army Corps of
Engineers, 1994). The thirty-year monthly mean observations show an annual cycle
of seasonal variability of river discharge for both rivers. Usually high freshwater
runoff from both rivers occurs in the spring period, with springtime average
transport of about 20,000 and 10,000 $m^{3}/s$ for the Mississippi and Atchafalaya
Rivers, respectively. During the summer, the average river flux decreases to about
one-half that of the spring flood season. Unusual freshwater runoff from both rivers
reached record values during the summer flood of 1993, with fluxes comparable to
the average values of the river discharge during the spring period.
Many studies have been conducted on the circulation patterns on the
Texas-Louisiana shelf. However, the first comprehensive description of the
seasonal circulation scheme on the Texas-Louisiana shelf is given by
Cochrane and Kelly (1986) based on the M/V GUS III hydrographic data collected
during 1963-1965. They used the monthly mean geopotential anomaly to infer
general seasonal circulation patterns over the shelf in a low-frequency view,
which recently have been supported by detailed hydrographic surveys (Jochens
and Nowlin, 1994, 1995; Li et al., 1997). The results show that a shelf-wide
cyclonic (anticlockwise) circulation dominates the mid-shelf region from September
through mid-June (non-summer season). During
the non-summer season, the near-shore coastal current, carrying low-salinity
water, prevails westward and southwestward and the shelf-break current
propagates in the opposite direction.
Cochrane and Kelly (1986) and Li et al. (1997) indicated that the along-coast
current is enhanced by the river discharge from the Mississippi-Atchafalaya
system; on the other hand, the coastal current is stronger during the
spring flood season than at other time of the year.
It is well known that the upper layer ocean current responds to wind on a
short time scale. In an analysis of the coherence between winds and sea
surface currents on the Texas-Louisiana shelf, Cochrane and Kelly (1986)
and Wang (1996) concluded that the inner-shelf current is strongly coherent
with the along-shore wind component. While the along-shore wind turns
upcoast (in direction from the Rio Grande to the Mississippi Delta) from
late-June through mid-August, the coastal current on the southwestern part
of the shelf also turns upcoast and an anticyclonic circulation forms in
the mid shelf. The right-bounded coastal current near the Mississippi
Delta disappears during the upcoast wind period. With regard to the M/V
GUS III data, it should be mentioned here that Dinnel and Wiseman (1986)
pointed out the Mississippi and Atchafalaya Rivers had relatively small river
discharge during the 1963-1965 period. It is of interest to study the
variability of the summer circulation pattern caused by unusual river discharge
events such as the summer flood of 1993. Does the southwestward along-shore
coastal current persist due to the large river fluxes during the upcoast wind
period under flood conditions? Also, what is the physical mechanism by which
the cross-shelf front is influenced by winds over the inner shelf?
In drift bottle studies of the plume and density-driven current associated
with the Mississippi River discharge, Chew et al. (1962) suggested that there
is a stagnant region near the delta off Pass \`{a} la Loutre, the southeast
pass of the Mississippi River, separating an eastward and a westward flow
along the shelf. Wiseman et al. (1976) and Wiseman and Dinnel (1988) suggested
that an anticyclonic circulation within the river plume off Southwest Pass has
been found. The turning current separated into two parts as it approached the
shore; one flows toward the downcoast (westward) becoming the along-shore coastal
current and one returns eastward toward the delta. Wright and Coleman (1971)
indicated that the plume dynamics for South Pass, the Mississippi River, involve
mixing processes and entrainment. When freshwater discharges onto the shelf off
South Pass, where the depth changes rapidly, the buoyant plume detaches
rapidly from the bottom associated with vertical mixing, and subsequently
lateral entrainment is associated with plume spreading. In contrast to
the plume dynamics of South Pass, the Atchafalaya River plume can be
described as a two-dimensional feature that is basically dominated by
lateral entrainment, because the plume is well mixed vertically when
freshwater discharges onto the shallow Atchafalaya bay (Wang, 1984).
A variety of modeling studies have been applied to the Texas-Louisiana
shelf in particular. Several coastal models have focused on the shelf
circulation in response to wind stresses, but the effects of riverine inflow
have not been included (Barron, 1994; Current, 1996). Chen et al. (1997)
developed a two-dimensional (a transect in the cross-shelf direction)
model to study the influence of river discharge, weak tides and winds
on the shelf off Atchafalaya bay. The model predicts that, in the
absence of all external forcing except river discharge, two significant
circulation cells are found within the frontal zone near the shelf break:
a clockwise cell with downwelling flow on the onshore side and an anticlockwise
cell with upwelling flow on the offshore side of the front. The cross-shelf
circulation pattern is similar to that predicted by a three-dimensional
model with idealized bottom topography (e.g., Chapman and Lentz, 1994),
but the along-shelf component of flow with a maximum velcity of 160
$cm s^{-1}$ seems unreasonably swift. Perhaps because the potential energy
associated with river discharge is accumulated in the model domain if
the along-shelf variation of the plume is neglected. Oey (1995)
applied a three-dimensional, prognostic numerical model to the entire
Gulf with uniform 20-km grid resolution horizontally in order to study
the relative effects of wind stress, river discharge and offshore eddies
interaction on the Texas-Louisiana shelf. The modeled circulation patterns
are in reasonable agreement with those proposed by Cochrane and Kelly (1986),
but the detailed structure or mixing processes of the river plume are still
unclear.
