Proc. Nat. Ac4d. Sci. USAVol. 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 beenmapped for more than 40 lakes, marginal seas, estuaries,and lagoons. All are within the northern hemisphere,and all except one are known to have a counterclockwisepattern. This consistent pattern is attributed to the dragof wind blowing across the bodies of water. Warmer sur-face water is displaced to the right-hand shore zone (fac-ing downwind), where it produces greater surface turbu-lence and, thus, greater wind drag. This effect leads tocounterclockwise water circulation regardless of the direc-tion and, within limits, the duration of the wind.

During studies of northern hemisphere lakes and water bodiesmarginal to the ocean, we have noted a consistent counter-clockwise circulation of surface waters. "Circulation" is heredefined to mean a long-term pattern of motion, or residualmotion remaining after the irregular water movements in-volved in wind drift, seiches, and other short-term phenomenaare averaged. The averaging period is taken to be long com-pared with the typical passage time of weather cycles. Ex-perimentally, such long-term patterns of flow may be directlydetermined, e.g., by releasing batches of drift bottles andtracing their paths of long period drift.

Charts of this circulation pattern were assembled, and thecause of the pattern was examined in the expectation that itmay be useful to other workers, particularly in connectionwith predictions of pollution down-current from points ofsewage and industrial discharge into large bodies of water.Information about circulation patterns of lakes is very scarcein limnological journals, as these mainly are limited to strictlybiological problems. Moreover, most studies of water move-ments in lakes are restricted to seiches, internal waves, andother movements in a vertical plane. Investigations of cir-culation in marginal seas and estuaries are more commonthan in lakes, possibly because of the natural landward ex-tension of oceanographic methods. Many marginal seas areseparated from the ocean by barriers caused by crustal de-formation that allow little exchange of water. These are in-cluded in the discussion below. Estuaries and lagoons sepa-rated from the ocean by barriers produced by sand deposition,and marginal seas widely open to the ocean (Kars Sea, Chuk-chi Sea, Norwegian Sea, Bering Sea, and the North Sea) oftenhave circulation patterns similar to those of lakes and thenearly land-locked seas, but they are omitted here because ofpossible control by currents from the open ocean.

Patterns

The charts of horizontal circulation in lakes and nearly land-locked bodies of ocean water are so thinly and widely scatteredin physical and geological literature that we probably havemissed some of the published examples. Most of the ones wefound are illustrated in simplified form in Figs. 1 and 2. Ex-amples of patterns from lakes of North America listed from

north to south are: Lake Superior (1), Lake Huron (1-3),Lake Michigan (1, 4), Lake Ontario (1, 5), Lake Erie (1, 6),Great Salt Lake (7), and the Salton Sea (8, 9). Patterns alsoare available for the following lakes of Eurasia: Lake Con-stance-Bodensee (10, 11), Lake Neuchatel (12), Lake Geneva-Liman (13), Aral Sea (14), Caspian Sea (A. F. Mikhalevskiiin ref 15), Dead Sea (16), and Bitter Lake (17).

Circulation patterns for water bodies of North Americathat are nearly separated from the ocean or from large ad-jacent lakes by structural barriers have been published for:Baffin Bay (18, 19), Hudson Bay (20, 21), Gulf of St. Law-rence (22, 23), Passamaquoddy Bay (24), Grand TraverseBay (25), Bay of Fundy (26, 27), Gulf of Maine (22), andLong Island Sound (28). In South America the circulationin Lake Maracaibo (29) has been mapped. Similar waterbodies of Eurasia for which surface circulation are known are:the White Sea (V. Timonov in ref. 30), Baltic Sea (31), BlackSea (32), Adriatic Sea (33, 34), Japan Sea (ref. 35, Sizova inrefs. 30 and 36), the Mediterranean Sea (37), and the PersianGulf (38, 39).These enclosed or nearly enclosed bodies of water span a

range from 720 to 9 North latitude; unfortunately, no dataof surface circulation were found for similar water bodies inthe southern hemisphere. Where the methods by which thecirculation was measured were reported, they consisted vari-ously of drift bottles or drift cards, drogues, buoyed fishingnets, measurements with drift lines and current meters fromanchored ships, tracing of increased salinity caused by excessevaporation, and computations from dynamic topographyabove prominent thermoclines. The short-term methods aresignificant only during average conditions. Some examplesare based upon several methods.The circulation patterns for all but one of the lakes and

seas of Figs. 1 and 2 are generally counterclockwise. Thepattern for the Aral Sea, however, is reported to have aclockwise circulation; whether this uniqueness is due topeculiarities of bottom topography or to perhaps erroneousinterpretation of measurements is unknown, and it must re-main an exception for the time being.

