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Estuaries
Vol. 13, No. 2, p. 125-132
June 1990
Tidal Straining, Density Currents, and
Stirring in the Control of
Estuarine Stratification
J. H. S IMPSON
J. BROWN
J. MATTHEWS
G. ALLEN
School of Ocean Sciences UCNW
Marine Science Laboratories
Menai Bridge
Gwynedd
United Kingdom
ABSTRACT:
Buoyancy input as fresh water exerts a stratifying influence in estuaries and adjacent coastal waters.
Predicting the development and breakdown of such stratification is an inherently more difficult problem than that
involved in the analogous case of stratification induced by surface heating because the buoyancy input originates
at the lateral boundaries. In the approach adopted here, we have adapted the energy considerations
used in the
surface heating problem to describe the competition between the stabilizing effect of fresh water and the vertical
mixing brought about by tidal and wind stirring. Freshwater input induces horizontal gradients which drive the
estuarine circulation in which lighter fluid at the surface is moved seaward over heavier fluid moving landward
below. This contribution to stratification is expected to vary in time as the level of turbulence varies over the tidal
cycle. The density gradient also interacts directly with the vertical shear in the tidal current to induce a periodic
input to stratification which is positive on the ebb phase of the tide. Comparison of this input with the available
stirring energy leads to a simple criterion for the existence of strain-induced stratification. Observations in a region
of Liverpool Bay satisfying this criterion confirm the occurrence of a strong semidiurnal variation in stratification
with complete vertical mixing apparent around high water except at neap tides when more permanent stratification
may develop. A simulation of the monthly cycle based on a model including straining, stirring, and the estuarine
circulation is in qualitative agreement with the main features of the observations.
Introduction
tion, so the development of stratification depends
on the vertical fluxes of density which result from
the mixing processes.
In the most basic approach to the problem of
predicting stratification, we assume that the stratifying effect of buoyancy inputs and the mixing
produced through mechanical stirring by winds and
tides act independently. The competition between
these influences determines the existence or absence of stratification. This approach has achieved
some success for areas of the shelf seas, remote
from estuarine influence, where the only stratifying agency is the input of heat at the surface. Models
incorporating
surface heating together with stirring by tidal currents and wind stress give a satisfactory first-order account of the partitioning
of
the European and other shelf sea areas into wellmixed and stratified regimes separated by transitional frontal zones (Simpson et al. 1978; Simpson
198 1). The positions of these fronts are satisfactorily predicted by the h/u3 criterion which is based
on the simplest model in which only heating and
Understanding the development and breakdown
of stratification is a key objective of shallow sea and
estuarine oceanography. The level of stratification
in the water column is crucial in controlling the
intensity of vertical mixing and hence the vertical
fluxes of water properties such as heat, salt, momentum, and the nutrient elements. The latter may
be of critical importance in limiting biological production. By inhibiting vertical displacement, stratification also serves to influence the degree of light
exposure experienced by marine organisms. Phytoplankton located in a shallow layer above a strong
pycnocline receive a much more generous input of
light energy than in an environment where vertical
mixing is complete and the plankton are regularly
displaced over the full depth.
Stratification
is thus a fundamental control on
Its relationship
to vertical
primary production.
mixing is equally a question of considerable physical interest and some subtlety since, just as the
level of vertical mixing is controlled by stratificaQ 1990 Estuarine Research Federation
125
0160-8347/90/020125-06$01
SO/O
126
J. H. Simpson et al.
tidal stirring are considered (Simpson and Hunter
1974). More elaborate models include the effect of
wind stirring and allow the surface heat flux to be
influenced by sea-surface temperature
so that the
seasonal cycles of temperature
structure and heat
storage can be predicted (Simpson and Bowers
1984). These models have also been adapted to
allow for the fact that the efficiency of stirring is
not constant but is dependent on the level of stratification (Simpson and Bowers 1981).
