Surface Circulation of Lakes and Nearly Land-Locked Seas - PNAS
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Proc. Nat. Ac4d. Sci. USA
Vol. 70, No. 1, pp. 93-97, January 1973
Surface Circulation of Lakes and Nearly Land-Locked Seas
(marginal seas/wind drive/water movements)
K. 0. EMERY AND G. T. CSANADY
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
Contributed by K. 0. Emery, October 30, 1972
ABSTRACT The pattern of surface circulation has been north to south are: Lake Superior (1), Lake Huron (1-3),
mapped for more than 40 lakes, marginal seas, estuaries, Lake Michigan (1, 4), Lake Ontario (1, 5), Lake Erie (1, 6),
and lagoons. All are within the northern hemisphere,
and all except one are known to have a counterclockwise Great Salt Lake (7), and the Salton Sea (8, 9). Patterns also
pattern. This consistent pattern is attributed to the drag are available for the following lakes of Eurasia: Lake Con-
of wind blowing across the bodies of water. Warmer sur- stance-Bodensee (10, 11), Lake Neuchatel (12), Lake Geneva-
face water is displaced to the right-hand shore zone (fac- Liman (13), Aral Sea (14), Caspian Sea (A. F. Mikhalevskii
ing downwind), where it produces greater surface turbu- in ref 15), Dead Sea (16), and Bitter Lake (17).
lence and, thus, greater wind drag. This effect leads to
counterclockwise water circulation regardless of the direc- Circulation patterns for water bodies of North America
tion and, within limits, the duration of the wind. that are nearly separated from the ocean or from large ad-
jacent lakes by structural barriers have been published for:
During studies of northern hemisphere lakes and water bodies Baffin Bay (18, 19), Hudson Bay (20, 21), Gulf of St. Law-
marginal to the ocean, we have noted a consistent counter- rence (22, 23), Passamaquoddy Bay (24), Grand Traverse
clockwise circulation of surface waters. "Circulation" is here Bay (25), Bay of Fundy (26, 27), Gulf of Maine (22), and
defined to mean a long-term pattern of motion, or residual Long Island Sound (28). In South America the circulation
motion remaining after the irregular water movements in- in Lake Maracaibo (29) has been mapped. Similar water
volved in wind drift, seiches, and other short-term phenomena bodies of Eurasia for which surface circulation are known are:
are averaged. The averaging period is taken to be long com- the White Sea (V. Timonov in ref. 30), Baltic Sea (31), Black
pared with the typical passage time of weather cycles. Ex- Sea (32), Adriatic Sea (33, 34), Japan Sea (ref. 35, Sizova in
perimentally, such long-term patterns of flow may be directly refs. 30 and 36), the Mediterranean Sea (37), and the Persian
determined, e.g., by releasing batches of drift bottles and Gulf (38, 39).
tracing their paths of long period drift. These enclosed or nearly enclosed bodies of water span a
Charts of this circulation pattern were assembled, and the range from 720 to 9 North latitude; unfortunately, no data
cause of the pattern was examined in the expectation that it of surface circulation were found for similar water bodies in
may be useful to other workers, particularly in connection the southern hemisphere. Where the methods by which the
with predictions of pollution down-current from points of circulation was measured were reported, they consisted vari-
sewage and industrial discharge into large bodies of water. ously of drift bottles or drift cards, drogues, buoyed fishing
Information about circulation patterns of lakes is very scarce nets, measurements with drift lines and current meters from
in limnological journals, as these mainly are limited to strictly anchored ships, tracing of increased salinity caused by excess
biological problems. Moreover, most studies of water move- evaporation, and computations from dynamic topography
ments in lakes are restricted to seiches, internal waves, and above prominent thermoclines. The short-term methods are
other movements in a vertical plane. Investigations of cir- significant only during average conditions. Some examples
culation in marginal seas and estuaries are more common are based upon several methods.
than in lakes, possibly because of the natural landward ex- The circulation patterns for all but one of the lakes and
tension of oceanographic methods. Many marginal seas are seas of Figs. 1 and 2 are generally counterclockwise. The
separated from the ocean by barriers caused by crustal de- pattern for the Aral Sea, however, is reported to have a
formation that allow little exchange of water. These are in- clockwise circulation; whether this uniqueness is due to
cluded in the discussion below. Estuaries and lagoons sepa- peculiarities of bottom topography or to perhaps erroneous
rated from the ocean by barriers produced by sand deposition, interpretation of measurements is unknown, and it must re-
and marginal seas widely open to the ocean (Kars Sea, Chuk- main an exception for the time being.