Cause of counterclockwise circulation:physical descriptionThe general consistency in circulation patterns demands ageneral explanation. For estuaries and some small marginalseas the chief mechanism may be the inflow of light fresh waterat the landward side and the outflow of mixed water at themouth, where it is largely counterbalanced by inflow ofdenser ocean water. Similarly, the flow of light fresh waterinto lakes having no outlet (Salton Sea and Dead Sea) maybe important. Such inflows of light water would produce asurface slope down which movement of water would be de-

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94 Geophysics: Emery and Csanady

FIG. 1. Circulation patterns for lakes simplified from originalillustrations cited in the text: Lake Superior, Lake Constance,Lake Geneva, Aral Sea, Lake Huron, Lake Michigan, Lake On-tario, Lake Erie, Caspian Sea, Salton Sea, Dead Sea, and BitterLake.

flected to the right (in the northern hemisphere) by theCoriolis force of earth rotation. In most examples, however,the water bodies are too large to be much affected by therelatively small inflow of light water. Likewise, a decrease indensity of water above the shoal nearshore zone through solarheating could produce a slope that may give rise to a counter-clockwise current, but this effect must be small; if it were im-portant, the current would be counterclockwise only duringthe spring and early summer-before the development of ahomogeneous surface layer-a restriction that seems not tobe present. In some specific instances one would be inclinedto attribute the observed circulation pattern to the topog-raphy of the basin, but in most examples such an argumentalso is unconvincing. The generality of the counterclockwisecirculation in the northern hemisphere suggests that the causeis independent of basin shape and depth distribution, andwithin limits also of size. Therefore, it will be convenientto examine how a counterclockwise circulation pattern maybe set up in a circular basin of constant depth, which repre-sents a theoretical model sufficiently idealized to excludeirrelevancies.

It is well known that water movements in lakes and shallowseas are produced mainly by wind, that they are stronglyinfluenced by the vertical stratification of the water column,and that in the larger bodies of water they are also affected

FIG. 2. Circulation patterns for nearly land-locked bodies ofwater separated from the open sea by structural barriers. Pat-terns are simplified from original illustrations cited in the text:Baltic Sea, Hudson Bay, Gulf of St. Lawrence, PassamaquoddyBay, Grand Traverse Bay, Bay of Fundy, Black Sea, AdriaticSea, Japan Sea, Long Island Sound, Persian Gulf, and LakeMaracaibo.

by the rotation of the earth. In a circular basin, constant-depth model of a stratified lake, the motions produced by theirregularly occurring wind impulses may be elucidated inconsiderable detail analytically (40), by use of linearizedequations of motion. These equations describe large bodiesof water quite faithfully, and the qualitative features of theanalytical solutions are in good agreement with observation.With a uniform wind blowing over the basin, "coastal jets"more or less along the direction of the wind are produced atboth right-hand and left-hand shores, with Ekman driftoccupying the central part of the basin.One key property of wind-induced motions in a symmetrical

basin is that the circulation pattern is also symmetrical, unlessthe wind stress distribution itself possesses significant asym-metry or "curl." If the basin is small compared to the dimen-sions of weather systems (this is true even for very largelakes), any such asymmetry, if present, must be produced bythe basin itself, through some interaction with the air flowabove. To explain an anticlockwise average circulation, we

have to show why there should be a positive (cyclonic) curlin the wind stress, regardless of the direction in which thewind blows. In simple terms, we have to show why the windshould drag the water along more effectively on the right-

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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 contactwith a water surface colder by several degrees than the airsome distance above may completely suppress turbulence andreduce wind stress to zero. In the Great Lakes it is common toobserve a completely smooth band of cold water, while thewarmer water a few hundred meters away is covered bycapillary waves, a clearly visible sign of wind stress. Evenwhen the contrast is not quite so extreme, the wind stressmagnitude is significantly affected by surface temperaturechanges of the order of 10, or even 0.5°. This effect is furtherdiscussed quantitatively below.

