96 BULLETIN AMERICAN METEOROLOGICAL SOCIETY
Notes on the Horizontal Circulation of Ocean Currents
GERHARD NEUMANN Department of Meteorology and Oceanography, New York University
ABSTRACT The effect of a variable depth of the wind driven oceanic circulation on the steady state current systems is discussed with the aid of a simple model. There is much evidence that in the Atlantic Ocean the depth of the layer of no motion increases poleward proportionally to the sine of the geographical latitude in both hemispheres. It seems not unlikely that the oceans react to the planetary vorticity effect in such a way that they rather tend to adjust the level of no motion than to displace the whole gyre of the wind driven circulation to the west.
NE of the most striking features of ocean This is concerned with variations of the depth of currents is the concentration of the Gulf the moving surface layers. O Stream along the east coast of the United The study of the horizontal circulation of wind States. It has its counterpart in a similar concen- driven currents in a stratified ocean has called at- tration of the Kuro Shio along the east coast of tention to the effect which the variable depth of Asia. In the Indian Ocean, the Somali Current, the circulation system may have on the hydrody- crossing the equator either in the northerly or namic analysis of the problem [5]. This "variable southerly direction according to the season, and depth," in a stratified ocean, is the depth where the the Mozambique Current between Madagascar current velocities vanish. It seems at first not and the African Continent, are also relatively quite understandable why the currents should be strong currents compared with those in the East- so strongly affected by the depth of a motionless ern Indian Ocean. The intensification of these layer. The purpose of this short note is to explain currents toward the west must be considered an the physical background for the discussed effects established fact. However, there are some re- in simple terms with the aid of a very simple markable exceptions observed with other ocean model, since the basic physical meaning may es- currents: in the South Pacific, the Humboldt Cur- cape in the detailed mathematical analysis. rent in the eastern part of the ocean off the coast The large oceanic current systems, such as the of North Chile and Peru is the strongest, and in great gyres circulating clockwise in the Northern the South Atlantic there is no evidence that the and counterclockwise in the Southern Hemisphere Brazil Current is stronger or more concentrated around middle latitudes are considered to be driven than the Benguela Current off the coast of South mainly by the pulling and dragging forces of the West Africa. wind at the sea surface. Little is known about In a barotropic ocean of constant depth, H. the details of the vertical stratification of the ocean Stommel [3] has shown that, due to the variation currents except for the fact that the current ve- of the Coriolis parameter with latitude the whole locity in general decreases with depth until it large scale circulation system must be strongly practically disappears at a level often called the displaced to the west. This produces an asym- "zero layer" or the "depth of no motion." This metrical flow with swift currents along the east depth is not constant, but varies considerably coasts of the continents, and weak and broad throughout the oceans. It is in some way related currents along the west coasts of the continents, to the vertical density stratification and friction. regardless of the hemisphere. An elementary ex- There is much evidence that the depth of no mo- planation of this effect has been given (H. Stom- tion is only a few hundred meters deep in tropical mel [4] ). However, the question arises as to why regions. It increases with latitude. In polar re- the ocean currents are not everywhere strongest gions for instance near the Antarctic continent, in the west, if the variation of the Coriolis param- the currents induced by the wind may even extend eter with latitude is the only cause which produces to the bottom some thousand meters below the this asymmetry. In the following note an addi- surface. tional factor will be discussed which might alter If the current system has arrived at a state of the theoretical picture of the oceanic circulation. steady motion under the stress of the wind, the sea
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vertically, but also horizontally, especially in meridional direction, it is necessary to introduce a meridional variation of the density. This is very important, since the vertical density gradient, mainly as a result of climatic influences, decreases with increasing latitude, almost approaching ho- mogeneity in high latitudes. It can be shown that in a meridional section with a density stratifica- tion as indicated schematically in FIGURE 2, a level of no motion, d, must exist for the zonal currents, and this level d becomes deeper from equatorial regions towards higher latitudes [5]. This agrees with our qualitative experience, and is schemati- cally indicated in FIGURE 2 which represents the conditions in section B'B. The exact topography of the depth of no motion depends in a rather complicated way on the circu- lation, the mass distribution and the friction. In wind driven ocean currents, where friction is a substantial part of the system, the