THE MOVEMENT OF POLLUTED SEA WATER
,.
NEAR MARMORILIK, GREENLAND;
ITS CAUSES & POSSIBLE CURES
..•.....
THE MOVEMENT OF POLLUTED SEA WATER
NEAR MARHORILIK , GREENLAND;
ITS CAUSES & POSSIBLE CURES
E. L. LEWIS
Frozen Sea Research Group
Institute of Ocear. Sciences , Patricia Bay
9860 r1est Saanich Road
Sidney, B. C., Canada
vaL 482
ttAY 1978
-~
..
CONTENTS
1.
Introduction and summary of recommendations
3
2.
Oceanographic data from the·Marmorilik district
7
3.
Circulation in arctic fjords
14
4.
Hethods of retaining polluted waters within Agfardlikavsa
fjord and their probable consequences
23
5.
A floating boom dam
28
6.
Suggested programme of environmental observations
31
)
Appendix - Hydrodynamic effects of a break in the floating dam
D.M. Farmer
33
References
38
2
FIGURES
1.
General view of the location 9£ the Black Angel Mine giving
the positio~ pf measurement stations.
4
2.
Bathymetry in the vicinity of the Black Angel Mine.
5
3.
Water depth profiles along Afgardlikavsa and Qaurnarujuk fords.
6
4.
Mean summer and winter profiles of tell'perature, salinity, and
9
density from Site 4 in A fjord.
5.
Mean SUl'IUIer and winter profiles of tenperature, salinity, and
density from Site 10 in Q fjord.
10
6.
Temperature and salinity variations in moving from the head
of A fjord out over the sill and seaward in Q fjord.
12
7.
A schematic of wind set up.
15
8.
The typical structure of sea ice.
17
9.
Increase of mixed layer depth due to salt rejection by sea ice
19
during growth.
)
10.
Dissolved lead concentrations in A fjord.
21
11.
Resonance periods for internal \o'9-ves on the interface between
seawater and a fresh water layer trapped behind a dam.
26
12.
Schematic of an ice boom floating darn for fresh water retention
in A fjord.
29
3
l~
Introduction and Summary of Recommendations
Tailings dumped into Agfardlikavsa fjord from the Black Angel Mine at
Hanrorilik, in Greenland, are to some extent soluble in sea water and high
concentrations of dissolved heavy metals exist in the fjord basin. During
winter months, vertical cO,nvective circulation caused by the rejection of
salts by sea ice during growth mixes these high concentrations up',;ards into
the surface waters which are then moved out into the neighbouring Qaumarujuk
fjord by tidal exchange. Figures 1, 2 and 3 show respectively a plan of the
general area defining measurement stations referred to in the text, the loca~
bathymetry ) and approximate depth sections along lines defined by 1-4-10 and
10-12-16 on Figure 1.
The oceanographic and meteorological data available from the area is
fragmentary and satre of it is of questionable accuracy. A selection has been
mace and the fjord studied in terms of the basic dynamical. processes common
to arctic fjords in as far "as the data would allO'.o1. This has proviced a base
for evaluating possible solutions to the dissolved heavy metal transport problem but has sharply defined the need for furtiter i:lvestigations.
"In spite of the lack of data it has proven poss~le to make a clear
suggestion of the optimum method of pollution control though quanti tati ve
detail awaits acquisition of better data from the fjord, particularly tiT:!e
series records.
As a ~ethod for permanent control of the pollution it is recOr.h~~ded
that the discharge point for tailing disposal be moved to near t1te bottom of
the fjord, that the density of the tailing t-laters be increased to be significantly above that existing within the fjord at that depth at present. This
should be done by cooling the \.,rater prior to discharge and increasing its
salt content either by removal of water by distillation to be used for domestic
purposes and discharged separately or by the addition of rock salt. The optimUJ
salinity for discharge cannot be computed on the basis of the present data but
the matter is so important that it is suggested that an increase to 40 0 / 00
salt should be instituted as soon as possible as a stopgap measure. The full
effect of this introduction of more dense tailing 'tolaterS will not hecorr.e
apparent for a number of years but should still minimise -the spread of heavy
"rretals even after the mine has closed. ~"1hile the mine is still operating i t
"is recommended that a fresh water surface layer be retained in Afgardlikavsa
fjord by reeans of a floating darn across the sill. This recommendation is
subject to the COl:!!Ir.ent of a competent engineer with experience in ice boom
construction on the feasihili ty of such a structure.
)
It is furthe~ recommended that a program of environmental measurements
be instituted imrrediately enabling proper quantitative design criteria to be
applied to the above recommendations for fresh water retention and tailing
water density increase. Approximately $35,000 \'lorth of instrurr.ents would be
used for at least one year.
)
,'
-,,
o
1
L
!
2
km
FIGURE 1
General view of the location of the Black Angel
mine giving the positions of measurement stations.
I
o
o
,oo~
Q
-/
(
FIGURE 2
DEPTH IN METERS
o
I
1
•
km
2
I
Bathymetry in the vicinity
of the Black Angel inine.
~STATION
(y
'NUMBER
4
~_ _ _ _+,1_ _ _ _-t~2_ _ _ _-t3L+_':""'-i4~_ _ _-i5
km
25
50
75
,
0"
FIGURE 3
Water depth profiles along
Agfardlikavsa and Qaurnarujuk
fjords.
100
The location of the
station numbers is shown in
Figure 1.
125
150
175
10
2
3
12
STATION
4
NUMBER
5
G
@
7
8
9
25
50
..
::;
'.
75
,
100
~
.< 125
'-
,"
150
175
I
I
200
225
I
I
)
2.
Oceanographic Data from the" l>Jarmorilik District
The data available derives from two sources; that tabulated in
the reports issued by the Geological survey of Greenlnnd under the
general heading Recipient unders¢gelse Agfardlikavsa and Qaumarujuk
Fjords (hereinafter A ~ Q Fiords) from 1972 through until the latest
report covering 1976-77, and from casual observations made by staff
collecting data for these reports.
TWo thousand tons per day of tailings in 6,000 m3 of salt
tailing water of varying salin"ity and of temperature about 16°C are
pumped through an outlet into A fjord at a depth of 25 rn where the
water is 50 m deep. Sea water for use with the tailings is extracted
in the region of the sill at a depth of a few meters. The tailings
are fairly evenly distributed and except when air bubbles are inadvertently discharged with the tailing waters no turbidity has been
noticed on the surface of the fjord at any time of year. It is
remarkable that no suspended tailing materials have been noticed
outside A fjord at any time, and increases in the lead and zinc concentrations in the bottom sediments of Q fjord have" been attributed
to chemical processes causing deposition of dissolved material.
Measurements were made in one year when there was a labour strike
in the mine but no "changes in pollution levels were noticeable.
Run off from the nearby ice cap has been estimated as 2 m3
per second during September, a figure which would appear to be
conservative. Flows of this type normally show a strong diurnal
variation, a function of the incident solar radiation, and a discharge peak in Mayor June of the year at the time of surface
snow melt from the land. Probably 90t of the run off occurs in
the period June - october inclusive. It has been said that half
the total volume of A fjord is avail~le as discharge fresh water
each year. A thumb nail calculation shows that if this flowed
evenly into the fjord over 5 months, about 4 m3 per second of
fresh water would be required.
Tides are mixed diurnal and semi-diurnal with a range of about
180 cm (spring) and 100 cm (neap). No measurements have been made of
tidal currents over the sill of A fjord but if one assumes that tidal
currents are uniform in the water mass a simple calculation of the
volume exchange required in the tidal period would indicate that
velocities were below 3 crn/sec. It must be emphasized that this does
not mean that velocities over the sill are beneath that value but
that those that can be ascribed to tidal forces acting alone on a
homogeneous water mass are.