chi Sea, Norwegian Sea, Bering Sea, and the North Sea) often
have circulation patterns similar to those of lakes and the Cause of counterclockwise circulation:
nearly land-locked seas, but they are omitted here because of physical description
possible control by currents from the open ocean. The general consistency in circulation patterns demands a
general explanation. For estuaries and some small marginal
Patterns seas the chief mechanism may be the inflow of light fresh water
The charts of horizontal circulation in lakes and nearly land- at the landward side and the outflow of mixed water at the
locked bodies of ocean water are so thinly and widely scattered mouth, where it is largely counterbalanced by inflow of
in physical and geological literature that we probably have denser ocean water. Similarly, the flow of light fresh water
missed some of the published examples. Most of the ones we into lakes having no outlet (Salton Sea and Dead Sea) may
found are illustrated in simplified form in Figs. 1 and 2. Ex- be important. Such inflows of light water would produce a
amples of patterns from lakes of North America listed from surface slope down which movement of water would be de-
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9394 Geophysics: Emery and Csanady Proc. Nat. Acad. Sci. USA 70 (1978)
FIG. 1. Circulation patterns for lakes simplified from original FIG. 2. Circulation patterns for nearly land-locked bodies of
illustrations cited in the text: Lake Superior, Lake Constance, water separated from the open sea by structural barriers. Pat-
Lake Geneva, Aral Sea, Lake Huron, Lake Michigan, Lake On- terns are simplified from original illustrations cited in the text:
tario, Lake Erie, Caspian Sea, Salton Sea, Dead Sea, and Bitter Baltic Sea, Hudson Bay, Gulf of St. Lawrence, Passamaquoddy
Lake. Bay, Grand Traverse Bay, Bay of Fundy, Black Sea, Adriatic
Sea, Japan Sea, Long Island Sound, Persian Gulf, and Lake
Maracaibo.
flected to the right (in the northern hemisphere) by the
Coriolis force of earth rotation. In most examples, however,
the water bodies are too large to be much affected by the by the rotation of the earth. In a circular basin, constant-
relatively small inflow of light water. Likewise, a decrease in depth model of a stratified lake, the motions produced by the
density of water above the shoal nearshore zone through solar irregularly occurring wind impulses may be elucidated in
heating could produce a slope that may give rise to a counter- considerable detail analytically (40), by use of linearized
clockwise current, but this effect must be small; if it were im- equations of motion. These equations describe large bodies
portant, the current would be counterclockwise only during of water quite faithfully, and the qualitative features of the
the spring and early summer-before the development of a analytical solutions are in good agreement with observation.
homogeneous surface layer-a restriction that seems not to With a uniform wind blowing over the basin, "coastal jets"
be present. In some specific instances one would be inclined more or less along the direction of the wind are produced at
to attribute the observed circulation pattern to the topog- both right-hand and left-hand shores, with Ekman drift
raphy of the basin, but in most examples such an argument occupying the central part of the basin.
also is unconvincing. The generality of the counterclockwise One key property of wind-induced motions in a symmetrical
circulation in the northern hemisphere suggests that the cause basin is that the circulation pattern is also symmetrical, unless
is independent of basin shape and depth distribution, and the wind stress distribution itself possesses significant asym-
within limits also of size. Therefore, it will be convenient metry or "curl." If the basin is small compared to the dimen-
to examine how a counterclockwise circulation pattern may sions of weather systems (this is true even for very large
be set up in a circular basin of constant depth, which repre- lakes), any such asymmetry, if present, must be produced by
sents a theoretical model sufficiently idealized to exclude the basin itself, through some interaction with the air flow
irrelevancies. above. To explain an anticlockwise average circulation, we
It is well known that water movements in lakes and shallow have to show why there should be a positive (cyclonic) curl
seas are produced mainly by wind, that they are strongly in the wind stress, regardless of the direction in which the
influenced by the vertical stratification of the water column, wind blows. In simple terms, we have to show why the wind
and that in the larger bodies of water they are also affected should drag the water along more effectively on the right-
Downloaded by guest on May 23, 2021Proc. Nat. Acad. Sci. USA 70 (1973) Surface Circulation of Lakes 95
hand shore than on the left-hand one (in the northern hemi-
sphere, and "right" and "left" if we look downwind).