By contrast with these developments
for the
heating-stirring
problem, we do not yet have useful
models capable of predicting the onset and breakdown of stratification for regions where there is a
significant input of buoyancy in the form of fresh
water. The fundamental difficulty is that, unlike
buoyancy input by surface heating which is more
or less spatially uniform over large areas of the
ocean, freshwater buoyancy is mainly input from
one or more discrete sources at the lateral boundaries. This form of input effectively precludes the
straightforward
use of local exchange models like
those employed in the heating-stirring
problem.
In this paper we aim to address the question of
freshwater-induced
stratification from a viewpoint
stimulated by some recent experiments on the interaction of density currents and vertical mixing
(Linden and Simpson 1986) and a time-series of
salinity stratification obtained from a mooring in
Liverpool Bay. We shall develop a model of the
growth and decay of stratification based on energy
considerations and including local contributions to
stratification from the estuarine circulation and the
interaction of the tidal shear with the horizontal
density gradient. The important role played by the
latter in inducing short-term periodic stratification
is then explored in a simulation of the springsneaps cycle.
Model Framework
Following the approach used in previous models
of the heating-stirring
competition (e.g., Simpson
and Bowers 198 l), we consider the processes modifying the stratification
which is specified by the
scalar parameter 4:
,G=;
s
_’ p dz
h
where p (z) is the density profile over the water
column of depth h. C$(units Jmms) is the work required to bring about complete mixing. When only
heating and stirring are important, we can describe
the time development of 4 by
d4 -%Q
-=
dt
25
& ckp$
- bkspsF
The first term on the right represents
the increase
in stratification due to surface heating at a rate Q,
while the second and third terms are due to stirring
by a tidal current of amplitude ui and wind of
speed W, respectively. E and 6 are the corresponding efficiencies of mixing and k and k, are the effective drag coefficients for bottom and surface
stresses. (Y and cr. are the thermal expansion coefficient and specific heat of seawater and p, is the
density of air.
This formulation
is readily extended to situations where buoyancy is also input by fresh water
if we can regard this additional buoyancy source
as being uniformly distributed over the surface as
we assume for the Q input. Freshwater input as
rain may approximately fulfil this condition so that,
for a precipitation rate I) (m s-i), we can write the
combined buoyancy source term as
(gh=;($+hp)
where Ap is the density difference between sea water
and fresh water.
In areas within and adjacent to estuaries, however, the main input of freshwater buoyancy is from
river discharge (R) which enters from sources at
the lateral boundaries. In this case, the buoyancy
is distributed in the horizontal by the local current
system which will be at least partly buoyancy-driven. It is not therefore generally possible to make
any simple assumption about the local input of
buoyancy in terms of the total river discharge.
Nonetheless,
attempts have been made to relate
the distributions of stratification and the tidal stirring intensity in areas of freshwater
influence,
sometimes with a fair degree of success (e.g., Bowman and Essaias 1981). Such correlation
of the
distributions suggests that the flow regime acts to
distribute the buoyancy in a more or less uniform
way over the stratified area. If generally true, this
would seem to open the way to application of the
model with a freshwater buoyancy input corresponding to R/A where A is the stratified area.
We should note, however, that A is itself a function
of the freshwater input R and the stirring and is
part of the solution rather than a fixed input parameter (see Fig. 1).
It would seem, therefore, that there is no simple
way to deal with the problem of freshwater input
as specified by the discharge rate R, and we proceed
to explore an alternative viewpoint.
Stratification Induced by the
Estuarine Circulation
The freshwater input from rivers induces substantial horizontal gradients of density in estuaries
and the surrounding waters. These density gradi-
Estuarine Stratification
127
-p_
---
(OCEAN)
Fig. 1.
circulation
P
+-
A__
(ESTURRY)
UC3
\
Schematic of a stratified region maintained by freshwater input in competition
with bottom stirring. The estuarine
u(z) moves light water offshore at the surface and heavier water onshore in the lower layers thus increasing stratification.
ents drive a shear flow circulation with low density
water flowing offshore at the surface and higher
density water moving shoreward at the bottom (Fig.