The fjord freezes up around Christmas time and ~ m of sea ice
grows by the following April. One of the most remarkable features
of the data available from the reports is the difference in the fall
and winter profiles of zinc and lead concentrations shown in Table 1,
taken from the 76/77 report. It is seen that during the summer period
heavy metal concentrations are at a low level outside A fjord and
that within the fjord high concentrations are only seen below the
SeptelI'be!:' 1976
Station
Narch 1977
ph
No.
Depth, m
1
0
10
20
30
SO
53
3.5
4.2
8.0
149
682
708
118
521
643
4
0
10
20
30
50
68
5.5
4.8
9.9
125
884
942
10
0
10
20
30
50
75
100
112
0
10
20
30
SO
75
100
150
178
17.2
31
18.5 8.6
0
10
20
30
50
75
100
150
200
5.7
2.8
0.9
1.2
1.7
6.7
11.0
5.1
5.4
12
)
16
TABLE 1:
Zn
2.1
3.5
Zn
183
151
153
142
179
177
141
3.6
3.9
5.2
93
631
635
197
165
137
123
108
-119
169
138
138
110
112
112
7.3
4.2
2.9
9.7
8.0
20.9
28.0
26.2
1.3
2.3
1-6
4.4
5.6
12.3
16.1
150
132
16.3
3.6
1.5
5.7
7.4
~.8
195
145
194
13 .0
2.5
2.6
2.6
2.2
2.1
127
89
56
1.7
1-5
2.0
0.9
0.5
8.0
2.6
2.9
4.6
5.7
12.3
22.6
12.3
1-7
150
125
42
2.5
3.9
1.3
2.6
1.4
3.1
124
90
30
0.7
1.2
0.5
1.3
0.6
1-0
5.0
3.3
1.6
2.0
2.6
6.5
9.0
5.5
3.1
79
44
15
5.7
1.5
1.0
0.9
0.3
41
23
9
1.8
1.6
0.6
0.2:'
- 0.3
1.6
"73
at.. -._-the- -various
-Dissolved
- - - - - . - _zfnc
. _ - - and
- - - -lead
- - - -co~centrations
- - - - - - - - -_._- _._-- .. _-.-.
stations in
Ph
~b~
0.3
9
SITE
4
TEMP. ,"C ...•........
1
-+I ______+-____
I
-2~____
-_'~____ 0
I
I
SALINITY
30
0/00
2
-+~
I
32
25
24
33
I
srGMA-T
23
~4
I
-----
31
I
I
____3+-____
I
-~-.-.-
26
27
28
29
Ot-----~--~~--~----~----~--~
-' _. _. _. -.-: -:::."7:.-:-,,' ....... .;.-:"....... - - -:.:...::': .:..::.::...: ....: ~-..:.
.. ' . . . .
\
-- ..... ' ,
I
,c
40
.
>-
nrm
!1.
0
\
I
\
I
I
i
:z:
w
'\
SUMMER
rrrm
rJm
80
)
o
T
I
I
I
I
I
40
E
I
...:z:a.
I
ll.I
o
I
rrhrr
80
WINTER
120
FIGURE 4
l1ean summer and winter profiles of temperature,. salinity
and density from Site 4 in A fjord.
as (p Ip
-1) 10 3 where P
Sigma-T is defined
is the density of the sea''''ater
T
T' max
at temperature T and p
the maximum density of fresh
water (near 4 D C) .
max
.
a
1
2
TEMP. "C. . ..........
1
4
3
2
I
SALINITY
32
31
D/ OO
- - - ---
34
33
I
I
SIGMA -T .-._.-._.
23
24
a
25
26
- - --=-.=.!..-:...:..-::: '--..:, -=';:;:
E
.....
40
w
0
...., ---- ..
.,
I
\
\
,
'.
......
',
"
,
"
~
\
.
80
29
'
~
:.
:J:
2&
:....-..-. -:-:,.... • .:...:.:... . . . . . . . . . . . . . . . . . . . . . . . . . .
.............
....
27
\
.
.,!
SUMMER
,,
,
1
1
rr/m
min
m'm
,,
\
.
120
,,
T
1
1
I
40
E
..
"
\
..
\
.
..
,
:J:
....
w
0
\
\
80
WINTER
FIGURE 5
)
\
\
\
.. .
.
120
\
,,
,
,
\
i
1
\
I
firm
rrtm
rdm
Mean summer and winter profiles of temperature, salinity
and density from site 10 in Q fjord. Sigma-T is defined
as
(p Ip
-1) 10 3 where P is the density of the seawater
T
. T' max
at temperature T and p
the maximum density of fresh
max
water (near 4 D C) .
)
11
depth of tailing injection. In the winter of 1977 the concentrations
are more or less even from top to bottom and it is clear that
material is being moved out over the 5111 (depth 21 m) to contaminate
the upper waters of Q fjord. The higher levels shown in the deeper
waters of station 10, in September 1976, are present at Station 12
but not at Station 16 (Figure 1).
They appear to be remnants of the
values at that station found in March, 1976, circulation during the
summer of 1976 having reduced concentrations above SO m to those
shown in the table. Clearly, there is a difference in water movement
between summer and winter and to interpret this the 'density profiles
at the various stations are required, calculated from measurements
of terrperature and salinity. Figures 4 & 5 show these parameters as
a composite of information acquired from all the reports_ A selection
has had to be ~ade on a subjective basis as some of the measurements
would appear to be erroneous. For example, on occasion, more dense
water apparently overlies less dense water, a situation that can only
occur for a short period under ext~emely dynamic conditions_
Data collected through the sea ice in winter ~particularly
subject to observational error. A common problem is due to \-later
freezing in the oceanographic bottle before samples are withdrawn.
As the ice formed is almost pure the salinity of the remaining water
is enhanced giving a false reading \-lhich, combined with temperature,
giVes densities that are too high. More puzzling is the "warm winter"
as indicated by the ~Brch 77 readings in A fjord. Waters beneath
growing sea ice must usually be very close to their freezing point
due to the vertical circulation induced by the salt rejected by the
sea ice during growth but these data show waters nearly l~C above
freezing point. If this is not an instrumental error it ~~uld appear
to be possible only as a highly transient condition that might result
from a sudden exchange of the waters in A fjord with those outside, a
point that will be discussed later. As all of the other winters shOl"
values close to freezing we will assume that freezing is the "normal"
state, there being insufficient information to make any other comment
on this curiosity.
Summer data Sho~ no density inversions but a normal spread of
values from year to year and indeed from day to day as the flow of
fresh water into A fjord causes changes in the surface layers or
strong winds mix in this fresh water downwards. Occasionally strong
winds are sufficient to remove the fresh water layer completely; the
September '74 data show4fa surface layer in A fjord of about 3J.~%o
salinity at a temperature of about 2.7°C.
Figure 6 shows salinity/temperature/density data out to
Station 16. There is an increase in the surface salinity as one progresses a\'Iay from A fjord and the development of a distinctive mixed
iayer down to a depth of about 20 m, almost certainly a result of the
wind blowing over an increasing fetch.
Helicopter operations from Narmorilik have produced an intermittent record of wind velocities and air temperatures in the latter
half of 1977. It is clear that little significant cooling of the
water takes place before October 20th when air temperatures, for the
first time, drop below freezing. There~ a rise in air temperature
',.. 26
'c. -2
28
0
30
2
32
4 ' -2
r""=::::::-;/,>
0
2.
26
-2
4
1---1..---'--
28
30
2
32
4
1=-=':'=:-:--:"'"
St 10
SI 1
-20
2
26
4-2
1----'----'--7'>
St 12
28
30
2
o
1-.L..-~?7
St 1(;
E
....Q.I
W
"
FIGURE 6
Temperature "and salinity variations in moving from
the head of A fjord out over the sill and seaward
in Q fjord.
m
"
32
4
Station positions defined in Figure 1.
