Small scale structure in temperature and salinity
near Timor and Mindanao
By HENRY STOMMEL, Massachusetts Institute of Technology, Cambridge, M m s .
and K . N . FEDOROV (UNESCO-Paris), Institute of Oceanology, Moscow
(Manuscript received May 16, 1966)
ABSTRACT
For some time it has been known that continuous soundings of temperature and
salinity as functions of depth in the main thermocline of the ocean have much complicated detail: small inversions, extrema, and indications of homogeneous regions
separated by sharp gradients. On two occasions during the summer of 1965, closelyspaced stations were occupied in order to discover whether or not there is extensive
spatial coherence horizontally in these features. It was found that they are in fact
very thin horizontal laminae, extending from 2 to 20 kilometers horizontally, and from
2 to 40 meters vertically. After describing several different cases where the laminae
are particularly clearly discernible, the implications of the structures in understanding
the vertical mixing processes that occur in the ocean are explored. Estimates of the
probable time scale and dissipation time of the laminae are made.
Introduction
Sample soundings
I n the course of observations made in the
ocean with newly developed continuous recorders of salinity and temperature against
depth (STD recorders) oceanographers have
discovered much fine scale “microstructure” in
both the temperature and salinity traces.
We had a n opportunity for two whole days
to use a n excellent model of such a recorder
(Hytech Model 9006) kindly loaned to us by
Drs. Richard Barkley and John Marr of the
U.S. Bureau of Commercial Fisheries at Honolulu on board the research vessel AtZantis I I
of the Woods Hole Oceanographic Institution.
The first day (July 28-29, 1965) south of
Timor (13’ S, 120” E) we made a nearly random
pattern of lowerings (station numbers 2-13)
within a circle of three-mile radius. Three other
lowerings (station numbers 14-16) were made
at 10 mile intervals on leaving the area (Fig. 1 ) .
The second day (August 6-7, 1965), east of
Mindanao ( 6 ” N , 129”E), was spent making
lowerings in the form of a large cross, with
spacing between lowerings of approximately
1 mile (Fig. 2: stations 18-35). The navigation
was done with respect to drifting floats with
drogues. The data obtained during these two
days forms the basis of our discussion.
Two complete sample soundings are shown
in Figs. 3 and 4. Fig. 3 shows STD station 13
off Timor; Fig. 4 shows STD station 21 off
Mindanao.
Let us first consider station 13. There is a,
deep (135 meters) nearly mixed surface layer,
immediately beneath which is a 10 meter thick
temperature inversion layer. Beneath the
surface layer to 500 meters depth there is a
generally higher salinity 34.65(-.75) % and in
which is embedded a layer of higher salinity
(maximum layer) between 240 and 290 meters
depth, reaching 35.05 yo. The temperature
sounding is drawn on a more open scale, so
that the origin of the temperature axis had
to be reset four times during descent. The many
small features shown on the temperature sounding are doubtless real, but on the salinity trace
there are numerous small scale spikes pointing
toward low salinity which are a n artifact of
the instrument due t o imperfectly matched
time constants of the temperature and conductivity sensors and consequently some falsification in the computed salinity. This falsification appears to be limited to finest scale
“spikes” in salinity associated with strongest
vertical gradients in the temperature trace;
Tellus XIX (1967), 2
SMALL SCALE STRUCTURE IN TEMPERATURE AND SALINITY
307
120,040'E
1200 IO'E
I
.
___~__
I 3'0C
S
15
I3'3G-
s 1
I
L
120"D'E
120"b'E
Pig. 1. STD Stations off Timor are shown as solid circles. Location of reference buoy is triangle. Hydrographic station 781 is square. Rectangular area at lower left is magnified two times on lower right. Stations
14, 15, 16 are more widely spaced than close group in inset.
in fact below 400 meters the salinity trace
gives a better indication of tiny temperature
gradients than the temperature trace.
Fig. 4, showing station 21 of Mindanao, has
a much shallower mixed layer and a very steep
thermocline dropping 10°C in 50 meters. An
: :1
attempt was made to compare STD traces
with Nensen bottle casts by lowering a Nansen
bottle close to the STD suspended on the same
wire and it was found that the differences
between salinities and temperatures obtained
from water samples and reversing thermometers on the one hand and the STD recordings
on the other were roughly the same for the
whole range of temperatures and salinities
measured. The difference in salinity w w
-0.09 % and the difference in temperature
about +O.O7"C. To facilitate the direct use of
recordings for our purposes we did not introduce
these corrections into any salinity or temperature figures quoted further on in this paper.
The "mixed layer" near Timor
L-L
I Z P IJ'E
129. 20' E
06. 05'
N
Pig. 2. STD stations in form of crow of Mindanao.
The cross is roughly 10 miles by 10 miles.
Tellus XIX (1967), 2
Fig. 1 shows the positions of stations made in
the Indian Ocean south of Timor. Stations 2
through 13 are irregularly spaced within a circle
of 3 mile radius. Stations 14 through 16 extend
toward the north a t intervals of ten miles.
Fig. 5 shows the temperature and salinity
soundings in the upper 150 meters of each of
these stations, redrawn from the original records
308
HENRY STOMMEL AND K . N . FEDOROV
0
100
200
m
300
400
Fig. 3. Photographic copy of actual STD trace (not retouched) of STD station 13 off Timor. The
depth scale is 500 meters, each small division being 5 meters. The salinity curve is labeled S, the scale
of salinity is labeled at two points 34 and 35, thus each smallest division in the abscissa is 0.05%,,.
The temperature curve is labeled T (the labels A , C, and P refer to particular points of interest
on the temperature curve. At the top two temperature points on the abscissa are labeled 25" and 2 6 T ,
thus each smallest division is 0.05OC. The temperature curve has origin reset at successive depths
where it tends to go off scale. This is done in steps of 4°C as indicated by the numerals 21, 17, 13, 9
thus point A is at 21.32'C. The pens cannot both traverse the same path mechanically so the temperature curwe is offet downward by 5 meters and hence always reads 5 meters too deep. On tracings this
has been allowed for and corrected. On this photograph of the original i t must remain uncorrected.
The salinity scale is not offset in depth. A uniform correction has been determined for the STD records,
and is described in paragraph 2 of the text, but has not been applied to any of the data as it is only a
smell constant value. All temperatures should be corrected by O.O7"C, all salinities by - 0.09 %.,
Fig. 4. STD StBtion 21 off Mindanao. See Fig. 3, legend, for comments.
Tellus XIX (1967), 2
SMALL SCALE STRUCTURE IN TEMPERATURE AND SALINITY
309
0
50
m
100
150
I
1
I
Pig. 5. Soundings in the mixed layer off Timor. These are tracings of the upper 150 meters of records
for stations 2 through 16. The temperature depth scale has been corrected so that both temperature
and salinity now have the same depth scale. Gross differences of properties in the different locations
are self-evident. There is considerable variation in the vertical structure, but each sounding shows a
nearly homogeneous region near the surface (for example station 13) but some stations (for example
station 7) have shallow irregular layers overlying the mixed layer.
for clarity of reproduction. The most striking
feature of this upper 150 meters is the deep
mixed layer which extends almost the full
depth. The irregular part of the soundings a t
greatest depth is the beginning of the thermocline
and is typical of records obtained here and
elsewhere of the small scale micro-structure
observed in the oceanic thermocline. We will
discuss this microstructure of the main thermocline separately below, and confine ourselves in
this section to a description of this remarkable
mixed layer.