I)*
We can determine the contribution
of such a
shear flow to 4 as follows: the derivative of 4 with
respect to time is
Substituting
in (1)
i.e.,
(2)
where we have neglected the periodic change in 4
due to the tidal variation in h. For horizontal flow
in the x direction the density advection equation
is just
ap
dt=
ap
-“ax
ap
which, if - is independent
ax
a;
-=
at
of z, implies
_u- ap
ax
Alternative forms of u(z) based on different bottom boundary conditions lead to closely analogous
results with the difference only in the numerical
factor. A result similar to eqn. 2 was obtained by
Bowden (198 1) and estimates of this stratifying term
in the equation were made by Czitrom (198 1) on
the basis of measured profiles of velocity and density.
If estuarine circulation is the only stabilizing influence and is opposed only by tidal stirring, then
we may write as the condition for the maintenance
of stratification:
a@
4E
z-kkps
37r
h
4E
-~1 g2h4 0 -ap * z-kkps
320 N,p dx
3~
h
0
so that
dt,
(u - tYi)zdz
(I)
a result which allows us to calculate the input to 4
for any known form of the velocity profile u(z).
To represent the velocity shear due to estuarine
circulation, we use the well-known steady state flow
in which the pressure gradient is balanced by frictional forces. With a no-slip condition at the bottom boundary, the velocity profile is given by (e.g.,
Officer 1976, p. 118)
9
3
or
L 136;
CkN
g2
X constant
(3)
This result, equivalent forms of which have been
derived for other velocity profiles (Bowden 198 1;
Van Aken 1986; Nunes and Lennon
1987) is
somewhat akin to the much-used ah/u3 criterion
for the heating-stirring
case. It differs from the
128
J. H. Simpson et al.
quent increase in the horizonital fluxes and the
rapid development of a stratified structure.
Contribution
Fig. 2. Schematic of tidal straining: (a) isolines vertical at start
of ebb (b) stratification induced by shear on the ebb modified
by top and bottom mixing.
latter in that it depends on the local horizontal
density gradient, which is determined by the overall advection-diffusion
balance, rather than the
source strength R for freshwater input which is the
ap
equivalent of a. Since z is not readily obtained
except by reference to observation, the criterion
represented by eqn. 3 is less fundamental and more
difficult to apply than the heating-stirring
condition.
It should also be remembered that the eddy viscosity, N,, cannot properly be treated as a constant
because of the very large changes in the tidal current and, hence, the intensity of turbulence and
vertical mixing over the tidal cycle. The variation
in N, may be described by the simple form (Bowden
1953):
N, = ylulh
(4)
where 1Q 1 is the depth mean speed of the current.
Large values of N,, occurring during the main
flood and ebb when mixing is strong, may effectively suppress the density current and restrict its
stratifying action to times near slackwater. This
alternation of periods of density current flow and
strong vertical mixing has been illuminated in a
recent series of experiments using a lock-exchange
tank equipped with an air bubble system to induce
vertical mixing (Linden and Simpson 1986). The
density current regime set up by the removal of a
barrier between different density fluids is disrupted
by mixing induced by the bubbles. The vertical
structure is largely destroyed and what horizontal
transport there is in response to the horizontal
gradient may be regarded as a shear diffusion process. When the mixing is switched-off the density
current regime is rapidly restored with a conse-
from Tidal
Straining
In the real world, the simple picture of alternating periods of high and low mixing is complicated by the influence of the vertical shear in the
tidal current which is not (as yet) represented
in
the laboratory experiments.
The shear acts on the horizontal density gradient
to induce vertical structure by the mechanism illustrated in Fig. 2. Isolines of salinity which are
initially vertical at the start of the ebb are distorted
by differential displacement, with the lighter surface water moving faster seaward and overtaking
heavier more saline water in the lower layers and
thus generating a stable structure. Vertical mixing
by wind stress near the surface and tidal stress at
the bottom will tend to transform the structure
into a two-layer profile with a sharp halocline.
Knowing the velocity profile we can readily estimate the contribution
to C$of the shear process.