13
St
about November 15th, 1977 which remained moderate until the end
of the month and then progressively got colder until December the
16th when a combination of calm and increased cold probably indicated freeze-up. Studies of water structure beneath sea ice depend
greatly on knowing the initial conditions just before ice formation
and for the present purpose we are only able to make an intelligent
guess based on the September data and some knowledge of the rate of
heat extraction. The wind records indicate that most of the winds
were along the axes of A or Q fjords which is to be expected
)
from a local topography and the location of the heliport.
The stronger winds were towards the mouths of A and Q fjords and
storms had typical long term values around 20 knots. A maximum of
37 knots was recorded on December 8th. As observations were taken
only during helicopter operations it must be emphasized that the
stronger winds may not have been recorded and that there may be a
bias in the data because it is being taken at the same time of day
rather than regularly throughout the 24 hrs. It has also been said
that the winds in the center of the fjord are much stronger than at
the helicopter site. Thus, the data should be taken as indication
of a meteorological situation rather than a quantitative description.
Dissolved oxygen values of around 9 mg/l in A fjord independent of depth in summer showed that the waters were not stagnant.
As a whole the data gives "snapshots" of conditions in A and
Q fjords without giving clues to the circulatory processes involved
in water exchange. Of the very many relationships between energy
input and water movement possible in the typical fjord, only a fet"
are present usually and it is necessary to obtain indication of
dominant factors from time series measurements before an adequate
analysis of the system can be carried out. No such clues are available from the }~rrnorilik data and much of it is of questionable precision. Under these circumstances it is simply not worthwhile to
apply sophisticated methods of data analysis; the best that can he
done is to indicate probable processes involved in water movement
and to see how these serve to explain the observed water structure.
An enhanced observational program is required before the pollutant
transport problem can be properly described and suggestions along
these lines are the subject of Chapter 6.
14
3.
Circulation in Arctic Fjords
The outstanding feature of Arctic fjords compared to those at
a more southerly latitude ~s the absence of significant run off from
the land and the isolation of the waters of the fjord from wind mixing
for a significant part of the year. The paper "Oceanography of an
Arctic Bay" by Gade et al (1974) gives a good description of seasonal
changes and mechanisms to be expected in a fjord at 700N which probably
may be applied to the Q-A fjord system with a suitable change in dates
for- freeze-up and melt. Some of the unusual features occuring during
the winter under the ice cover are the subject of a paper by Perkin
and Lewis "Mixing in an Arctic Fjord" (1978).
Energy inputs to Arctic fjords occur from the wind, from the
tides, from the melting of floating ice masses, from the fresh water
input, and from the salt rejection by sea ice during growth. Floating
ice masses are absent from A fjord but are present in Q fjord. To
understand the circulation of A fjord)wind mixing and tides should be
considered during the summer and tides and the salt rejection by sea
ice during growth during the winter. A further possibility is exchange
of waters over the sill of A fjord due to the density differences between waters in A and Q fjords. Such a density difference may be
caused by a reduction in salinity of the lower layers of A fjord due
to upward diffusion of salt as the fresh water run off proceeds seaward near the surface.
Winds blowinq down the fiord transfer part.of the~r energy to
and by shear forces cause a mixed layer to develop at the
s'urface which increases :in depth as the wind fetch increase"s:- i'1hen
fully developed this produces a two layer system, a near homogeneous
surface layer above a layer with considerable density gradients.
Assuming a uniform density gradient near the surface in early summer
and following Pollard, Rhines and Thompson (1973) gives a wind mixed
depth of 6 m at the sill for 20 knot winds over A fjord which is in
good accord \yith observation. Eventually the density differences
between these layers prohibits further mixing due to simple shear
proc~spses aI:ld the wind.. _tnav_be .thQught~::tp_ '~s.et uP" the surface laver
against a coastline so that it is deeper at the downwind termination
and the interface between the two layers tilts upwards in the upwind
di.rection~
Such "set-ups·' are accompartied"by-a,--s.urface current in:
the wind direction balanced by a return flow beneath. These processes
are indicated diagramatically in Figure 7 - a & b. Following Hellstrom (1941) a difference in height of about 3.8 m is calculated
between the position of the interface at the end of A fjord and at
the sill for a 20 knot wind. An extreme case of the wind "set up"
phenomenon is shown in Figure ?-c where the constant density line
terminat~in the surface under continuous high wind.
Under these
conditions very extensive mixing can occur, probably ~o the fjord
bottom. On one occasion an observer measuring dissolved metal concentrations in A fjord on a very windy day observed high concentrations in the surface waters moving out into Q fjord and we presume
that on that occasion some such happening occurred but the general
form of the summer heavy metal concentrations as given in Table 1
indicate that this is not common.
~e. water
15
CALM
( a)
<E'<_W:...c..1 ND
(b)
«
WIND
(c)
FIGURE 7
A schematic of wind set up. Extreme winds (c) can
remove the fresh surface layer entirely from part
of the basin and cause strong vertical mixing.
16
Wind/water interactions can also give rise to transient phenomena that can be of great importance in considering vertical pollutant
transport. For example the sudden cessation of a steady wind responsible for set-up often res.ults in abrupt changes in surface layer
thickness being propagated down the fjord. Such wave fronts may be
reflected and/or amplified by local topographic features. Whether or
not such phenomena play an important part in water circulation in A
fjord awaits analysis of time series data.
Winds are rarely steady and a record taken over a long period
will frequently show energy peaks at certain frequencies. A two
layer system
in the £j ord \'li11 allow internal waves to exist on the
interface whose velocity is a function of the layer depths and the
difference in density between them. Waves are partially reflected
from the coast and dimensions between coastlines, across fjords, etc.
define lengths, which in turn define resonant frequencies for the
given interfacial wave velocity. With the usual complexity of headlands, embayments, etc. frequently many such resonant frequencies
exist and if the wind spectrum contains energies at these frequencies
large scale transfers from wind to fjord are possible. For example,
with summer conditions and a 6 m deep surface layer in A fjord, as
defined in Figure 4, one would anticipate an interfacial velocity of
39 cm/sec and a resonant period bebqeen the fjord head and sill
!l/4 wave lenqth because the interface lies abov_e sill depthl of
about 11.4 hours. An energy input near this period would be available from the tides; other possible resonances in the system might
take energy from the winds.
If we suppose that such energies are
--- ~"
'"'~
- -"
aval..lable the internal vlaves may cause signl..ficant additional mixing
betWeen water layers by partially breaking as they are reflected on
the shores of the system and by direct shear mixing, typically just
below the layer interface.
The discharge of 6,000 cubic rn per day of water at 16 DC leaves
another unsolved problem although as has been noted, no surface concentration of suspended tailings has been noted in the vicinity of
the tailing discharge outlet. A calculation shows that this amount
of heat entering the fjord would be sufficient to raise its temperature by .1DC in about a hundred days if the loss to the surroundings
were minor. Data for winter water temperatures in A fjord often seem
to be about .1DC above freezing point; this could be the cause. It
should be noted that close to freezing point temperature only has a
very minor effect upon density which controls vertical movement in
the water column. In summer it would have a larger effect and steps
should be taken either by control of salinity or temperature to ensure
that these tailing waters cannot_cause vertical circulation.
As the fresher water moves seaward in summer more salty waters
are entrained into the lower part of this fresh layer and taken seaward so that the density of the basin water in A fjord is continually
being reduced. Conditions outside the sill may be ~fected by a
variety of conditions which are not consequent upon those within the
sill to produce a situation where the sill separates two water masses
of different density below a uniform-layer above -sill depth. This
density structure is unstable under any perturbation, a situation
that pertains to all fjords and causes exchanges of basin waters at
AIR
-POLyCi1'is-iALLINC AND-TRANSITION
REGIONS
COLUMNAR
CRYSTALS
l - - - I C E PLATeS WITH BRINE INClUSIONS
AS ~SANDWJCH FILLING-
'.