A cursory glance at Fig. 5 shows that from
one station to another there are fluctuations
of the temperature and salinity of the "mixed
Tellus XIX (1967), 2
layer", of rather large amplitude considering
the fact that the stations are not very far apart.
For example, the "mixed layer" on station 2
has a temperature of about 25.68OC wherew
that a t station 8 is 25.25"C. I n both of these
stations there is a shallow surface layer which
is a little warmer, but there is no mistaking
the deeper "mixed layer" itself. These stations
lie only 1.5 miles apart! Other stations nearby
show similar lateral heterogeneities in temperature and salinity. I n order to see whether there
is also heterogeneity in density, the values for
the mixed layer, as scaled from the most mixed
portions of the soundings, and tabulated in
Table 1, have been plotted on the S-T plane
310
HENRY STOMMEL AND K. N . FEDOROV
the difference in vertically integrated freshwater content is 72 em of fresh water! It
would require hundreds of days for normal
Table 1. Salinity and temperature of
the “mix& layer”
Station No.
34 3
342
34 4
%
s.
Fig. 6 . S, T Diagram of values of properties in
mixed layer at different stations. Sloping lines are
computed sigma-t. The stations 2-13 have widely
different T and S but nearly uniform sigma-t.
in Fig. 6. The sloping lines are lines of constant
density. It is seen that the points representing
stations 2 through 12 all lie on a constant density line (sigma-t 22.66 1). The points representing stations 14, 15 and 16 show a greater
deviation from this density, but then these
stations are further away. We are led to the
interesting conclusion that the vertically mixedlayer tends toward lateral homogeneity of
density, but not toward lateral homogeneity
in temperature and salinity individually.
This layer is also dynamically the Ekman
layer, so that we must expect relatively strong
vertical shear of the horizontal velocity within
it, involving displacements of the upper portions of perhaps ten miles a day. How then is
the vertical homogeneity preserved? The phenomenon is paradoxical and needs to be studied
more systematically and a reliable set of measurements of current shear in the upper layer
obtained simultaneously with the temperature
and salinity data. One also wonders whether
this is a phenomenon peculiar to the particular
geographical region off Timor, or whether it is
of more general occurrence.
I n order to fix the paradox with numbers
consider stations 2 and 8 further. The difference
in temperature is 0.43OC, of salinity, 0.19%.
The average depth of the “mixed layer” is 130
meters. Thus the difference in vertically integrated heat storage is 5600 gm cal cm-*; and
*
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Salinity %. Temperature (“C)
34.36
34.33
34.28
34.31
34.26
34.30
34.17
34.25
34.20
34.20
34.25
34.20
34.37
34.35
34.34
25.68
25.62
25.53
25.60
25.48
25.57
25.25
25.40
25.27
25.29
25.40
25.30
25.85
25.92
25.75
air-sea interaction processes to establish such
immense differences in the locally stored heat
and fresh water. I n fact it seems very doubtful
that they can do so a t all because the scale is
too small for such persistent local differences
in air-sea exchange.
The vertically integrated transport of an
Ekman layer in these latitudes is approximately lop cmr sec-l, so that if the Ekman
transport were uniform at all depths within
the vertically “mixed layer” it would move it
horizontally a t a rate of 0.77 cm sec-l, or 0.67
km day-’. At this rate the whole column could
be moved laterally the distance (3 km) separating stations 2 and 8 in 4.5 days and this
would not destroy any pre-existing lateral
heterogeneities. I n order for the wind-induced
velocity in the upper layer to be nearly independent of depth we should have to suppose
to be much greater than 104 cm or v > 3 x lo8
cma/sec perhaps a t least los cm*/sec. Eddy
processes aa great as this should be directly
observable, indeed if they were isotropic they
would reduce the lateral inhomogeneities to
half their magnitude in less than 6 days by
lateral diffusion alone; which evidently they
cannot do because the time required for reestablishment is so much longer.
On the other hand, if the vertical eddy
viscosity is significantly less, then we would
expect a strong dependence on depth of windTellus XIX (1967), 2
SMALL SCALE STRUCTURE IN TEMPERATURE AND SALINITY
induced velocity in the “mixed layer”. Because
this layer is homogeneous in density we do not
anticipate extra dynamical complications to
distort the local Ekman dynamics. Let us
suppose that, schematically, the effective depth
of the Ekman layer is a fraction E of the “mixed
layer” depth, then a displacement of 3 kms in
the wind-driven layer can occur in 4.5 E days;
after which the upper eth of the mixed layer
would everywhere have widely differing temperature and salinity but not density from that
below. As a consequence of the lateral advection, there would no longer be vertical homogeneity unless very strong vertical mixing were
constantly reducing the vertical gradients as
produced by lateral advection. The combination of the lateral wind-driven advection in the
upper 130 E meters and violent vertical mixing
in the upper 130 meters would tend to reduce
pre-existing horizontal differences of scale L
(kilometers) to half their intensity in 1.5L days.
Although we might expect a rather intensive
vertical mixing to occur here due to winter
cooling from the surface (the great depth of
the homogeneous layer being its proof) the
lateral wind-driven advection cannot effectively
reduce the large-scale ( lo2 km) horizontal differences in salinity which exist in the surface
mixed layer because of the strong evaporation
near the Australian coast (see Fig. 1). Given
the constant source of a considerably more
saline water, the horizontal non-homogeneity
and transitory nature of the wind field, we
might expect to find in our observations both
departures from the strict vertical homogeneity
(due to newly-developing Ekman layers) and
a certain transitory horizontal non-homogeneity
of temperature and salinity which cannot be
formed locally as was proved above, but which
can be accounted for by the non-uniformity
and transitory nature of the lateral wind-driven
advection.
I n fact, all the STD stations in this area from
Nos. 2 to 16 can be divided into two distinct
groups based on their T oand S%,values.
Group I (Stations Nos. 2 to 7 and 14 to 16)
T O : 25.7’ k0.2
So/,: 34.3 k0.05 %
Group 2 (Stations Ns. 8 to 13)
To:25.3’ kO.1
So/,: 34.2 k0.05 %
Tellue XIX (19671, 2
311
It is interesting to note that on the map these
two groups of stations occupy two distinctly
different areas which can be separated by an
approximate boundary (broken line on Fig. 1).
Nearly all the stations of Group 1 have a very
characteristic vertical non-uniformity of T o
and So/,in the upper part of the mixed layer
resembling fairly well (particularly at stations
5, 6, 7 ) what might have occurred as a result
of the Ekman transport of slightly warmer and
more saline water from the area of stations 14,
15, 16 (i.e. from the north-east) to the area of
stations 2 to 7 (i.e. towards the south-west).