A widely used form of u(z) is that given by Bowden
and Fairbairn (1952) which can be written in the
simple form:
~(0 = ti(a - b {*)
a = 1.15; b = 0.425
Substituting into eqn. 1, the rate of increase
due to tidal straining is
of 4
Hence
0x
a4
=
0.031ghCi$x
St
On the flood the process will be reversed and, even
in the absence of mixing, the stratification induced
on the ebb will be eliminated by the end of the
flood so that there will be a periodic fluctuation in
stability. Tidal stirring will oppose the development of stratification on the ebb and accelerate its
breakdown on the flood. A condition for the occurrence
of significant Strain-Induced
Periodic
Stratification (SIPS) is that the average input over
the ebb half cycle
0
a4
2 x
atst=7r
0.03lghu
ap
-
lax
should be greater than the mean tidal stirring power over the same period
Estuarine Stratification
5
km. 0
-5
km. O-
AS %.
Fig. 3. Liverpool Bay with contours of ur near the mooring
position which is marked by the diamond symbol. The positions
of CTD stations (marked by ‘&) have been corrected for tidal
displacement to show the equivalent position at mid-tide. The
location of the E-W section of Fig. 6 is shown by the straight
line at latitude 53”35’.
P, = & ek$
so-k”’
that is,
1.0
-5-10i
(5)
where k = 2.5 x 10m3 and we take 6 = 0.004, a
value determined from the distribution of thermal
stratification
in shelf seas (Simpson and Bowers
1981).
At a chosen location where h and u, are fixed,
this condition determines the minimum horizontal
density gradient parallel to the tidal flow necessary
to produce SIPS. Comparison of this threshold gradient with observed salinity gradients should permit the ready identification
of candidate regions
for the occurrence of SIPS.
Observations in Liverpool Bay
To assess the importance
of these stratifying
mechanisms and their possible interaction, we have
examined a month-long series of observations of
the vertical salinity, velocity, and temperature
structure obtained as sea-truth data during the 1985
OSCR H.F. radar experiment
in Liverpool Bay
(Matthews et al. 1988; Prandle 1988). Current meters with temperature and salinity sensors were located at 3, 30, and 35 m above the seabed in water
of mean depth 44.5 m at a position north of the
Great Orme (Fig. 3) where strong E-W gradients
AS %.
I
16
17
18
I
May 1985.
19
Fig. 4. Salinity difference and displacement data from the
mooring in Liverpool Bay for the period April 24-May 20,
1985. (a) Difference AS between near-surface and near-bottom
salinity. Interval between arrows indicates the time of the CTD
section of Fig. 6. (b) High-pass-filtered
eastward (positive) displacement as determined from the near-surface current meter.
(c) High-pass-filtered
relative displacement between the surface
and bottom current meters. (d) Low-pass-filtered displacement
for the near-surface and near-bottom current meters (top-bottom). (lower section) Expanded scales plot of AS with relative
and absolute displacements for period May 16-18, 1985. The
displacement data were processed using complementary
highpass and low-pass filters with a cutoff at a period of 24 hours
and roll-off of 12 db per octave.
of salinity generally prevail (Czitrom 198 1). At the
time of the deployment (April 24-May 2 1, 1985),
observations of the spatial distribution of temperature and salinity indicated that the E-W gradient
in the vicinity of the mooring was given by
I ap
--_-N
P ax
3.2 x lop8 m-i
behaviour at the following neaps though the effect
is less clear. In both cases there is a weakening of
the semidiurnal signal for a period close to neaps.
The occurrence
of episodes of more enduring
stratification near neaps may be attributed to the
direct effect of reduced tidal stirring and also possibly to enhancement
of the density current when
N, is reduced. There is, however, no clear indication of the latter effect in the plots of low-passfiltered displacements of the top and bottom layers
shown in Fig. 4d. Flow in the bottom layer is generally onshore at a speed 3 cm s-l while in the upper
layer it is rather variable with a mean offshore
movement - 1 cm s-’ over the period of observation.
Simulation of the Springs-Neaps Cycle
On the assumption that the contributions
to
stratification by tidal straining and the estuarine
circulation are independent, we may combine the
formulations
of sections 3 and 4 and, providing
wind stirring is negligible, write
08
6
04
(ms-11
o
-04
-08
Fig. 5. Model simulation of stratification over one month.