FIGURE 8
~he
typical structure of sea ice.
See text for discussion.
18
intervals. Fjords have been observed with annual exchange, exchange
every three years, every thirty years, etc, etc., depending on conditions. Gade (1973) has given a formula for basin water renewal based
on the arumal salinity red,uction and the variation characteristic of
the water density profile outside the sill but this cannot be applied
to Q & A fjords due to lack of data. In the case of a shallow fjord
such as A fjord, it might be thought (there being no firm experimental
evidence whatsoever) that such an exchange might occur every few years.
Whether or not this can explain the "warm winter" of 1977 cannot be
said; we may be looking at a measurement error only and whether this
additional circulation is of importance in terms of pollutant
transport will depend on the velocity with which the incoming
exchange water rolls down the inside face of the sill and the
depth to which it penetrates.
It appears certain that the most important form of circulation with regard to the winter transport of dissolved pollutants
into Q fjord is that associated with salt rejection by sea ice
during growth. This occurs because ice does not form solid
solutions except with a very few exotic materials and that all the
constituents of sea water are unifor.mly rejected by the ice crystal
lattice. As this process is of importance in tailing ponds in
Arctic regions as well in the present context it is tol0rth discussing
it in some detail.
Although the salts are rejected by the growing ice inclusions
of brine get trapped between ice platelets and this is illustrated
in Figure 8. A poly crystalline region of small ice crystals with
random orientation is above a region of columnar crystals where the
axis of symmetry of large crystals lies very close to the horizontal.
The "skeletal layer" illustrated is the lotl1er extremity of these
crystals and the entrapped brine exists between small plates protrUding down into the underlying water. As the sea ice grows the
temperature around each brine inclusion drops as the freezing interface leaves it behind. Further freezing must then occur within each
inclusion for the brine to stay in thermodynamic equilibrium with a
solid phase surrounding it and the expansion associated with this
freezing causes cracking. When very large numbers of such inclusions
are discussed the overall effect is the production of brine drainage
channels which look like vertical river estuaries complete with tributaries extending up into the sea ice to maybe two thirds of its depth.
Brine drainage occurs both at the freezing interface and from these
channels and the potential energy so released into the water column
is the driving force for vertical convective circulation. It should
be noted that ice will clear almost any impurity from the water and
that on an average about 10% of the initial pollutant or salt concentration remains locked tl1i thin the inclusions in the ice during the
winter.
Once the snow melts from the sea ice surface in early summer
the brine drainage channels act as foci'- for internal melting within
the ice sheet. The walls of the channels'can melt at a lower temperature than can the surrounding ice due to the presence of salt and
concentrated brine. The channels are also disrupt'ions in the crystalographic pattern of the ice sheet so the sun's incident , radiation is
scattered and absorbed. Once the dense brine trapped in the channels
is released by melting it moves downwards under the influence of
DAYS AFTER INITIAL ICE FORMATION
o
15
30
45
60 75
FIGURE 9
Increase of ~xed layer depth
due to salt rejection by sea ice
during growth.
Assumptions: -
•
salinity of ice is 3 D /
10
DO
- constant ice growth of 1 ern/day
- one dimensional model ignoring
sloping sides to fjord or bottom
irregularities
20
-
E
-
-
-
- ~"'- -SILL DEPTH
initial profile has a 6 m thick
wind mixed layer of 31.7%0
water at freezing point. The
remainder of the profile is taken
from the summer data ,(Figure. 4) .
30
-0---0--INITIAL
- no advective exchanges
PROFILE
I
- heat from the water column has
negligible effect on the ice
growth rate.
I- 40
D...
W
o
50
GO
•
70}---------------~--------------+_----------~~~---25.5
26.0
26.5
27.0
. SIGMA
T
)
2Q
gravity into regions of higher temperature en~ling it to cause
further melting of the surrounding ice. While still remaining above
its freezing point the di~uted brine will continue to descend causing
further melting until it runs right out of the ice sheet into the
underlying water.
The salinity of this draining brine has h,een
measured at over twice that of the water from which the sea ice .,.las
originally formed and thus it penetrates to a-considerable depth
below the now disintegrating ice sheet.
For the immediate purpose freezing during the winter and the
circulation associated with it is considered. This problem was first
posed and solved by Zubov (1943) and experience indicates that his
calculations are quite adequate in the context of the present data.
Based an an educated guess of the density profile at the time that
freeze-up commenced (around mid December) Figure 9 shows the increase
of the mixed layer depth due to salt convection as a function of
time assuming that 1 m of ice grolY'th occured evenly during the period
Jan 1 to March 31, 1978. It is seen that convective mixing occurs
right to the fjord bottom.
On the basis of the existing observations it would appear
certain that significant vertical transport of dissolved pollutants
to depths where they become available for movement out over the sill
by tidal circulation results from saline convection. The_only
practical way to prevent this which carnes to mind is to arrange for
retention of a fresh water layer from the summer of sufficient depth
to allrnY' the ice to grow with little salt rejection and to confine
the resulting circulation to trivial)depths by the very large vertical
density change at the fresh salt/water boundary.
Before considering various ~ethods of keeping a fresh water
layer on the surface of A fjord throughout the year it is necessary
to realize that one important consequence of this action cannot be
predicted with any accuracy, the rate of change of the dissolved
heavy metal concentration depth profile with time, when the annual
winter outflow of heavy metals into Q fjord has been stopped. Taking
the concentration of dissolved lead as an example, Figure 10 shows
the profile measured in September 1976 at Station 4 in A fjord
together with that from the following March. The more or less uniform
March profile is about 140 ppb less than wofild have been obtained by
mixing the concentrations from the September profile to produce uniform distribution of lead, and the real export of lead must have been
in excess of this as further material must have dissolved into the
water from the tailings during the September to March interval. The
exi~ting data sh0wf the ~~~~ __ .~~eady st~te Sept~~.t: _profile re,sulting
from an annual winter extraction but, as we have nO knowledge of the
. rate at which lead will e.nter sO,lution fr'?gt the tai~~ngs when there is
no annual extraction, it is irl!Possible to compute the shape of a ne\Y'
September curve. This is illustrated schematically on Figure 10
showing that an enhanced lead concentration is anticipated just above
the tailings and that the profile shape will change vlith time. We do
not know whether suc,!;,.a change l-Till occur in years or decades. It is
clear that the rate ~ which lead enters solution depends on the concentration of dissolved lead immediately adjacent to the tailings and
any water movement in the area tending to reduce the local lead
,.
LEAD; . parts in
~
\J1
o
109
\J1
o
'"o
o
o
o
,
:
It,
,,
10
20
®
: MAR.1977
, -'-'-'-'-'-' -'-'-'
~ "'-- ------
-'-'-'-'-'-'-'SEPT. 1976 ---- --------_"'--..,
'-:': -·-·-·_· __ .C-....A).-.....
... ®
~
.~
-~
30·
;---.
~
E
40·
r
50
:
~
-......
,
"
--~,~, "~~, '''\,
,
~
L
Ll 60 .
\
i
.I
)
I
I
I
•
~!
70
80'
PIGtmE 10
Dissolved lead concentrations in A fjord. The curve labelled I'A" is speculative
and is intended to show what might happen if the annual winter transport into
Q fjord ceased.
)
22
concentration Nil! encourage further flow of lead from the tailings.
In the limit the molecular diffusion coefficients for lead will be
of importance as well as the levels of oxygen concentration and pH.