This phenomenon corresponds well to the
general direction of winds (from SE) as recorded
in this area a t the time of observation.
When looking into the physical reasons for
the small-scale horizontal non-uniformity of
T oand S % in the upper mixed layer south of
Timor other types of motion should not be
forgotten. One of these may be associated with
the large-scale horizontal difference in salinity
(already referred t o above) coupled with a very
low vertical stability, particularly where strong
evaporation is added to the winter cooling
from the surface. The natural tendency towards
greater stability would resolve itself not only
in the vertical but also in the horizontal convective flows. Since neither the wind field nor
the evaporation conditions are uniform or
stable it is reasonable to expect these convective flows to be non-uniform and non-stable.
One thing is certain, however, namely that this
convection is guided by gravity forces and
therefore any of its surface branches would
have the same density (but not necessarily
To and S %) as mixed layer, otherwise the
water would just sink below it.
The temperature inversion beneath
the “mixed layer” near Timor
STD recordings made south of Timor show a
very marked temperature inversion just below
the “mixed layer”. Its position on different
stations varies slightly, most probably because
of the internal waves, but on average i t is
situated at a depth of 130 m and represents in
its maximum an increase of temperature of
about 0.5’C relative to the “mixed layer”.
It is accompanied by an increase in salinity
which makes the density of water in the inversion layer slightly greater than that in the
31 2
HENRY STOMMEL AND K . N . FEDOROV
v- s
150
-I
‘C
----+=~/
Fig. 7. Comparison o f STD station 11 with neighboring Diamantina station 297 later in the year
shows that the deep mixed layer is seasonal.
“mixed layer”, and thus the whole stratification appears to be stable. Fig. 5 shows characteristic traces through the temperature inversion at STD Stations off Timor. For comparison purposes, the temperature curve obtained by Nansen bottles at the same spot in
September 1960 by Diamantina is shown in
Fig. 7 and there appears to be no temperature
inversion. Also, the homogeneous layer in
September is much shallower, as one would
expect it to be with the beginning of spring
heating. Fig. 8 shows the densities of the upper
“mixed layer”, the inversion layer and the
underlying waters, and demonstrates that the
density of the inversion layer is much closer to
the density of the water above.
Careful study of the data of other expeditions reveals that temperature inversions of
the same type exist in other parts of the World
Ocean. Bathythermograms obtained by Cruwford in the proximity of station 308 in the
northern tropical waters of the Atlantic Ocean
show the same persistent feature just below the
“mixed layer” which is only 50 m thick on the
average, looking like a lens of water spreading
along the latitude 16’15 N for more than 120
miles. The thickness of the inversion layer
varies from place to place from 20-40 m and
the temperature increase reaches 0.8”C. Station
No. 128 of Geronimo made in 1963 a t 11’07’s
also shows a similar inversion (see Fig. 9).
As in the case of the STD stations of Atlantis
11, the correlation of densities as presented on
Fig. 8 for the Crawford BT soundings is exactly
the same. It looks as though the warm water
lens is well stabilised on top of the cooler
and denser water of the main thermocline, or,
perhaps (to choose a better expression), this
lens “floats” on the discontinuity surface
between the “mixed 1ayer”and the main thcrmocline.
It is rather remarkable that all three cases
of temperature inversion referred to above
pertain to waters in close proximity to the
Equator, also not very far from the coast
and always in the winter season for a given
hemisphere. Since the extensive upper “mixed
layer” is characteristic of tropical waters in
the winter season it is not unreasonable to
suggest that the homogeneous layer has something to do with the formation of the temperature inversion beneath it. It is rather difficult,
to imagine that this inversion layer might be
formed as a result of winter convection having
in this locality a shallower limit than summer
heating. Therefore the only hypothesis which
might hold would be to think that such inversions are the result of a sliding down along
oblique isopycnic surfaces of more saline water
formed somewhere on the surface not very
far from the point where the inversions are
found, while the surface layer above is being
cooled through winter convection.
Fig. 10, taken from the Provisional Oceanographic Charts of the Tropical Atlantic Ocean
(1962) and representing temperature distribution in the Tropical Atlantic, shows that tho
only area with temperatures higher than 28OC.
and salinity of more than 36% (which corresponds to the characteristics of the inversion
layer found by Crawford) exists in summer in
close proximity to tho place where Crawford’s
station No. 308 is located. While there we
trace this water on the surface in September,
we find it beneath the “mixed layer” already
a t the end of November.
PI
Allantis
II
13eZB’S,IPO’12’E
Crowford
16’14’N,59*4Z1W
Fig. 8. Density relations of the subsurface temperature maximum.
Tellus XIX (1967), 2
SMALL SCALE STRUCTURE I N TEMPERATURE AND SALINITY
24.0
25 0
26 0
27.0
28.0
2 8 X I 57
59'42'W
Geronlmo
313
16°14'N;
ore0
of
the C r o w f o r d % I . 308
s t . 128
50 -
M
Fig. 9. Salinity maxima in the Atlantic.
I n the case of the inversion found by Atlantis
I I a t the end of July 1965, the only data which
show the existence of corresponding water on
the surface are those used by Rochford (1962).
From the maps of salinity and temperature
distribution on the surface drawn by Rochford
it is evident that there exists an area of relatively high salinity water (8 of more than
34.7 %) just north of the Australian coast
around 120'E and between the latitudes of
20's and 16' S which can also be seen on the
Diamantina Section (Fig. 11). It is rather difficult to estimate from Rochford's maps in
which months this water would have a temperature corresponding to that of the inversion
layer, i.e. between 25" C and 26" C since Rochford combined the data of several cruises to
construct his maps. We can more successfully
use the original data of two Diamantina
cruises-2/61 and 3/61-conducted in May and
August 1961 respectively, to trace this particular water in space and time. Fig. 12 shows the
interpolation of salinities and temperatures in
space and in time along the section of Diamantina 3/61 referred to above (Fig. 11) between
May and August. On the part of Fig. 12 related
to the surface one can see the shaded area
progressing northward from 18" S to 16's from
June to July, and one can see the same area
spreading further northward a t a level of 70 m
in August. This interpolation looks rather conclusive in confirming the hypothesis that the
water which we found in the inversion layer
originates on the Australian continental shelf,
sinks down along the isopycnal surface of
ut =23.0 which limits the "mixed layer" from
below at 13OS, and accumulates in the form of
a lens somewhere around latitude 13' S where
the isopycnal surfaces have a peculiar bend.
Tellus XIX (1967), 2
According to the interpolation presented in
Fig. 12, this water needs approximately 1 4
months to sink from the surface to a depth of
130 m, which is equivalent to the vertical speed
of sinking which is 3.3.10-s cm/sec or about
3 m/day, which is rather a high speed, although
perhaps not an improbable one. I n a horizontal
direction the same water should travel about
550 km during the same 14 months, which would
amount to 14 cm/sec, also not unreasonable.