These studies give a good view of the characteristics of the Mississippi
River plume. However, questions remain about the spatial and temporal
structure of the plume on the Texas-Louisiana shelf. What is the influence
of winds on the Mississippi River plume? Also, how is the river plume
modulated by the weak tides found on the Texas-Louisiana shelf, where the
tidal range is generally less than 0.5m (Zetler and Hansen, 1972; Reid and
Whitaker, 1981)?
Irregular coastline configuration and variable bottom topography have been
recognized as important mechanisms for influencing the flow in the coastal
ocean. Based on a diagnositc calculation of the interaction between bottom
topography and the density field, Holland and Hirschman (1972) found that the
``JEBAR'' term plays a important role in the potential vorticity balance; the
term refers to a vorticity tendency resulting from the joint effect of
baroclinicity and bottom relief. Theoretically, the JEBAR term can be separated
into two parts; one is the bottom pressure
torque induced by the interaction of bottom pressure and bottom topography,
and one is the compensation by the density stratification for the effect of
variable bottom topography (Greatbatch et al., 1991). From the dynamical point
of view, the JEBAR term is a component of forcing that drives transport of fluid
across isobaths; in other words, a barotropic current is induced by the JEBAR
torque to satisfy the condition of no divergence of horizontal transport when
density varies along isobaths (Huthnance, 1984; Csanady, 1985; Sheng and Thompson,
1996).
Several studies have shown that eddies are generated behind headlands
due to the lateral friction of the shores (Zimmerman, 1978; Signell and Geyer,
1991), and due to the flow trapped by submarine canyons (Howard, 1992; Chapman
and Gawarkiewicz, 1995). The Mississippi Canyon is located on the shelf near
Southwest Pass of the Mississippi River. Is the river plume trapped or
influenced by the submarine canyon? If so, what is the structure of the
plume and the current in the vertical near the canyon?
D. Objectives and Hypotheses
Recently, detailed hydrographic surveys on the Texas-Louisiana shelf have been
conducted as part of the Louisiana-Texas Shelf Physical Oceanography Program
(LATEX) at Texas A\&M University during the 1992-1994 period (Jochens
and Nowlin, 1994, 1995). These observations permit study of the dynamic
processes of the currents and the seasonal variability of low frequency
currents over the Texas-Louisiana shelf, but questions about the contributions
of the Mississippi River discharge remain. This study addresses the question:
Can the evolution of the river plume and associated shelf currents be characterized
by a numerical model using LATEX hydrographic data to initialize and verify the
model?
River plumes are among the most interesting physical oceanographic phenomena
in the coastal ocean, and they are important to the management of fisheries
development and the prediction of river-borne pollutants. Several
estuarine-shelf areas have been studied and partial work has been done on the
Texas-Louisiana shelf. The principal objective of present research is to study
the formation and evolution of the Mississippi-Atchafalaya River plumes on the
Texas-Louisiana shelf by means of an existing numerical model. Particularly,
the following questions are addressed.
- (1) What is the spatial and temporal structure of the Mississippi River plume
under different wind regimes?
- (2) What physical mechanisms are important in the plume front near the river mouth
and downstream?
- (3) What are the important mixing processes of the cross-shelf front over the
inner shelf?
- (4) How is the model-predicted summer circulation pattern on the Texas-Louisiana
shelf affected by the summer flood of 1993?
Two hypotheses or assumptions are made in this study:
- (1) The river plume structure is primarily affected by winds. The influence
of tides, the Loop Current, eddies detached from the Loop Current, and surface
heating/cooling are expected to be relatively small and are not considered here.
It is reasonable to make this hypothesis based on observations. Cochrane and Kelly
(1986), Wang (1996) and Li et al. (1997) demonstrate that the low-frequency circulation
pattern over the Texas-Louisiana inner shelf is principally dominated by local
winds and river discharge.
- (2) For convenience, the vector wind stress is taken to be spatially uniform over the
entire model shelf at any given time. Wang (1996) analyzed observed wind data by an
objective method to a $1^{\circ} \times 1^{\circ}$ resolution over the Texas-Louisiana
shelf. The results show that wind stress is quite uniform over the shelf during the summer
and fall season except during severe storms of small scale, such as hurricanes. While the
vector wind stress is nearly uniform over the shelf, the along-shore and cross-shelf
components vary significantly because of the shelf configuration.