There may be other factors as ,...el1. It has already been pointed
out that the eventual exchange of the basin waters in A fjord is
inevitable unless the sill is closed off by a solid dam. At that
time a considerable proportion of the dissolved heavy metal above
the tailings are bound to escape into Q fjord.
23
4.
Hethods of retaining polluted waters within A fjord and
their probable COnsequences
An obvious method of controlling the discharge into Q fjord
is to build a dam across the A fjord sill complete with a sluice gate
to control the
rW1
off of waters.
It is understood that this is im-
practical on two grounds; cost, and the fact that the ore carriers
docking facilities are in A fjord. Nevertheless it will be considered
because, in effect, A fjord is then a tailings pond and similar considerations would apply to any alternate location. Suppose then that
the dam were built and the gate were controlled to produce a fresh
water layer 4 or 5 meters thick on the surface of A fjord at mid
summer. It has been seen that the usual depth of wind mix in A fjord
with a typical summer density profile Nas about 6 meters, but with
the retention of fresh water this would be significantly reduced, and
it is probable that little mixing would take place along the salt/
fresh water interface. Winds blowing across the surface would cause
set-up and calculation indicates that a steady 20 knot (10m/sec) wind
blowing down A fjord would cause a difference in level of 52 cm between
the two ends of the fresh/salt water interface - a matter of little
consequence. The period of oscillation of internal waves on the
densi ty interface is shown in Figure 11 a,s a function of the fresh
water layer depth. These will be excited if there is .significant
energ}r~ In the wind field" at these frequencies-~
It- Is- ant-:LcJ.pate.d
that in the late fall, just befo-re -freeze-·up;--t'he-s-urface 'layer
salinity should not exceed 5% 0 on average. Vertical convective
circulation associated with surface cooling will be greatly restricted
even within the upper layer itself as the maximum density of water of
this salinity occurs at temperatures above freezing point. Thus, the
sensible heat available from the water column will be greatly reduced
and one would visualize that freeze-up could occur up to two weeks
earlier than if the surface layer were not controlled. Ice would
begin to form and eventually develop the structure as shown in Figure
8. Even if all the salt were rejected from the ice during growth the
salinity of the upper layer would still only increase to an average
of about 6 or 7%°' far below that of the underlying waters and no
downward interlayer miXing would occur.
Sea water for use in the extraction process would be taken
from outside A fjord·at a depth where the salinity would at 1east
equal that at the bottom of A fjord and care taken that it was ejected
into A fjord with an enhanced salinity and at a temperature not far
above freezing. The 6000 m3/day tailing 'inflow constitutes about
aIm layer laid over A fjord during a year so that 'vithout wind
mixing the fresh/salt interface would move up by this amount annually.
By adjusting the thickness of the upper layer the top meter of the
lower layer could be wind mixed into the upper layer which would
then have to be replaced each year to avoid a cumulative salinity
build up. This, in turn, sets a minimum required elevation of the
top of the sluice gate above the high \vater mark in Q fjord - that
of the desired fresh water layer, say 3 m as a compromise to allow
some mixing by wind in summer but none by vertical saline convection
in 'vinter.
RESONANT PERIOD
OF INTERNAL MODE
l-+-----A/2·4km
,.'
--~---------1-------r_-----
7
0
h
6
,0 - 1.027 gm/,m 3
SOm
0
5 -
0
~
lfl
L
:J
0
4-
.J::
o
~
3-
o
0
0
n::
o
o
w 2
o
Q
FIGURE 11
1
Resonance periods for internal waves on the
interface between seawater and a fresh water
layer trapped behind a dam (solid or floating).
o~--------+---------~---------+----------~------~1
5
2
3
4
HEIGHT h
(m)
25
The overall level of the pond or fjord would then be dropped
as far as possible just before the main snow melt ,.,hile checking the
electrical conductivity of the discharged water and raising the sluice
gate if it exceeded some predetermined level. During this period the
rotting sea ice would prevent wind mixing to any appreciable extent
while the fresh surface layer was being replaced.
The significant environmental difference between a dammed A
fjord and a tailings pond is probably the volume of run off but as
winter vertical convection is not really of great importance when
pond and sea are totally isolated)ice growth itself may be used to
purify the surface waters. If it may be assumed that the annual ice
g:~~~_~xceeds the annual increase in ~ater height due ,to discharge
of tailings, in theory it is always possible to run off that amount of
'-'neai:'ly pure 1jah~-r' every--year so it-s to--return- to t.he"same level for
the start of the next years cycle. Year by year, concentration of
dissolved metals will, of course, build up in the pond and it has already
been noted that these profiles are not predictable on the basis of
existing knowledge. However, impurities will be excluded from a
surface water laye~,. at least ~qual t9 .. ~~, maximl.Ull ice thicknes!=i: __ ,_ ,E~~.e:~tial fac;.:t,ors for success in ss=~e;~~~._~£, ._thi~ __ ti"pe are~q;t.low!?:_-:-.
1)
that a sufficiently thick layer of fresh water can be retained
each year on the surface to reduce wind mixing to small proportions
2)
that internal wave systems existing on the interface between the
two layers do not exceed a certain amplitude where shear mixing
may occur. This, in turn, depends on the natural frequencies of
the basin and the energy content of the wind.
3)
the volume of tailings discharged converted to a water level
increase over the year does not exceed the annual ice growth
thickness.
The sluice gate would be dropped just after freeze-up to allow the
escape of possible pure water, then raised by 3 or 4 meters. Ice growth
in the winter would purify another meter layer and hopefully the snow
melt would once again fill up the pond to where \"ind mixing was effectively eliminated. Of the blO water control proposals available for use
with a tight dam, a fresh water layer summer and winter, or summer only
using ice growth to purify surface.water, the latter is preferable as
it eliminates the need to remove salt annually to compensate for the
tailing input. In addition it is not necessary to know the rate of
solution of the heavy metals. Only the former proposal is available
for non water tight systems.
Because of difficulties associated with bringing vessels through
locks in a solid dam it has been suggested that a "dam with gap" should
be built leaving a passage for ships in and out of A fjord. This would
retain a thicker fresh water layer than existed before through th,e
greater part of the year, but at the critical time just before freezeup when we anticipate that flow from the glacial streams ...sill have
reached a very low level it would do nothing to prevent the eventual
escape of the remaining fresh water; no t~...o layer system would be
possible and saline convection would, once again, occur to the bottom
26
of A fjord.
A dam of this type may have positive disadvantages as i t
would increase the velocity of flow of tidal waters in and out of
A fjord to the level where it is quite possible that significant
entrainment of the lower waters might occur and, as a result, heavy
metal discharge might occur at all seasons of the year.
The pollutant
concentration above the tailings ''''culd be reduced at all times of the
year r not just during the ,,,,inter so that more would go into solution
and the annual discharge of heavy metals would increase.
Allother possibility is a "leaky dam" formed by a loose rock fill
across the mouth of the fjord and sill.
Such a dam
~7ou1d
do Ii ttle
to retain the fresh water layer but would act as a diffuser for the
tidal currents so that if, due to the density structure, any high
velocity levels existed with a potential for downward mixing, they
would be eliminated.
A more useful idea would be a rock darn faced_or cored for the
upper three or four meters to be water tight and fitted with a
sluice gate/lock system for water control and entrance to the ships.
This would appear to provide most of the necessary factors and the
reduction in current velocities both by control of the outward
flowing current in the upper layer and of tidal diffusion to the
lower layer would probabl~ extend the period of the inevitable basin
water exchange greatly.