Further on in this paper (see page 320)
we consider simplified models of discrete water
types which produce salinity or temperature
inversions while the whole system approaches
maximum gravitational stability. One of these
models (Fig. 2 1 4 resembles closely the process
described above.
Laminae in the thermocline
The oceanic thermocline (and halocline), a s
can be seen for example in Figs. 3 and 4, are
not smooth gradual transitions between the
60-W
40.W
20.W
020.N
E9
20 s
Fig. 10. Area of surface formation of the subsurface
salinity maximum in the Atlantic.
314
HENRY STOMMEL AND K. N . FEDOROV
Drn 3/61
122’E
18’s
17*
14-18-Vlll-1961
16O
IZO’E
15’
14’
v , ond
13’
S%.
12-
1190
IIo
10’
0
20
40
60
80
100
120
I40
160
Fig. 11. Diamantina section from Australian shelf.
contrasting values of temperature (and salinity)
in the upper surface region of the ocean and in
the deep water below, but are made up of hundreds of superposed laminae from 2-30 meters
thick, each fairly “homogeneous” in temperature and salinity, and separated from one another by “interfacial” regions of much more
than average gradient in temperature (and
salinity).
Consider the temperature profile shown in
Fig. 3, and note the small feature in temperature
associated with a lamina at 180 meters and
21.26”C. Although the details of this lamina
are obscured by the thickness of the pen trace
it is evident that the temperature is almost uniform in this lamina (the salinity trace also is
nearly constant here too). The thickness of the
lamina is about 5 meters. There are many similar features at other depths-but this lamina is
quite clearly indicated and identifiable. We
will call it, for simplicity, lamina “ A ” .
I n order to get some idea of how large the
lamina is horizontally, we have constructed
Fig. 13. Each little square is a portion of a
record off Timor, the abscissa being temperature from 21.25 to 21.75”C and the ordinate
being an interval of 50 meters depth. Internal
waves move the isotherms vertically, and since
our measurements were unsynchronized with
these waves the absolute depth of the lamina
may be expected to vary in time. The position
of the 175 in depth point on the depth scale
is indicated by the small arrow head-generally
in a different position a t each station. The
numerals in the lower left corner are the STD
station numbers. The arrangement of the squares
corresponds roughly to geographical position
as shown in Fig. 1, for convenience in trying to
visualize the three-dimensional structure of
the lamina. The positions of stations 14, 15, 16
are actually much more widely separated than
indicated in Fig. 13 (see Fig. 1 ) . The lamina
can be identified at all stations 2-13, although
not elways at the same temperature. Thus a t
stations 2 and 3 for example it lies a t temperatures greater than 21.5OoC, but a t stations 8
and 9 it is less than 21.25”C and hence lies
outside the squares and is shown by a continuation of the trace in dashed form. The lamina
cannot be seen a t the distance of stations 14-16.
Lamina A seems to be about 3 miles-or 5 kmin radius.
A similar small lamina, B, at STD station 21
(Fig. 4) off Mindanao can be readily identified
because of a clear temperature inversion of
0.05”C a t about 8.80”C and 385 meters depth.
Fig. 14 is another schematic diagram with
squares arranged to show how lamina B can be
found a t almost every station in the 5 mile
radius cross. The temperature of lamina B
is more nearly uniform horizontally than that
of lamina A .
Referring back again now to (Fig. 3) station
13, this time we can choose a larger feature:
the 0.30”C inversion at 16°C and 245 meter
depth-a lamina perhaps 12 meters thick, which
we will call lamina C. Fig. 15 shows thermal
structure neighboring stations: evidently lamina
C is noticeable only a t stations 10 through 13,
and not elsewhere. Also the temperature in the
middle of lamina C varies from 15.70 to 16.49”C
whereas the salinity remains close to 34.99
.01.
x0
181
17O
I
16’
15’
I
I
14O
I
13’
I
12’s
I
Fig. 12. Interpolations of properties south of Timor.
Tellus XIX (1967), 2
315
SMALL SCALE STRUCTURE IN TEMPERATURE AND SALINITY
1k l:
1
0 me!.
I
Loom
I
-
2
.
rn#l*S
1
81.
21 5
OC
Fig. 13. Composite chart-graph of temperature in
lamina A (Fig. 3). Each small square is 0.5’C wide
and 50 meters high. The central value of temperature is indicated as 21.5’C and does not differ for
any square. The small arrow indicates the position
of the depth 175 meters in each square. Because of
internal waves the origin of the depth scale is
shifted from square t o square, but the arrow always
indicates the position of the 175 meter depth. The
numerals in the lower left hand corner of each square
are the STD station number. The arrangement of
squares on the figure are meant to correspond
roughly to the actual geographic positions of the
stations indicated in Fig. 1. However, they are only
approximate: in particular the stations 14 through
16 are actually much further apart than indicated
here-they are really 10 miles apart as shown on
Fig. 1, but are crowded together in the upper right
hand portion of this figure simply because of
graphical restraints.
Vertical scales less than two meters are not
clearly resolved by the STD we used. It seems
certain t h a t smaller scales do in fact exist, and
t h a t exploration of their details would be of
fundamental interest. We fortunately found
indirect evidence for these smaller scale structures in the following way. After the STD instrument had been lowered t o 500 meters on
S T D station 13 (Fig. 3) it waa raised t o the
depth corresponding t o 17.63OC where a very
small gentle inflexion point P is observable on
t h e temperature trace, and the winch then
stopped. The chart waa then advanced in steps
of one small division by hand each minute,
obtaining the 51 minute record of both salinity
and temperature shown in Fig. 16. During the
first four minutes the salinity and temperature
Tellus XIX (1967), 2
90.
Fig. 14. Similar composite chart-graph for temperature of lamina B off Mindanao (Figs. 4 and 2).
The large geographical extent of this small thin
lamina is self-evident.
STD
STL
Owth
2
242
3
242
4
240
5
242
m
.1
I2
235
I3
235
14
252
I5
230
16
225
Fig. 15. Temperature in lamina C (Figs. 1 and 3)
with origin of depth scale listed alongside of STD
station number. Not arranged geographically on
account of graphical restraints. Lamina C does
not appear to be very extensive, nor a t constant
temperature--a different situation from that indicated by lamina B.