(a) Current velocity based on constituents M,, S,, and N,. (b)
Mean cubed speed which controls the intensity of tidal stirring.
(c) @based on a model incorporating straining and tidal stirring
only. Model parameters:
h = 45 m; $2
$!=($).+($-ekpy
= O.OSlghD$
+ 0.0031-
g2h4
= 5 x lo-* m-l. (d) 4
based on model including the density current. N, is allowed to
vary with u according to eqn. 4 with y = 3.33 x lo-* and the
condition that N, does not fall below a minimum of 0.15 m* SK’.
which may be compared with the requirement
of
eqn. 5 with ui = 0.64 m s-l (MJ and h = 44.5 m
that is,
--1 ap 2==4.5 x 1O-g m-l
P ax
The clear inference is that the straining term will
dominate and produce periodic stratification,
a
conclusion confirmed by the time series of the surface-bottom
salinity difference plotted in Fig. 4a.
Episodes of significant stratification
(AS > 0.4),
lasting for several hours, were found to alternate
with periods of complete vertical mixing, (AS = 0)
at the semidiurnal frequency. The maximum stratification occurs close to low water slack at the limit
of the westward tidal excursion. Comparison of the
phase of the relative displacement between the top
and bottom current meters with that of AS strongly
suggests the operation of the tidal straining mechanism (Fig. 4e).
At the same time, there are indications of more
permanent stratification developing at the time of
minimum mixing around neaps. A continuous period of stratification of 3 days occurs, for example,
April 2’7-30 and there is a tendency toward similar
N,P
dp
-
* _
0 ax
tkplw
-
h
To introduce the main features of the springs-neaps
cycle, we represent u by the three largest semidiurnal constituents (M2, S2, N2) that is,
3
Q
=
a,cos(qt
C
+ Xi)
1
where wi is the constituent frequency and the amplitude (a,) and phase (Xi) are determined from the
data by the standard least squares procedure.
N,
may be held constant or allowed to vary over the
tidal cycle in accordance with eqn. 4.
With these assumptions
and taking $
from ob-
servation, we may integrate eqn. 5 forward in time
from an initial condition of 4 = 0 at highwater
springs tides. Results of such computations,
with
and without the estuarine circulation included, are
shown in Fig. 5. Including only tidal stirring and
straining results in semidiurnal ‘pulses’ of stratification separated by short periods of complete mixing. The semidiurnal signal is strongest at springs
and weakest at neaps in accord with the trend noted
in the observations.
Adding the estuarine circulation (Fig. 5d) introduces periods of more permanent stratification at
neaps, again in qualitative agreement with the observations. In the example shown, N, varies with
Estuarine Stratification
u according to eqn. 4 with y = 3.3 x lo-* but is
not allowed to fall below a minimum value of N,
= 0.15 m* S-r. This value of y, which is about an
order of magnitude higher than normally used, is
necessary to avoid the development
of runaway
stratification.
Rather similar results are obtained
if the value of N, is fixed at a constant value of N,
= 0.28 m* s-l, which corresponds to the value of
N, at peak Q with y = 8 x lo-+. The numerical
values of 4 may be roughly converted to an equivalent AS by assuming a two-layer structure for which
the potential energy anomaly is just
3’5O’W.
o-
E’
.
f
D
m
zo-
3
40 -
c
La‘
34.0
50
h, and h, are the upper and lower layer
and /3= *.
With h, = 15 m
ell
and h, = 30 m
<
&l
G 30-
’ = 2(h, + h2)
depths, respectively,
3’2O’W.
10 -
g@Ashh,
where
131
Fig. 6. E-W section on 53”35’N (see Fig. 3). CTD stations
were worked between 2217 h May 6, 1985 and 0015 h May 7,
1985. High water time = 0027 h May 7.
C
AS = 0.0254
so the maximum AS N 0.18,
than the observed values.
which is rather
less
Discussion
The clear implication of our observations and
the model simulations is that the main controls on
stratification in this area of Liverpool Bay are (i)
tidal straining, (ii) tidal mixing, and (iii) estuarine
circulation. Other processes such as surface heating and wind stirring will also be important at times
and would need to be included in more realistic
simulations of the time evolution of stratification,
but the known persistence of large horizontal gradients in the region ensures that there will usually
be strong inputs from mechanisms (i) and (iii).