A further possibility, and much cheaper to construct, would be
an ice boom across the mouth of the fjord with a hanging curtain 3
or 4 m deep with a removable section or sections for the entrance
of shipping. Structures of this type exist on the St. Lawrence
River to protect sensitive areas from ice pressure. Such a floating
structure could not, of course, have a sluice gate but it would
appear that the most suitable design would allow escape of fresh
water over the curtain rather than underneath it in order to avoid
comparatively high velocity water corndng into contact with the lower
. laver. _At toe ~ame time it would b_e ,undesirable to "lose" large
quantities of fresh water due to surface waves,' etc •. "tn"'the al:iove- .. _surface portion the curtain might be a type of diffusing screen.
This is the author's presentl~i-favoured solution. The only signIficant disadvantage that is apparent is enhanced tidal flow velocities
due to the restriction in a cross sectional area available for tidal
exchange between Q and A fjords.
An entirely different form of solution would be to pump fresh
water beneath the growing ice, shortly after freeze-up, so as to
prevent vertical convective circulation. This would certainly work
providing always the temperature of the water discharged was a few
tenths of a degree above freezing point. As the bottom of the water
in Arctic lakes must be around 4°C this would become a problem in
insulation during transit from its source to discharge in A fjord.
After the ice had grown sufficiently to support the operators a
slot could be easily cut in the ice over the sill and a short
plastic skirt hung through to restrict the loss of fresh water into
Q fjord. Weekly monitoring would then be sufficient to ensure
that a fresh water layer was kept there at all·times.
)
27
Should any of these schemes be implemented the question
arises as to what situation would exist upon the termination of
mining activities, maybe 10 years hence. What further inspection
and control of the polluted fjord would then be necessary? There
is a hope that the tailing would be overlaid by a layer of rock
flour which must materially reduce their ability to go into solution. Another concern is what would happen if the floating boom
herein suggested as an optimum solution ruptured and the 4 or 5 m
layer of fresh water discharged into Q fjord? The floating boom
solution will naw be investigated in detail •.
)
28
5.
A Floating Boom Dam
Any structure placed over the sill of A fjord to retain fresh water
will have to withstand ice pressures when break-up occurs in the spring
and it is fortunate that the problems posed in designing ice booms have
heen quite well explored. Perham (1974 and 1977). 'give's design details of
structures used on the St. Lawrence River. The engineering detail of a
floating dam of similar design is beyond the scope of this report but in
theory it liOuld appear that a hanging curtain might be added to an ice
boom which would then be built in hinged sections that could be individually
transported without difficulty.
Suppose then such a darn were installed across the mouth of A fjord,
conplete with a "lock" section for ore carrier transit with an impervious
"sail" extending a distance h above the free water surface and a weighted
"keel" hanging dowmvards to an indefinite depth. Fresh water flowing into
A fjord would then displace salt water near the surface until a fre"sh water
layer, approximately SOh thick had been b~ilt up when further fresh water
would flow over the sail. If sail height and keel depth were limited to
the values required to produce the designed fresh water layer thickness
there would be losses due to surface waves over the sail and interfacial
waves under the keel. It is desirable that the main flow of fresh water
be over the sail to avoid comparatively high currents at the keel bottom
with possible entrainment of saline ~qater from beneath. Nevertheless, once
the ice has formed it may well be that no'flow route over the sail would
exist and any fresh water entering the fjord (possibly from underground
flows) would have to escape beneath the keel. This might occur suddenly
. <luring !i ,storm ~n?- would be p,art,iC;::,uf,?-rly undesirable. Poss;ibly the best
solution is that sail and keel should bot~_consist of solid sections surm:>unted by leaky diffusing plates. The 'upper diffUsing -plate would allow
a steady flow outward into Q fjord to balance input into A fjord and
normally prevent large scale water loss from waves. The lower plate would
not normally carry a steady flow but would tend to smooth out any escape
events. This is illustrated schematically in Figure 12. The mechanical
response of the system to surface waves would need to be investigated.
with a floating darn the escape of waters to'compensate for the
annual I'm layer increment associated with the deposition of tailings'
would no longer be necessary. Saline ~laters would move out over the sill
beneath the keel at miniscule velocities to achieve a volume balance. The
fresh water layer would be automatically renewed and there would be no
sluice gates to require attention. The layer thickness could be adjusted
in a practical design by blocking off apertures in the sail diffusing
plate. From Figure 11 it appears :that a suitable layer thickness to prevent wind mixing might give a two hour period to the longitudinal. mode of
the fjord and it is thought unlikely that energies at this frequency would
be dominant in spectra of the wind or tides.
The major uncertainty in this design is the time rate of change of
the pollutant concentration profile - a topic that has already been discussed and is illustrated in Figure 10. Whatever rates of profile change
are observedJthey can be minimized by lowering the tailing discharge outlet level to near the bottom of the fjord and taking precautions to ensure
that no vertical circulation of the convective plume type' can rise from
the discharge, specifically the water should be cooled and its salinity
--
_.-_...--.-----;z-:-n..r
-.. - ... - .....
~.~
..
,0'.
.........
~.~.;; .:.
....
FLOATION
"LOGS"
FLEXIBLE
SKIRT
I
I
00000000
o
STEEL
. ROPE
IGHTS
FIGtffiE 12
Sche~atic·
of an .
floating d
l.ce boom
.retention : . ~orfJord.
.fresh wate r
30
checked so that it is at least as dense, preferably denser, than the ambient
water at the point of discharge.
In the normal course of events an exchange of basin water in A fjord
would be inevitable as has already been discussed. In fact, restriction of
vertical circulation by the fresh surface layer would prevent the basin
getting its annual "salt supplement" and so hasten this exchange.
If, how-
ever, the tailing waters were returned at an enhanced salinity, significantly
greater than that existing outside, the exchange might be delayed indefinitely.
It is understood that part of the water extracted from the fjord is distilled
to provide fresh water and thus the salinity of the discharge water could be
increased materially above that of its source. This would have the additional
effect of creating a greater stability in the bottom waters of the fjord so
that the diffusion of pollutants upward from the tailings might almost reduce
to those levels predicted by the molecular diffusion coefficients~
In addition, if the salinity of the lower waters of the fjord could
be increased sufficiently the winter vertical convective circulation, the
main cause of the present problems, would cease ~vi thin the basin~ From the
Zubov calculations shown in Figure 9 it may be predicted that the winter
convection below 30 m would cease if the salinity of the basin \-later exceeded
35.5% 0 at DoC or 37% 0 at 10°C.
The floating dam is now seen as a temporary solution to be continued
tmtil the basin salinity has been increased to a suitable level. Even if
mining operations make the salinity enhancement of the tailing water difficult, presumably the enpty inco~ng ore carriers could bring rock salt which
could be crushed and fed into the discharge outlet~ The total weight of
rock salt required would be of the order of 10 5 metric tons~ Recommendation
of an optimum salinity for the discharged water will require considerable
further study as well as a much better data base.
An increase in basin water salinity would therefore reduce upward
diffusion of heavy metals, prevent winter time convective mixing and postpone
basin water exchange indefinitely. Hopefully the tailings, when covered
with natural sediment after the mine is closed will no longer go into solution
and it even may be possible that the rock flour ~.,ill tend to precipitate the
remaining dissolved heavy metals as has been postulated to happen in Q fjord.
Even if this is wishful thinking, the enhanced density of the basin waters
~ill cause the release of pollutants over the sill into Q fjord to occur
very slowly. How slowly cannot be predicted with the present data base and
is bound up with recommendation for discharge salinities.