316
HENRY STOMMEL AND K . N. FEDOROV
Fig. 16. Original records of temperature and salinity with winch stopped at point P (Fig. 3). Time increase upward, the smallest divisions being one minute intervals of time. The chart was not moved
uniformly but in steps of one division each minute. Temperature and salinity scales are indicated. The
temperature time scale is not the same as the salinity time scale but is offset one minute in the
same way as described in the caption to Fig. 3; thus in comparing the two traces the temperature trace
should be moved upwards one division. This can be seen clearly by comparing times of commencement
and termination of the run. The horizontal excursions of the pens during each one minute pause are
presumably due mostly to slight rolling of the ship and consequent variations in depth of sensors. When
there is a sharp gradient the horizontal excursions of the pen are large; when there is a homogeneous layer they are small. Both conditions occur on the record presumably because internal gravity
waves carry the laminar structure slowly up and down past the more rapidly moving sensors.
remain steady at 34.85 % and 17.63'C but
during the 5th minute a small spread of temperature is recorded, which increases its amplitude during the 6th and 7th minutes. The
interpretation of the difference is that there
is always a high frequency vertical excursion
of the STD instrument due to the roll of the
ship (here perhaps about 50 cm in all) which
scans the vertical structure over a small range
of depth and produces the spread in readings
while the chart is stopped at one of the minute
positions. If by chance the instrument happens
to lie within a truly homogeneous layer the
vertical scanning will produce zero spread, as
seen in minutes 0 to 3. Internal gravity waves
have much lower frequency than the roll of
the ship, so that the salinity and temperature
structure is slowly moved up and down past
the rapidly scanning STD sensors. During
minutes 4 through 13, 21 through 23, and 28
through 32 the homogeneous layer was probably raised above the STD sensors; during minutes 25 through 26 and 33 through 42 it was
evidently beneath the sensors. The values of
temperaturo and salinity at times of zoro
spread are always the same, as would be expected from the idea of a homogeneous layer.
The lowest mean temperature 17.26"C was
at minute 9, the highest, 17.97"C, at minute 39,
corresponding salinities being 34.75 % and
34.85 %. The total range vertical displacement
due to internal waves was thus 5 meters;
tha homogeneous lamina P may be 3 meters
thick.
Estimates of vertical temperature gradients
are as follows:
Mean, station 13, between 200 and 300 in:
.040"C/meter,
I n lamina P i.003"C/meter,
Directly above and below lamina P > .35"C/
meter.
The signature of lamina P is weak in Fig. 3
and cannot be identified on soundings at neighboring stations.
The large horizontal scale of the homogeneous
laminae is especially interesting in view of
measurements with horizontally moving probes
(Liebermann, 1951, Grant, Moillet & Vogel,
-
Tellus XIX (1967), 2
317
SMALL SCALE STRUCTURE I N TEMPERATURE A N D SALINITY
1963) which suggest much smaller horizontal
scales. If the large scale laminae are wave-like
corrugated surfaces, the horizontally moving
probe would move in and out of the layers, the
presence of the lamina showing up only in a
square wave type of distortion of the wave
form. I n one sense the temperature fluctuations
shown in Fig. 16 exhibit an “intermittence”
in high frequency component due to change in
position of the sensor with respect to the
homogeneous layer. Could intermittence of high
frequency signal observed by Grant et al.,
1963, be associated with sampling in different
portions of lamina such as we observed?
It is rather interesting to see how these laminae
look on the T-S plot. Fig. 17 gives examples of
three laminae from STD stations 28, 29 and 30
situated between 100 and 175 m. All three
laminae ( D , E , P) retain their characteristic
form a t each station and the only doubt which
may be expressed is that perhaps lamina F is
composed of two separate layers, P, and F,.
It is remarkable that the density of water is
almost uniform along the vertical throughout
each lamina (8-20 m thick) a t each station.
It is worth mentioning, however, that the
density of water in each lamina changes from
station to station. This is seen from the respective positions of laminae on the plots, as well
as from the figures below obtained for the
characteristic points in the middle of the laminae
D and E (Table 2).
It was difficult to say definitely whether
these differences in density are due to instrumental errors or if a certain physical significance should be attached to them. We tend to
accept the latter supposition, particularly since
in the lamina C (discussed above, stations
10-13) even greater differences of density were
observed (from ut = 25.65 to crt = 25.83).
Fig. 17. Details of STD stations 28, 29, 39 on an
S-T diagram.
are not fluctuating, nor tidal, so only one is
shown here. The major feature is the maximum
in relative speed a t 100 meters (which appears
on all four records). The resolution of the current
meter is not so fine-scaled as that of the STD
and hence we cannot identify micro-variations
of the velocity structure that may coincide
with similar small scales in the thermal and
salinity structure. It would, of course, be
extremely interesting to be able to make such
comparisons. However, in a larger scale we
can identify the high relative speed layer with
the layer of high salinity between 65 and 200
Table 2
Current measurements
Toward the end of the period of experimentation off Mindanao with the STD we were able
to get a Savonius-type current meter working
so that we could obtain measurements of the
velocity a t various depths relative to the ship,
which of course was held a t constant heading
and without power during the current meter
lowerings. Fig. 18 shows STD station 37 and
Fig. 19, one of four current profiles obtained at
the same location. The four profiles were much
the same over a period of 12 hours, the features
Tellus XIX (1967), 2
Sta.
d
T”
S%O
ut
112 m
120 m
113 m
15O.10
15O.01
15O.04
34.90
34.84
34.83
25.89
25.87
25.85
E
132 m
145 m
140 m
14O.92
14O.75
14O.62
34.94
34.90
34.88
25.96
25.97
25.98
Lamina D
28
29
30
Lamina
28
29
30
318
HENRY STOMMEL AND K. N. FEDOROV
0
100
200
rn
300
400
Pig. 18. STD station 37; scales are same as in Fig. 4.
-
.
..
~
'
\
40
8
oi
.
i
speed
~
100
.
~~~~
200
m
300
o
.
400
Fig. 19. Speed in cm/sec indicated by solid dots;
direction from which the current came, open dots;
both measured relative to the drifting ship at station
37. Four other current soundings at intervals during
the following 12 hours all show same features.
Note the extreme shear between 80 and 100 meters.
The moving layer between 100 and 200 meters
corresponds to the salinity maximum layer.
s 7-
3400 3500
Fig. 20. Multiple salinity maxima off Mindanao,
arranged by station number, with only those
portions of the curves shown which exceed 34.75
salinity.
x0
meters. This layer, incidentally, has some
marked differences in form over the small area,
of the Mindanao cross, as can be seen from the
display of parts of the salinity soundings drawn
in Fig. 20; here we see some soundings have
only one marked maximum, others exhibit
several maxima.
The existence of the fairly reliable current
profile enables us to make a n estimate of the
Richardson Number from smoothed profiles
of density and speed, ignoring fine scale structure. Thus in the interval between 80 and
100 meters depth the mean velocity U increases from 7 to 47 cm sec-'; whereas t h e
density e increases by
gm/cm8. Therefore
the smoothed Richardson number Ri = ( g / e )
( a ~ / a z ) ( a U / a z )=- 1.2.
~
This is only slightly
larger than the theoretical critical value 0.25
(Yih, 1965). Any small kinks or steepnesses
which occur (and which we have smoothed out)
in both the velocity and density structure will
tend to produce smaller local Richardson
numbers, and there we might expect local shear
instability and mixing. I n fact, the main
thermocline in this part of the ocean is so very
close to marginal instability that it could not
be expected to be any steeper. This is not usually
the case in other parts of the ocean where more
gentle thermoclines, combined with estimated
Tellus XIX (1967), 2
319
SMALL SCALE STRUCTURE IN TEMPERATURE AND SALINITY
Table 3. Lifetime of laminae: Molecular
diffuaion
Thickness
Temperature
(h)
(TI
Salinity
resolution in the vertical than we were able
to make would be valuable, in order to obtain
some sort of spectral distribution of these very
small features.