It is also clear that in the presence of net surface heating ahorizontal temperature gradient tends to become established,positive in the direction of surface drift. In sufficiently largebasins (in practice, larger than a few km in size) and in thenorthern hemisphere the surface drift has a large componentto the right of the wind ("Ekman drift"). Therefore, in thepresence of net surface heating the water becomes warmer onthe right-hand shore and is, in fact, dragged along more ef-fectively by the wind. Aerial temperature surveys of theGreat Lakes, for example, show clear evidence of this warmingtrend across wind, the temperature contrast being of the orderof 1-2°. Fig. 3 illustrates this point. A much more pronouncedtemperature difference occurs between left- and right-handshores when the wind stress is strong enough and acts longenough to produce upwelling of cold water. The upwellingoccurs on the left-hand shore in the northern hemisphere,and it is under such circumstances that absence of wind stressmay be observed over the upwelled water, while the warmerwater not too far away is clearly acted upon by the wind.The exact dynamical effects on a stratified lake of such anasymmetrical distribution of wind stress are complicated, butthey undoubtedly include a tendency to produce counter-clockwise circulation of the wind-driven surface waters.At least in temperate latitudes the winds are variable:

as weather systems pass over a lake or marginal sea, wind-stress impulses are exerted on the water surface that changeirregularly both in magnitude and direction. As a result, cur-rents observable at any fixed point in such a lake or sea arehighly variable. Near shore, for example, they alternate ir-regularly between the two shore-parallel directions. Ac-cording to the above argument, however, the currents aresomewhat stronger when they leave the shore to the rightthan in the opposite case. When the flow is averaged over alonger period, most of the irregular motion is cancelled out,but not the portion directly due to wind-stress curl; this por-tion is of the same sense regardless of wind direction or veloc-ity and it should add up to a significant component of themean flow pattern.

In concluding this section, it may be useful to point out twononexplanations of counterclockwise circulation. One is thewell-known property of certain long waves to progress in acounterclockwise direction along the periphery of a suffi-ciently large basin. Thus, the phase of the seiches or "windtides" of Lake Erie progresses counterclockwise (42), as dotides in the Gulf of St. Lawrence (43) or long internal Kelvinwaves in Lake Michigan (44). However, particle orbits as-sociated with such wavelike motions are closed in a first ap-

FIG. 3. Observed surface temperature patterns of Lake On-tario from aerial infrared radiation surveys. Before surveys (a)and (b), the winds were generally westerly; before survey(c), they were easterly. Larger temperature contrast in (a) istypical of summer conditions, while that of (b) is typical of earlyautumn. Redrawn from illustrations by Irbe (48).

proximation, i.e., there is no net drift in the direction of phasepropagation. A second-order drift akin to Stokes drift insurface waves is possible (45), but such an effect has not yetbeen shown to be quantitatively significant in the above typesof waves.A second plausible explanation that does not work is that

nonlinear momentum transport by the mean motion fortifiesthe right-hand shore "coastal jet." This momentum transportis in fact to the right on both shores, i.e., shoreward on theright and offshore on the left. However, its net effect is todisplace the left-hand jet somewhat offshore and to stabilizethe right-hand jet against the shore, without interfering verysignificantly with the overall flow pattern.

Possibly other nonlinear or more complicated effects alsocontribute to the maintenance of anticlockwise mean circula-tion in enclosed bodies of water, but we have not been ableto identify any that were quantitatively significant. By con-trast, the surface heating-Ekman drift coupling of air andwater should be able to maintain a significant circulationamplitude, as shown by the calculations below.

Quantitative considerations

To calculate the "typical" magnitude of the cross-wind tem-perature gradient, we assume that the wind has blown longenough from a constant direction to establish equilibriumbetween surface heating and advective heat transport in the