A final consideration, the effect of rupture of the floating dam is
dealt with in the appendix~ A small rupture of 5-10% of the length of the
dam, would cause a 4 m surface layer to be reduced to I m over the course
of a couple of days, which would give plenty of time to get busy on repairs
(spare sections might be stocked for the purpose). Sudden removal of the
entire dam would produce less easily predictable consequences, but there
are reasons to expect that the transient respOnse time of the fjord would
be 20 hours or more. Entrainment and exchange would be lim! ted to the \...ater
above sill depth and most likely to the upper 10 m. Realizing that significant dam breaks must occur in open water conditions Table 1 indicated that
this loss should not be serious. Finally and obviously the removal of the
fresh layer leaves the fjord sUbject to wind mixing hut probably not more
so that it is at present.
31
6.
Suggested programme of environmental observations
The fjord responds to the energies in tides, winds, surface
run off and ice growth, and it is essential to gain information about
the time scales of these inputs and of the response of the system.
Most of the necessary data can be obtained from recording instruments
but one essential parameter, salinity, cannot yet be measured automatically at the level of accuracy necessary for useful density
determination. Specific recommendations follow. in each case, explaining the use of the proposed measurement.
1)
Meteorology
'An automatic weather station should be installed to
give wind speed and direction, air temperature and,
if possible, air pressure throughout the year. The
sensors should be located so that the values recorded
are not~ffected by the immediate buildings, rock
outcrops, etc. They should also be as close to the
shore of the fjord as possible but it is probable that
the recording unit woUld need to be kept indoors during
the winter. The measurements would be utilized to
estimate the maximum depth of shear wind mixing and to
obtain the wind energy spectrum and examine it for peaks
when optimizing the fresh water layer thickness in terms
of the resonances possible within the fjord.
2)
water Density Profiles
A simple "conductivity-temperature-depth" (CTD) system
should be purchased and records taken every two weeks
at Stations 4 and 10. A member of staff from the mine
should be trained to make these readings and contracted
to do so. He should be also required to go through a
standard calibration procedure prior to making each set
of measurements, water density is the most important
of all the parameters to be measured. It controls eve~
type of water movement discussed in this report from
internal waves to vertical convection due to sea ice
growth.
3)
Water Movement
It is recommended that two recording current meters,
complete with sensorS for conductivity and temperature
be installed just on the A fjord side of the sill where
the water is, say 30 m deep. One current meter would be
placed at mid water depth and the other l'lithin two meters
of the bottom: they would record for a year. The data
would give information on basin water exchange processes,
if any, seasonal changes in density as well as provide a
record of any long period internal waves existing at
these depths.
32
4)
Temperature Profile
To supplement
info~tion
taken with the "CTO" survey
a recording thermistor chain should be installed close
to site 4 taking readings at five minute intervals over
a period of a
fe~"
weeks in summer conditions.
The instru-
ment could be installed and recovered during the usual
September survey. These mea5u~ements are required to
record the amplitude and frequency of internal waves
existing in A fjord. It should also be deployed in
the vicinity of the tailing discharge outlet during
the winter survey trip to record the associated water
movement.
5)
Tides
A tide gauge should be put just outside the sill in Q
fjord during both summer and winter surveys and set to
record at 5 minute intervals to look for high frequency
water height fluctuations. These often exist in complicated fjord systems and are a major energy source for
driving internal waves.
6)
Run Off
It is essential that the fresh ''later run off into A fjord
and its seasonal variation be known in order to predict
filling rates behind the dam, entrainment of the lower
layer waters at various times of the year, etc. etc.
If and when such time series are av~~able it will enable
selection of those processes that are truly important in terms of
vertical water movement in A fjord from the very large number of·
possibilities that exist. It is estimated that the total value of
equipment to be used would be about $35,000.
In addition to these field studies it is necessary to Obtain
further information about the tailings themselves; maybe in a flume
tank. What water velocities are re.quired to keep the tailings in
suspension? What velocities are required to resuspend them?
(usually quite different). What are the rates at which the heavy
metals will go into solution as a function of the concentration
immediately above the tailings? The need for this information has
already been pointed out in detail.
If all the information listed above comes to hand the present
report can be rewritten and the optimum tailing disposal system
designed on the basis of the observed physical processes with little
need for speculation. lfuether or not this work is undertaken it is
recommended that the tailings discharge point be lowered and the
salinity of the tailing water increased to 40%°' at DoC as soon
as is practi caL
33
Appendix
HYDRODYNMIIC EFFECTS OF A BREAK IN THE FLOATING DAN
•
From the engineering point of view two practical considerations
arise if the dam breaks:
1)
How rapidly will the trapped fresh-w'ater layer disappear?
2)
What are the dynamic processes that are likely to draw
pollutants from the deeper layer as a result of the darn break?
Background
This is a cOng;llex problem of the "selective withdrawal" type studied
in reservoir dyanamics. Due to the poor data base, it has not been thought
useful to carry out a full analysis alo?9 these lines in the present report.
There are also other unpredictable influences due to the wind and ocean.ographic
processes outside A fjord.
In view of these difficulties the following calculations should be
considered as no more than first order estimatesi they can only be relied
upon to give a ro,ugh estimate of likely events following a break in the dam.
Further study as well as much better field data and possibly some laboratory
measurements are required to resolve the consequences of a dam break in detail.
The basic and conservative assumption is made that the water
layer
. .
,
interface remains level at all times following the dam break. In practice,
a small decrease in depth near the mouth of the fjord would be expected.
Any error involved in this assumption would have the effect of underestimating
the time required to drain the surface layer.
,,
A model for withdrawal
The maximum transport of a two-layer fluid through a constriction
occurs when
2
Fj
+
(1)
= 1
h
and h1' h2 and U1' U2 are the layer depths and
were
Fi = Ui ( g ~.)-Y2
P l.
velocities of each layer. This problem was first investigated by Stommel
and Farmer (1952, 1953) in connection with overmixed estuaries. An important
exception occurs in the presence of barotropic forcing (stigebrandt, 1976),
but this is not expected to be relevant in the present case.
For a shallow surface layer in which the lower layer is essentially
motionless, critical conditions limit the flow when the flow velocity
equals the internal wave speed; approximately:
u.
Uj •
(g
~j) ~
p
A higher velocity would imply supercritical flow in one layer with hydraulic
transitions to subcritical flow and internal wave breaking ,along the interface. It seems unlikely that such conditions could be maintained, so that
equations (1) and (la) seem useful -for estimating an upper limit to the depth
mean velocity. Wind shear could introduce further conplications but is not
considered here.
(I-a)
34
From the fluid dynamical point of view there is an important difference
between a relatively small break, for example a break between two segments
of the floating dam, and the more catastrophic case of the entire dam being
carried away. In the first case.the area of high shear in which entrainment
or mixing will occur is confined to the region immediately adjacent to the
break so that estimates of the loss of surface water may be based On the
physical reasoning underlying equation (1) or (I-a).
For a large break, or the removal of the entire dam, quite different
physical processes will apply and a simple two-layer model would give misleading results. In what follows we shall model the simpler and perhaps
more likely case of a limited break. Some of the additional physical considerations applicable to the full-scale darn break are also briefly discussed,
but no attempt has been made to model this latter example. This is an aspect
that would require further study prior to detailed planning of a floating
dam.
Consider the events immediately following a lirni ted r,upture of the
floating dam. The lighter surface water would rapidly accelerate through
the break, radially spreading out to a thin, slow moving layer beyond the
dam. Beneath the dam salt water would move inwards to replace the lost
surface layer, but this inflow could occur throughout the full width of
the channel. Thus no rapid opposing current immediately beneath the outflow
is e~ected.
Cqnsider a break of width b in a dam of total W~h B at ~he mouth
The rate" of change of volume
of a channel of length L and uniform breadth.
of fresh \-rater is then given by
d
dt (BLh,) "'" - bU,h,.
(2)
But from (I-a), substituting for U, and henceforth dropping the subscript,
we obtain
d: (BLh) = - bh
(gl!.~ h)~
(3)
or
h-~
db = - bg':!:;:
dt
(4)
BL
where g' = g ~
p
is the reduced gravity.