(T)
A spaamodic model for determining the rate
2 days
200 days
70 years
10 cm
1 meter
10 meters
100 days
30 years
3000 years
velocity structure, suggest that the smoothed
Richardson numbers are well removed from
instability.
Thoughts about dynamics of laminae
If the life-time of a lamina were determined
by vertical molecular diffusion alone, it could
be fairly long, even if it were not being continually renewed by advection from high latitudes (this seems most unlikely because
laminae in the thermocline have limited horizontal extent and very likely do not exist as
permanent continuous layers connected to the
surface anywhere). The computation of lifetime is very simple:
where T is the lifetime, h the characteristic
half-thickness, and k the molecular coefficient.
Table 3 shows sample times. On the other hand
there is much evidence that the thermocline
of the ocean is actually the site of turbulent
mixing which in the long run amounts to the
equivalent of a turbulent “eddy” coefficient
of 1 cma sec-l, about 1000 times that of the
molecular coefficient for temperature and 50,000
times that for salt. With this turbulent coefficient the lifetime of laminae will be the same
for temperature and salt (Table 4).
The very short lifetimes of scales less than
1 meter suggest that there may be a “smallest
scale” lamina, and that experiments with higher
Table 4 . Eddy coefficient ( I cma/aec)
10 cm
1 meter
10 meters
Tellus XIX (1967), 2
A 3 1 cma sec-l.
The mean vertical gradient of the temperature
6 is roughly 20°C in 500 meters or
a
-
=
dz
occm-’.
4x
The mean turbulent diffusive flux of temperature is therefore
a6
-A - = - 4 x
oc
cm sec-*,
aZ
ha
T=2k’
h
of reforming laminae
Suppose that mixing in the main thermocline
occurs by spasmodic forming and reforming of
laminae. The vertical eddy coefficient A for
temperature has been computed in many ways
(see for example section 9 of Robinson & Stommel, 1959) and the value we take here is
T
1 minute
0.2 days
20 days
which when multiplied by the density and the
specific heat of water becomes 4 x
gm
cal cm-’ sec-l.
Now turning to a specific mixing process
(very much idealized of course and possibly
very misleading) let us suppose that a t time
t = O the true thermocline actually consists of
n-laminae, each of thickness h with interfaces
a t z = 0, h, ...jh, ..., nh (nh = D )the temperature 6,of the jth lamina being
...
i
6 --60,
’-n
where 6, denotes the overall amplitude of
temperature contrast between top and bottom
of the thermocline (as before 6, = 20°C, D = 500
meters).
At time t = P / 2 strong mixing occurs a t each
interface z = jh, so that the upper half of each
lamina mixes with the lower half of the lamina
immediately a.bove-but not across the planes
h 3h
z=- 2’ 2 ’
... ( j + ) ) h . . .( n - ) ) h ,
320
HENRY STOMMEL AND K. N. FEDOROV
where new interfaces form. Between these
planes there are new laminae with temperatures
$,+* = [ ( j + 3)/n]6,. I n the course of this half
cycle there has been a transport of heat across
planes z = ... jh of (6, D/2n2)cpgm ca1/cm2,but
no flux across planes z = ... ( j + t ) ... At time
t = T , however, we can return to the original
distribution of temperature by mixing across
planes z = ... (i + 4) h ... and not across z = ...jh ...
This completes the cycle, and provides for a
regular down-the-gradient flow of heat from the
top of the thermocline to the bottom. A typical
value of n from our measurements can be taken
as 100, meaning h =500 cm and A@,, =0.2OC as
parameters of laminae. The flux of heat by this
idealized process, is therefore
6,D
1
P
-~- cg-=--
2n2
50 gmcals
P cm’cycle’
where P is seconds/cycle. Evaluating P, we
obtain P = 1.2 x lo4 seconds/cycle or about 4
hours/cycle-a most remarkable short period.
Another way of writing P is
.BOD L
c 0’
p =c L -==
2na
d6
dz
A-
2n2 A
’
Evidently very small layers (large n ) would
require very rapid recycling. The time P is also
self-evident from “mixing length” theory-the
length being taken as h-but
it seems worth
while to recast it in terms of changing laminae.
If laminae have such short lives as a day how
can they be so homogeneous on such large
horizontal extent-are
they self-propagating
horizontally? It is difficult to believe they form
sirnultaneowrly over such large areas. It should
be possible to take advantage of the intermittent
nature of mixing in the ocean to determine
directly the vertical flux of heat and salt. We
know that determination by trying to evaluate
the w‘6‘ is nearly impossible technologically;
but the statistics of a random spasmodic process
would give interesting numbers. With such short
lifetimes, it is not conceivable that the laminae
originate at the surface a t very different latitudes and have a long history within the ocean;
we suspect that they are produced and destroyed by the mixing processes in the thermocline and are actually evidence of the mixing
process and a feature of its physics. This in
-
turn suggests that even such remarkable microscale features as the small layer of temperature
inversion B may ba produced locally-and that
this may be direct evidence of the more exotic
types of two-diffusivity convection (Yih, 1965;
Turner & Stommel, 1964).
I n order to illustrate how easy it is to build
inversions, let us suppose that the basic fields
of temperature and salinity decrease with depth,
but the density increases with depth. I n Fig.
21a the points 1 and 4 correspond to such a
distribution, and so do the points 2 and 3.
Either sounding is gravitationally stable. I n
this preliminary discussion it is assumed that
there are only discrete values of T and S
present (“lumped” or “box” values). These
values are marked by the heavy dots. I n fact
of course, soundings are essentially continuous
functions, although there can be more of one
kind of water than of another. Across the top
of the figure we have arranged (1) a diagram
showing the vertical arrangement of such water
types in a volume of the ocean where the two
masses happen to lie side by side, ( 2 )the salinity
values, (3) the temperature values-which are
(4) the density values.
drawn identical-and
The final diagram (5) is a salinity temperature
diagram showing the arrangement of the different points; the lines of unity slope are lines
of constant density. The line joining points 1
to 4, and joining point 2 to 3, are meant to
indicate that these are two separate soundings
in nearby side-by-side water columns but there
is no water except at each point value. This
slight difference in neighboring volumes of the
ocean could easily occur by means of columnar
salt convection: for example sinking of salt
columns from shallower regions where the
salinity is high into the levels which we are
considering could raise the salinity of the
sounding 1,4 to that of 3,2 without changing
the temperature a t any depth. Similarly, salt
columns sinking out of the bottom of the levels
being considered could reduce the salinity of a
region originally at 3,2 to that at 1,4. Both of
these soundings are gravitationally stable of
course, but since they are side-by-side in the
ocean they will begin t o convect sideways aa
shown in the first picture on the second line:
thus portion 3 slips under portion 1, and portion 2 slips underneath portion 4. The resulting
final arrangement of density is shown in the
last picture on the right of the second line.