Our results highlight the particular contribution
of mechanism (i), tidal straining, in producing relatively large semidiurnal episodes of haline stratification in a way which has not been previously
emphasized in the literature, although it is clearly
apparent in many earlier observations. We would
expect similar behaviour to occur wherever horizontal gradients are strong enough to satisfy our
criterion (eqn. 5).
We have assumed in the model that the horizontal density gradient is spatially uniform and invariant in time. Trials suggest that a better fit to
the observed AS variation would be obtained using
an E-W density change which includes a quadratic
dP
term so that z varies with x. We have not pursued
this approach here, principally because our aim has
been to demonstrate the essential mechanisms with
the simplest model but also because we have no
sound basis for estimating
PM.
the nonlinear
term in
It is important to recognize that the observed
variation in AS is a time-dependent-effect
occurring
over a large area of Liverpool Bay and not a local
effect due to the tidal advection of a stratified structure past the point of observation. This interpretation is confirmed by E-W sections of density taken
near high water like that shown in Fig. 6 which
has virtually complete mixing over the whole section during periods when AS at the mooring position was very close to zero for a period of -4
hours (see Fig. 4a).
We might expect such periods of intense mixing
at the end of the flood, especially as the tidal range
increases toward springs, when the tidal straining
acts to produce vertical instability which will drive
convective mixing. In this respect straining, which
is otherwise reversible, can lead to the irreversible
transfer of salt through the water column and hence
contribute to the landward salt flux.
For the levels of mixing observed in Liverpool
Bay, the magnitude of SIPS is greatest at springs.
This is, however, not always the case. With increasing tidal stream amplitude, simulations show
that the us tidal stirring term in eqn. 5 becomes
progressively more significant and eventually dominates, so that complete mixing occurs over almost
the entire semidiurnal cycle for a period around
springs and the maximum SIPS occurs near neaps.
At some intermediate
level of stirring, the maximum SIPS occurs between neaps and springs.
The operation of the density current mechanism
is evident in the generation
of periods of more
permanent stratification near neaps when stirring
is reduced. The modulation of the density current
132
J. H. Simpson
et al.
on the time scale of the semidiurnal tidal and fortnightly cycles is less clearly defined in the observations. Enhancement
of the density-driven flow
around low water slack when N, is reduced should
result in a delay in the time of maximum stratification to some time after the maximum relative
displacement.
Such a phase lag is not readily inferred from the AS record which exhibits significant short-period variability during each episode
of stratification (see Fig. 4e).
There may, however, be indications of the preferential action of the density current during the
latter part of ebb in the asymmetric waveform of
the relative displacement
which shows westward
movement for - 7.5 hours of the semidiurnal cycle.
The maximum relative westward displacement is
delayed - 1.5 hours after slackwater at the surface
while at high water, when the column is vertically
mixed, the two turning points are virtually coincident. This asymmetry between ebb and flood may
reflect the interaction
of tidal straining and the
density current, that is, stratification produced by
straining on the ebb will reduce N, and hence facilitate the density current which will reach a maximum around slack water of the barotropic tidal
current.
Conclusions
1) Freshwater buoyancy inputs operate to induce
stratification in coastal waters by driving a density
current flow which will be modulated by tidal variations in vertical mixing.
2) Tidal straining acts on the horizontal density
gradient in a way which tends to produce periodic
stratification with stability increasing on the ebb
and decreasing on the flood.
3) Both these stratifying mechanisms are opposed by tidal stirring. Comparison of the stirring
intensity with each of the stratification inputs leads
to criteria for enduring and periodic stratification.
4) A first-order linear simulation of the competition between these processes with a fixed horizontal density gradient reproduces the principal
features of a time-series record of haline stratification in Liverpool Bay over two spring-neap cycles.
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