Integrating (4) and evaluating the constant of integration from the
requirement h = h at t = 0, gives
o
(5)
or rearranging
(6)
3S
As an illustration, consider the example of a break of 5% of
the dam width.
~p
Taking the channel length L = 4000 m, = 0.02 and
an initial depth h = 4 ro, equation (6) shows that it W~Uld take about
o
50 hours for the surface layer to drop to 1 m thickness.
This calculation almost certainly overestimates the withdrawal
rate since no account is taken of shallowing of the interface near the
break due to acceleration, or of the retarding influence of interfacial
shear stresses and entrainment.
It is assumed that the scale time of surface layer response was
significantly less than the scale time for withdrawal. This is justified
a posteriori in the present example if the time required to reduce the surface layer to 0.25 h is accepted as a suitable scaling. As indicated
above, the assumptiogs will tend to overestimate the rate of withdrawal
producing a "worst case" condition since the surface layer thickness at
the break wil~ tend to be less than that in the fjord.
Dynamic Processes associated with the dam-break
1)
When the dam breaks a wave of elevation change will travel back along
the interface towards the inlet head. If this wave tended to steepen
due to non-linear effects, short period waves with relatively high
shears could be generated and these might lead to the generation of
turbulence and mixing (c.f. Farmer & Smith, 1978).
This possibility may be checked by consideration of a first
order approximation to the non-linear equations of motion. For a
two layer flow' it can be shown that the coefficient of the non-linear"
term p is proportional to Jh2-hl)/hlhi, where hI and h2 are the surface
and lower layer thicknesses respectively. Moreover a wave of slope a,
in a coordinate system moving with the wave will al\qays tend to steepen
and break if both ~ and p are greater than zero. (For a particular
example, see Farmer, 1978).
In the present example, the surface layer withdrawal causes an
elevation of the interface. In a coordinate system moving with the
wave this implies that a>o. Since hI < h2 we have p > a and this
combination of parameters means that non-linear effects will decrease
the slope and so reduce the possibility of short period waves'
breaking following the in~tial darn break.
When the waVe is reflected it will eventually reach the fjord
mouth. Although reflection might be expected this \oIi11 be modified
to some extent by interaction with the critical conditions at the
break. "In this connection it should be noted that non-li!1ear effects
are enhanc;ed when the \oIave travels into an opposing shear, an effect
that would work in opposition to the effect of relative layer thickness described above.
'\
36
2)
Since the flow is hydraulically constrained at the location of the
dam break the existance of significant shears is implied. If the
flow really is two-layer in nature, the bulk Richardson Number
Rio ~ g'hl/U2 = 1 and with a thin, possibly turbulent layer, some
/degree of entrainment must be expected.
The entrainment rate E is hard to estimate. This value of
Rio lies between the experimental values determined by Lofquist
(1960) and by Ellison and Turner (1959). Nevertheless, by interpolation E may be estimated
(7)
where w is the vertical velocity and U is the relative velocity
between the two layers. The surface layer, being thin and more
turbulent, corresponds to the entraining layer represented by
the laboratory experiments referenced above. There are considerable
difficulties in extrapolating model results, especially interpolated
model results, to geophysical scales. It must be emphasized that
these are only first order estimates of what might occur.
From (I-a) and (5)
u
=
gl~ 2BL/(2BLh:~
+
b91~t)
•
(8)
For the example considered above, equations (7) and (8) would imply an
initial vertical velocity of 0.018 ms- 1 dropping down to .005 ms- l when
the surface layer thickness had reached 1 rn. These entrainment velocities
are initially quite large; however it.is important to note that much of
the entrained Hater will be dra~m from inflowing water entering the
fjord at, or just beneath the foot of the dam.
3)
As mentioned above, the simple model used here will only be
applicable for limited rupture of the dam. In the event of sudden
loss of the entire floating dam, the simple flow model used above
would almost certainly break down and equation (1) would no
longer be applicable. since the area of rapid flow would no
longer be confined to the immediate vicinity of the break, significant entrainment, together with corresponding interfaced
shear stresses, would occur over a ·large area. This would have
the effect ·of slowing down the seaward movement of surface water
and introducing a more gradual salinity gradient across the interface. The problem of estimating an exchange rate now becomes very
compl2x and highly nonlinear. Moreover the reduction in density
gradient would have the ~ffect of increasing the characteristic
transient response time of the inlet. It is possinle that
oscillatory effects would dominate the exchange process, a
possibility that might usefully be investigated with laboratory
models.
There is little observational evidence of transient surface
layer movements in fjords that can give guidance when estimating
the time scales to be expected in a large scale exchange. Observations we have made in Alberni Inlet of large scale wind induced
37
motions emphasise the dominant effects of shear stresses on the
response. A strong wind effect had a relaxation time of three
or four days over the upper reaches (10-15 km) of the inlet. The
relative density difference and layer depths were comparable to
the present example. Allowing for the shorter length of fjord A
and assurrdng the influence of shear stress to be similar~ one
might expect a response time of perhaps 20 to 30 hours. It seems
likely that a simple flushing out of surface water will not occur
over this period; a more probable consequence would be the loss
of a significant fraction, followed by the formation of a continuously stratified surface layer. Weak density currents would then
continue to replace this new surface layer with outside water but
at a more gradual rate.
DAVID M. FARMER
38
REFERENCES
Ellison, T. H. and J. S. Turner, (1959) Turbulent entrainment in
stratified flows. J. Fluid Mech. ~, 423-48.
Farner, D. M., (1978) Observations of long nonlinear waves in a
lake. J. Phys. Oceanog.·.!!, No.1, 63-73.
Farmer, D. M., and J. D. Smith (1978), Nonlinear internal waves
in a fjord, Hydrodynamics of estuaries and fjords, ed: J.C.H.
Nihoul, Elsevier, pp 465-493.
Gade, H. G. (1973) Deep water exchanges in a sill fjord: a
stochastic process. J. Phy. Oceanog. Vol 3, No.2, pp 213-219
Gade, H. G., R. A. Lake, E. L. Lewis
Oceanography of an arctic bay
5;
E. R. Walker (1974)
Deep Sea Research, Vol. 21,
pp·547-571
Hellstrom, B (1941) Wind effects on lakes and rivers
Ingeniorsvetenskapsakaaemiens Handlingar nr 158 Stockholm
Lofquist, K. (1960) Flow and stress near an interface between
stratified liquids. Phys. Fluids, ~, 158-75.
Perham, R. E. (1974) Forces generated in ice boom structures
Special report no. 200 U.S. Army CRREL Hanover, New Hampshire
Perham, R. E. (1977) St. Mary's River ice booms design force
estimate and field measurements U.s. Army CRREL Report 77-4,
Hanover, Ne'''' Harrpshire
Perkin, R. G. and E. L. Lewis (1978) Mixing in an arctic fjord
J. Phy. oceanog. To be published (tentatively scheduled for
Vol. 8 No.5)
pollard, R. T., P. B. Rhines, R. Thompson (1973) The deepening
of the wind-mixed layer. Geophy. Fluid Dynamics, Vol. 3, pp
381-404.
Stigebrandt, A (1976) On the effect of barotropic current fluctuations on the two-layer transport capacity of a constriction.
J. Phys. Oceanog. Z, 118-122.
Stommel, H. and H. G. Farmer (1952) Abrupt changes in width in
two-layer open channel flow. J. Mar. Res., II, 205-214.
Stommel, H. ahd H. G. Farner (1953) Control of salinity in an
estuary by a transition. J. Mar. Res., ~, 18-20.
Zubov, N. N. (1943) Arctic Ice (English translation) u.s. Navy
Electronics Lab., San Diego, Calif. pp 491.