As shown by Roll (41), the stress exerted by the wind on
a water surface depends critically on the air-water tem-
perature difference. The stability of the air layer in contact
with a water surface colder by several degrees than the air
some distance above may completely suppress turbulence and
reduce wind stress to zero. In the Great Lakes it is common to
observe a completely smooth band of cold water, while the
warmer water a few hundred meters away is covered by
capillary waves, a clearly visible sign of wind stress. Even
when the contrast is not quite so extreme, the wind stress
magnitude is significantly affected by surface temperature
changes of the order of 10, or even 0.5°. This effect is further
discussed quantitatively below.
It is also clear that in the presence of net surface heating a
horizontal temperature gradient tends to become established,
positive in the direction of surface drift. In sufficiently large
basins (in practice, larger than a few km in size) and in the
northern hemisphere the surface drift has a large component
to the right of the wind ("Ekman drift"). Therefore, in the
presence of net surface heating the water becomes warmer on
the right-hand shore and is, in fact, dragged along more ef-
fectively by the wind. Aerial temperature surveys of the
Great Lakes, for example, show clear evidence of this warming
trend across wind, the temperature contrast being of the order
of 1-2°. Fig. 3 illustrates this point. A much more pronounced
temperature difference occurs between left- and right-hand
shores when the wind stress is strong enough and acts long
enough to produce upwelling of cold water. The upwelling FIG. 3. Observed surface temperature patterns of Lake On-
tario from aerial infrared radiation surveys. Before surveys (a)
occurs on the left-hand shore in the northern hemisphere, and (b), the winds were generally westerly; before survey
and it is under such circumstances that absence of wind stress (c), they were easterly. Larger temperature contrast in (a) is
may be observed over the upwelled water, while the warmer typical of summer conditions, while that of (b) is typical of early
water not too far away is clearly acted upon by the wind. autumn. Redrawn from illustrations by Irbe (48).
The exact dynamical effects on a stratified lake of such an
asymmetrical distribution of wind stress are complicated, but
they undoubtedly include a tendency to produce counter- proximation, i.e., there is no net drift in the direction of phase
clockwise circulation of the wind-driven surface waters. propagation. A second-order drift akin to Stokes drift in
At least in temperate latitudes the winds are variable: surface waves is possible (45), but such an effect has not yet
as weather systems pass over a lake or marginal sea, wind- been shown to be quantitatively significant in the above types
stress impulses are exerted on the water surface that change of waves.
irregularly both in magnitude and direction. As a result, cur- A second plausible explanation that does not work is that
rents observable at any fixed point in such a lake or sea are nonlinear momentum transport by the mean motion fortifies
highly variable. Near shore, for example, they alternate ir- the right-hand shore "coastal jet." This momentum transport
regularly between the two shore-parallel directions. Ac- is in fact to the right on both shores, i.e., shoreward on the
cording to the above argument, however, the currents are right and offshore on the left. However, its net effect is to
somewhat stronger when they leave the shore to the right displace the left-hand jet somewhat offshore and to stabilize
than in the opposite case. When the flow is averaged over a the right-hand jet against the shore, without interfering very
longer period, most of the irregular motion is cancelled out, significantly with the overall flow pattern.
but not the portion directly due to wind-stress curl; this por- Possibly other nonlinear or more complicated effects also
tion is of the same sense regardless of wind direction or veloc- contribute to the maintenance of anticlockwise mean circula-
ity and it should add up to a significant component of the tion in enclosed bodies of water, but we have not been able
mean flow pattern. to identify any that were quantitatively significant. By con-
In concluding this section, it may be useful to point out two trast, the surface heating-Ekman drift coupling of air and
nonexplanations of counterclockwise circulation. One is the water should be able to maintain a significant circulation
well-known property of certain long waves to progress in a amplitude, as shown by the calculations below.