Tellus XIX (1967), 2
321
SMALL SCALE STRUCTURE IN TEMPERATURE AND SALINITY
s
-.
d
d
a
i/:
'1
a
C
I
2
3
.
4
__
d
Pig. 21. Proceesee which could produce laminae with inverted aalimity or temperature.
The vertical distribution of salinity, temperature, and density which results from this convection towards maximum gravitational stability is shown in the middle three graphs of
the second line. Temperature and density are
monotonic, but salinity has extrema. The S-T
relation would be indicated by a 2-shaped curve
1, 3, 4, 2.
Fig. 21 b shows another cme which involves
the stune S, T points as previously, but here
connected 1 to 2 and 3 to 4. This represents
two soundings with very slightly different
slope: a feature which could occur easily
differential vertical flux of salt by the columnar
regime without changing the temperature of
the points. As the second line of the figure
indicates, this leads to the same final state,
but of course the pattern of convection which
leads to it is somewhat different because the
initial arrangement of the portions of water
1, 2, 3,4 were different.
NOWwe turn to a case where approach to
stable configuration can generate a temperature
Tellua XIX (1967), 2
21 - 662898
inversion. Consider Fig. 21c. Here again we
have two nearly parallel soundings 1,4 and 3,2.
The gravitational stability of each is slight.
Were we to try to construct a 0880 analagous
to 13b, by taking the soundings to be 1,2 and
3, 4, we would find 3, 4 to be gravitationally
unstablehence we exclude this case from
discussion-it
would indeed lead to a final
state with everything monotonic. The convection pattern leads this time to a new configuration of points which has maximum gravitational stability and we see here that in addition
to a salinity inversion there is also a temperature inversion.
Another case resulting in a temperature inversion is shown on Fig. 21d. This time the
values of Toand S % for soundings 2, 4 and 1, 3
were selected close to those existing in the
upper 130-140 m south of Timor during the
winter -on.
As in the previous case, the
gravitational stability of each sounding is
slight. The convection pattern is almost the
same as in the model 21a. The maximum
322
HENRY STOMMEL A N D K . N . FEDOROV
gravitational stability requires a temperature
inversion as well as a maximum of salinity
coinciding with it.
Although the above examples were restricted
originally to small-scale phenomena like laminae
several meters thick and several miles in
diameter found in the main thermocline, one
can see from the last model that they may
explain in a simplified form features of much
greater scales as, for cxample, the temperature
inversion south of Timor, the origin of which
we discussed earlier.
Real soundings are continuous: there are
not discrete water types. But the processes
envisaged here will occur if there is a tendency
toward discreteness, that is, if there are laminae
in the density with different locations. The
laminae tend to spread to adjoining places where
less of that particular density exists. This is
the rationale of the discrete model illustrated
in the figures. Dynamically, processes other
than spreading can produce the inversions-for
example simple shear in a medium in which the
T-S relation has been broadened by random
small scale salt convection.
Let I be the half-wavelength of salt-column
type convection cclls extending from one
homogeneous lamina across a stable interface
into another lamina. The formula for the cell
size is
4
where 8, is the mean temperature gradient
across the stable interface and the coefficients
v and K , are of course molecular viscosity and
thermometric conductivity respectively. There
is nothing inconsistent with using molecular
coefficients here. We simply must think of
them as part of a cycle of processes, some occurring on larger scales which all taken together
have an overall effective mixing which is
expressed in terms of a larger eddy coefficient.
a is the coefficient of thermometric expansion.
Taking values
a
v
=2
=
x
10-4
"c-1,
0.01 cm2 sec-l,
S,
=3
K,
x
10-8
OC/cm,
= 0.001 cm2sec-',
we obtain I = 1.4 cm.
It is evident that small sensors will be necessary to detect these small columns of material
convecting across the interfaces, if indeed they
exist. The salt difference across the interface
may be quite small-perhaps
0.02 x. The
amplitude of the vertical component of velocity
in these columns is computed on the basis of
non-turbulent flow
w o= sAe l 2 = 0.02 cm sec - I ,
v 4n2
~
~
so that we can see that the Reynolds number
of these columns is roughly unity and it is
consistent to regard them as laminar.
If a lamina can lose salt to a lower lamina
by such convection, it will be less dense, and
could flow to higher levels in adjacent regions,
thus producing a layer of lower temperature
a t higher levels which has the appearance of a
temperature inversion: the lower lamina with
greater salinity can sink and appear as an
anomalously warm inversion layer.
On the other hand, the salt columns must
have a limited life-time on account of lateral
salt-diffusivity, which would reduce the buoyancy difference between ascending and descending columns. For 1 cm this is one day. The
distance which the columns can fall during this
time is 20 meters, and i t is unlikely that they
could flow further-in
fact we anticipate it
would be much less.
It is difficult to know whether the saltconvection plays any important role in the
physics of the laminae without careful observations. Studies in salt-free lakes would be interesting too. We do not expect to find temperature inversions in such lakes, a t any rate.
If laminae have limited horizontal extent
then there must be horizontal pressure gradients
within them, and they must tend to spread.
Let us compute some features of this spreading.
Let us consider a lamina of half-thickness h,
extending from the interface z =h(z,y ) to
z = -h(x, y) and of density e. Above the top
interface the density is e -At, and below the
bottom interface the density is Q + A@. Then the
horizontal pressure gradient in the lamina itself
does not affect the horizontal pressure gradient
beneath the layer-whatever it happens to be
it is the same above and below the lamina. If this
lamina were brought into existence abruptly,
with a sharp vertical edge at, say, x = 0 , and
extending to infinity on the positive side of
x = 0 , but not on the negative side, then there
Tellus XIX (1967), 2
SMALL SCALE STRUCTURE I N TEMPERATURE AND SALINITY
would be a tendency for a front to move inertially toward the negative direction in x, at a
speed u,= by Bernoulli’s Principle;
where the subscript “i” is meant to signify
“inertial”, and the prime on g means reduced
gravity, that is gravity multiplied by the
half-density difference Ae/e. For sake of definiteness we can consider the lamina with a
thickness 2 h = 6 meters and a difference of
temperature of 0.2”C which corresponds to
Ae/e = 4 x
SO that
vG
323
If the layer is very thin compared to the
Ekman layer z, then we may expect pure
viscous dynamics and then
g’-ah = y - a‘u
ax
az”
hence
9‘ ah a
a
u = - - (Z - h )
2~ ax
and
u, = - 3 cm sec-l.
If there were no friction we might expect a
geostrophic current to approach a geostrophic
equilibrium configuration flowing in the positive
y direction, with a width of 300 meters (the
“radius of deformation”), and a maximum
velocity of v o = -utr where the subscript “g”
is meant to signify “geostrophic”. This might
be the situation after a day or two. But in
general we do not expect such catastrophic
beginnings, and we must think of the possibility of geostrophic currents with arbitrary
x-scales which we determine by observation
instead of by frictionless approach to geostrophic equilibrium from arbitrary initial conditions. For these purposes, observation suggests x-scales more like 3-10 km and hence
geostrophic velocities in layers might be more
nearly 1 or 0.3 cm/sec. Such a current would
flow steadily forever in the absence of friction.