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96 Geophysics: Emery and Csanady

water, i.e.wO Hby CpV [1]

of the wind-stress curl, i.e., to

J l--dtbypwhere 0 is temperature (0C), H is net heat absorption by thewater in cal cm2 sec-', c. and p are the specific heat and den-sity of water, y is the direction perpendicular to the wind, andV is Ekman transport to the right of the wind (cm2 sec'1). Atypical magnitude of the net heat flux is 2. 10-' cal cm-2sec-' (about 180 cal cm-2 day-'), while the Ekman drift ina 6 m/sec wind ("10 meter level wind") at mid-latitudes isclose to 104 cm2 sec'1. These data yield a temperature gradient60/by of 2. 10-7 0C cm-', or 20 per 100 km. Actual observedtemperature gradients in the central part of Lake Ontario,during the heating season for example, (see Fig. 3a), are of a

similar magnitude to several times greater.In the absence of surface heating, temperature contrasts

in a cross-wind direction are also observed, although theytend to be somewhat smaller; in Lake Ontario, these effectsare of the order of 10 across the 70-km wide lake. An examina-tion of successive surveys suggests that these temperaturedifferences are caused by intermittent upwelling of cold wateron the left-hand shore, followed by some horizontal mixing.The wind-stress differences corresponding to temperature

contrasts of the above order of magnitude may be estimatedon a theoretical basis by the use of geostrophic drag coefficientspresented in (46). These drag coefficients are functions of twonondimensional parameters, the surface Rossby number andthe Lettau number

Ro =U9

fzo[21

Le=AT gLe=-

Tf~zo

where U, is geostrophic wind speed, f is the Coriolis parameter,z0 the roughness length of the surface, AT the temperaturedifference between air at geostrophic level and surface below,T the absolute air temperature, and g is the acceleration ofgravity. As a typical roughness length, we take z0 = 0.1 cm.

Assuming also U, = 10 m sec-', f = 10-4 sec-, we calculateRo = 108. Suppose that the air-water temperature differenceon the right-hand shore is exactly zero, while on the left-handshore the water surface is 10 cooler than the air-then Le = 0

on the right, Le = 109 on the left. The corresponding dragcoefficients and surfaces stresses are

Right

Left

Cd = 0.55 10-8To = Cdp.U,2 = 0.7 dyne cm2

Cd = 0.15 10 3

To = 0.2 dyne cm-2

The theoretically predicted wind stress is thus 3.5 timesgreater on the right than on the left, a very significant varia-tion indeed, considering the smallness of the temperaturecontrast. Direct experimental evidence to support theserather surprising results does not seem to be available, buteven if these figures are overestimates, they suggest thatsubstantial wind-stress curl due to surface temperature con-

trasts is, in fact, a likely possibility.Linear theory (47) shows that the circulation set up by a

nonuniform wind stress is proportional to the time-integral

Suppose that the above wind-stress curl was acting fora period of t = 8 hr, over a circular basin of 50 km in diameter,i.e.,

a = AO/p) = 10-7Cmsec-2

by \p/ 50kmW = 8 3600-10-7 = 2* 88- 10-8 cm sec

where we have assumed a linear change in stress across thebasin. The circulation produced by this wind stress curl ischaracterized by a tangential velocity at the shores of

WrV:=2#[41=2h

where r is the basin radius and h is the mixed-layer depth.Forr = 25km and takingh = 10 m, we find

Vt = 3.6 cm/sec

3.1 km/day

Note that vt is proportional to Wr, so that it does not directlydepend on radius, given a certain temperature contrast, andwith it A(To/p) across the basin, W containing the gradientA(To/p)/2r. Similar tangential velocities v: can, therefore,develop in smaller or larger basins, as long as the temperaturecontrast remains significant.

Concluding remarks

To sum up briefly, we have presented a possible physicalmechanism to explain the observed universal tendency towardcounterclockwise circulation in northern hemisphere lakes andmarginal seas. The salient parts of our argument are: (i) thereis usually a temperature contrast between the right- and left-hand shore, (looking downwind), the former being warmer;(ii) the observed temperature differences are sufficient toproduce cyclonic wind-stress curl of appreciable magnitude,which sets up the counterclockwise circulation. Climaticconditions allowing these physical factors to operate prevailfrom early spring to late fall. In midwinter, the circulationpattern should be different. In some lakes and other waterbodies, this appears to be true, but the evidence is scant as

most observations of circulation are made during the warmer

seasons. The rotation of the earth is involved in the establish-ment of the temperature contrast across wind, either throughEkman drift to the right, or the production of an upwellingon the left. In the southern hemisphere the opposite circula-tion should be observable. Unfortunately, as we remarkedbefore, evidence on this point is insufficient to confirm our

reasoning.

We thank the Office of Naval Research, which supported thiswork under Contract N00014-66-C0241. This is Contribution2965 of the Woods Hole Oceanographic Institution.

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