counterclockwise direction along the periphery of a suffi-
ciently large basin. Thus, the phase of the seiches or "wind Quantitative considerations
tides" of Lake Erie progresses counterclockwise (42), as do To calculate the "typical" magnitude of the cross-wind tem-
tides in the Gulf of St. Lawrence (43) or long internal Kelvin perature gradient, we assume that the wind has blown long
waves in Lake Michigan (44). However, particle orbits as- enough from a constant direction to establish equilibrium
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sociated with such wavelike motions are closed in a first ap- between surface heating and advective heat transport in the96 Geophysics: Emery and Csanady Proc. Nat. Acad. Sci. USA 70 (1M)
water, i.e. of the wind-stress curl, i.e., to
wO H
[1] 131
by CpV J l--dt
byp
where 0 is temperature (0C), H is net heat absorption by the Suppose that the above wind-stress curl was acting for
water in cal cm2 sec-', c. and p are the specific heat and den- a period of t = 8 hr, over a circular basin of 50 km in diameter,
sity of water, y is the direction perpendicular to the wind, and i.e.,
V is Ekman transport to the right of the wind (cm2 sec'1). A
a
typical magnitude of the net heat flux is 2. 10-' cal cm-2 = AO/p) =
10-7Cmsec-2
sec-' (about 180 cal cm-2 day-'), while the Ekman drift in by \p/ 50km
a 6 m/sec wind ("10 meter level wind") at mid-latitudes is W = 8 3600-10-7 = 2* 88- 10-8 cm sec
close to 104 cm2 sec'1. These data yield a temperature gradient
60/by of 2. 10-7 0C cm-', or 20 per 100 km. Actual observed where we have assumed a linear change in stress across the
temperature gradients in the central part of Lake Ontario, basin. The circulation produced by this wind stress curl is
during the heating season for example, (see Fig. 3a), are of a characterized by a tangential velocity at the shores of
similar magnitude to several times greater. Wr
In the absence of surface heating, temperature contrasts 2#[41
V: ==2h
in a cross-wind direction are also observed, although they
tend to be somewhat smaller; in Lake Ontario, these effects where r is the basin radius and h is the mixed-layer depth.
are of the order of 10 across the 70-km wide lake. An examina- For r = 25 km and taking h = 10 m, we find
tion of successive surveys suggests that these temperature Vt = 3.6 cm/sec
differences are caused by intermittent upwelling of cold water
on the left-hand shore, followed by some horizontal mixing. 3.1 km/day
The wind-stress differences corresponding to temperature Note that vt is proportional to Wr, so that it does not directly
contrasts of the above order of magnitude may be estimated depend on radius, given a certain temperature contrast, and
on a theoretical basis by the use of geostrophic drag coefficients with it A(To/p) across the basin, W containing the gradient
presented in (46). These drag coefficients are functions of two A(To/p)/2r. Similar tangential velocities v: can, therefore,
nondimensional parameters, the surface Rossby number and develop in smaller or larger basins, as long as the temperature
the Lettau number contrast remains significant.
Ro =
U9 Concluding remarks
fzo To sum up briefly, we have presented a possible physical
[21 mechanism to explain the observed universal tendency toward
Le Le=AT
=-
g
Tf~zo
counterclockwise circulation in northern hemisphere lakes and
marginal seas. The salient parts of our argument are: (i) there
where U, is geostrophic wind speed, f is the Coriolis parameter, is usually a temperature contrast between the right- and left-
z0 the roughness length of the surface, AT the temperature hand shore, (looking downwind), the former being warmer;
difference between air at geostrophic level and surface below, (ii) the observed temperature differences are sufficient to
T the absolute air temperature, and g is the acceleration of produce cyclonic wind-stress curl of appreciable magnitude,
gravity. As a typical roughness length, we take z0 0.1 cm.
=
which sets up the counterclockwise circulation. Climatic
Assuming also U, = 10 m sec-', f = 10-4 sec-, we calculate conditions allowing these physical factors to operate prevail
Ro = 108. Suppose that the air-water temperature difference from early spring to late fall. In midwinter, the circulation
on the right-hand shore is exactly zero, while on the left-hand pattern should be different. In some lakes and other water
shore the water surface is 10 cooler than the air-then Le = 0 bodies, this appears to be true, but the evidence is scant as
on the right, Le = 109 on the left. The corresponding drag most observations of circulation are made during the warmer
coefficients and surfaces stresses are seasons. The rotation of the earth is involved in the establish-
Right Cd = 0.55 10-8 ment of the temperature contrast across wind, either through
Ekman drift to the right, or the production of an upwelling
To = Cdp.U,2 = 0.7 dyne cm2
on the left. In the southern hemisphere the opposite circula-
Left Cd = 0.15 10 3 tion should be observable. Unfortunately, as we remarked
before, evidence on this point is insufficient to confirm our
To = 0.2 dyne cm-2 reasoning.
The theoretically predicted wind stress is thus 3.5 times We thank the Office of Naval Research, which supported this
greater on the right than on the left, a very significant varia- work under Contract N00014-66-C0241. This is Contribution
tion indeed, considering the smallness of the temperature 2965 of the Woods Hole Oceanographic Institution.
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