To see the influence of friction in producing
spreading we note that we might expect
Ekman spirals at the boundaries (interfaces) of
which in the range of Y from
thickness z, =
molecular (0.01 cma/sec) to eddy-turbulent
(1 cm*/sec) could be somewhere in the range
z,=lO to 100 cm. The x-transport across
isobars in both the boundary layers near the
interfaces is
qf
and hence from mass continuity within the
lamina
ah
g’z, a%
- = _ _
at
f az”
which is an expression for the rate of change of
thickness of the lamina.
Tellus XIX (1967), 2
The form of both of these equations is that
of the heat conduction equation, however the
purely viscous equation is not quite the same,
on account of the very strong dependence on h.
The effective lateral diffusivity of spreading
of the lamina is the same for either process
when z, =h/3, as can be seen by setting them
equal. At this critical depth, using our previous
values of the lamina’s parameters, we find
g’z,/f = 2 x lo4 cmp/sec aa the spreading diffusivity. We can see therefore that for structures
1 meter thick or thicker, friction will cause an
appreciable fractional change of the thickness
if the horizontal dimensions of the laminae are
less than 1 km. Layers much thinner, for
example 10 cm x 1 km, require 1000 days to
spread significantly; of course they would
decay thermally in much less time. The conclusion seems to be that layers as thin as 10 cm
could never occur by a process of spreading
from larger layers: by the time they reached
such fine dimensions they would be conducted
away. Is there a smallest observed lamina
thickness? What is the spectrum of lamina
thickness?
It is difficult to conjure up in our minds the
processes which cause the interfaces to form.
We know of course that mixing a t certain depths
would necessarily cause steepening of gradients
at other depths; but there is much more
definite feeling physically that interfaces, or
regions of steep gradients can be mixed by
shearing instability. Indeed, this has been
the subject of much theoretical study, and some
experimental work. I n particular Miles &
Howard (1964) give a treatment of the stability
problem for a layer of uniform gradient in
density and velocity between two very thick
homogeneous layers with constant velocity
324
HENRY STOMMEL AND K. I?. FEDOROV
(this is a model of our type, the interface being
the region of uniform gradients, the laminae
being the thick homogeneous layers of constant
velocity). Miles and Howard show that instability first occurs when the Richardson number
Ri = Aegh/V2
takes on the critical value 0.25. The quantities
A e , g , h, have the same meaning as above;
and 2V is the difference in velocity across the
stable interfacial layer. The wavelength of
critical size is
1, = 15 h.
If the 60 cm wavelength observed by Liebermann’s moving probe were due to this cause,
it would suggest very thin-8 cm-interfaces.
Observationally it might be more meaningful
t o try to observe the frequency of the waves
from a float moving in one of the adjacent
laminae. I n this case, if mixing is just marginally unstable, we would expect to observe
a frequency of 0.82 N where N is the local
Brunt-Vaisala frequency for the stable layer.
This might be an interesting thing to look for
when more detailed studies of the micro-structure become available. Good laboratory investigations of interfacial instability and mixing
are difficult to conduct on account of the many
outside disturbances to which the experiments
are subject. However, conditions may be much
more suitable in the deep ocean, and so some
“simple” regimes might actually occur. This
is not without precedent as the experience
of Grant et d in observing several decades of
Kolmogoroff spectrum in natural conditions
shows us.
Because further knowledge of these laminae
may help us to understand the actual mean
turbulent transport of heat in the main thermocline of the ocean we think many future experiments and observations ought t o be made of
them. One possible technique would be to use
a servo-controlled neutral float. For example
one could make temperature controlling, so
that the float could be “locked on” to a definite
observed feature of the thermal microstructure
and stay with it even in the presence of internal waves. One should be able to use it as a
vehicle for carrying various measuring instruments, cameras, etc.
Among the things which we would like t o
do with such a float are the following:
(a) Photograph small dye streaks in homogeneous laminae, and in the gravitationally
stable interfacial surfaces bounding them for
periods of about a n hour to obtain visual evidence of the nature of the regime.
(b) Photograph the relative (to the float)
motion of small sinking floats to get the microprofiles (micro-spirals?) of velocity as well as
temperature and salinity; and thus obtain a
measure of local Richardson number.
(c) Repeat Pochapsky’s 1961 experiments of
dispersion of floats with more precise control
of depth of floats.
(d) Measure frequency of interfacial waves
from a float locked to an adjacent homogeneous
lamina.
(e) Determine whether there is some correlation of micro-structural detail (for example
interfacial shear) with the phase of large internal
waves.
( f ) Watch for tendency for unidirectional
mixing across interfaces.
( 9 ) Determine characteristic “life-time” of
laminae; for example, if laminae spread out
they may become progressively thinner with
time.
( h ) Is there a “smallest” size of laminae?
(i) Look for very fine scale “salt convection”
or other evidence of two-diffusivity convection
with microconductivity cell mounted on arm
attached t o the float.
Tellus XIX (1967), 2
SMALL SCALE STRUCTURE I" TEMPERATURE AND SALINITY
326
REFERENCES
Grant, H. L., Moillet, A. & Vogel, W. M. 1963.
Turbulent mixing in the thermocline. I n press.
Liebermann, L. 1961. The effect of temperature
inhomogeneities in the ocean on the propagation
of sound. J . Acorntic. Soc. Amer. 23, 663.
Miles, J . V. & Howard, L. N. 1904. Note on a heterogeneous shear flow. J . Fluid Mech. 20, pt. 2 ,
331-336.
Pochapsky, T. E. 1961. Some measurements with
instrumented neutral floats. Deep-sea Rmearch 8,
269-276.
Provieional Oceanographic Charts of the Tropical
Atlantic Ocean, 1962, U.S. Navy Hydrographic
Office, Washington, D.C.
Rochford, D. J. Hydrology of the Indian Ocean,
Part 11.Awrtralian Journal of Marine and Freahwater Reaearch 13, No. 3, Dec. 1962, 226-261.
Stewart, R. W. 1959. The problem of diffusion in a
stratified fluid. Advancea in Qeophyka 6,303-311.
Turner, J. S. & Stommel, H. 1964. A new case of
convection in the presence of combined vertical
salinity and temperature gradients. Proc. Nat.
Acad. Sci. 52, 49-53.
Vitiaz Station Data: IQY Oceanography Report
No. 3, Sept. 1901. Dept. of Oceanography, Texas
A. & College M. Part IIa, Pacific Ocean.
Yih, C. S. 1965. Dynamic8 of Nonhomogeneowr
Fluids. Macmillan Co., p. 306.
MEJIKOMACIUTAEHAH CTPYKTYPA T E M n E P A T Y P b I B COJIEHOCTB BBJIB3B
TBMOPA B MBHAAHAO
Tellus XIX (1967), 2