level d is not FIG. 1. Symmetrical circulation in a rectangular ocean necessarily a level where the horizontal pressure basin. gradient vanishes exactly. In a baroclinic ocean without friction, a decreasing velocity with depth surface as the uppermost isobaric surface in the can only be connected with the baroclinity of the oceans, and the field of mass given by the distribu- fluid. However, in frictionally driven ocean cur- tion of potential density in the stratified water will rents, a vertical shear can also be the result of have adjusted to the field of currents, which also friction, at least to some extent. The concept of includes the adjustment of the lower boundary the depth of no motion in wind driven current is, of the circulation system. This adjustment is not therefore, connected with the baroclinity and the to be confused with the equilibrium between the friction of the fluid. The detailed analysis becomes field of mass and the field of currents as given in very involved. It may only be mentioned here the case of a pure geostrophic flow, although in that with a stationary flow as a result of the equi- some regions of the oceans this geostrophic equi- librium of all forces, variations of the level d in librium is approximately fulfilled. However, if zonal direction may also occur. However, for the current velocity decreases with depth, the field the purpose of this qualitative analysis, such vari- of mass will always tend to adjust in such a way ations need not be discussed. Here let us con- that less dense water accumulates in the center of sider only the fact that there is much evidence that the gyre. the depth of the layer of no motion increases in The following simple model may be used to il- some way with increasing latitude (see Appen- lustrate the relationships between the field of cur- dix). rents and mass. Consider in the Northern Hemi- Consider next a vertical column of water mov- sphere a large ocean basin, such as shown in ing between the streamlines in FIGURE 1 from ax FIGURE 1. With an anticyclonic wind system over it, the oceanic circulation will also be anticyclonic. In the Northern Hemisphere, the total mass trans- port of surface waters by the wind is clockwise to the wind direction. It accumulates in the center of the gyre, causing an oceanic "high" which is surrounded by anticyclonic currents. In a zonal section A A' (FIGURE 1) through the basin, the topography of the sea surface will be highest in the center C of the gyre, and also the isobaric surfaces in the deeper layers will be highest in the center FIG. 2. Schematic meridional cross section through the of the gyre. anticyclonic gyre of FIGURE 1. The dashed lines are lines Since the real oceans are stratified not only of equal potential density; d is the level of no motion.
Unauthenticated | Downloaded 09/23/21 05:09 PM UTC 98 BULLETIN AMERICAN METEOROLOGICAL SOCIETY to a2. The distance L, between the streamlines may be considered as constant, and the circulation as a symmetrical flow around the center C. When moving from a1 to a2, the vertical column of water undergoes a stretching due to increasing depth of the lower boundary of the current. With this, the moving water column gains cyclonic (positive) vorticity along the western boundary of the cur- rent system. A water column moving from b2 to br is shrinking due to decreasing depth and gains anticyclonic (negative) vorticity along the eastern boundary of the current system. FIG. 3. Average depth of the layer of no motion in On the other hand, a mass of water moving from the Atlantic Ocean as a function of latitude. The curves to a2 without horizontal convergence or diverg- are proportional to sin Unauthenticated | Downloaded 09/23/21 05:09 PM UTC VOL. 37, No. 3, MARCH, 1956 99 whole gyre of the wind driven circulation to the above the undisturbed water level, it follows that west. In very low latitudes, however, the rela- Vpd X Vd = g(pVh + dVp) X Vd. This can only tive vorticity f may not be negligible compared vanish if either Vh is exactly opposite from Vp, with the planetary vorticity, and it may follow or if the resultant vector P = pVh + dVp is that near the equator d = const (/ + f) has to exactly parallel to Vd. There is no reason to be used. assume that this should be strictly the case in H. Stommel [3] suggested that in the oceans the oceans, and in fact it is not. This is par- the effect of the planetary vorticity is to displace ticularly obvious when examining the density the subtropical gyre to the west. This is true, distribution at various levels along the eastern but it would explain the intensification of the and western boundaries of the oceans, in the Gulf Stream and the Kuro Shio only in the case region of prevailing meridional flow. (Only the of an oceanic circulation with a constant depth Gulf Stream and the Kuro Shio are two remark- of its lower boundary. It has always puzzled able exceptions.) oceanographers that similar intensification ef- Whether the non-parallelity of Vh and Vp is fects of ocean currents are not found in the South the result of the dominating influence of friction Atlantic and South Pacific. Intuitively, one and austausch (A. Defant [1]), or it has other would expect them at least similarly developed reasons, need not be discussed here; but it has as in the North Atlantic and North Pacific. If to be taken as a fact. Since the parallelity the effect of the variation of the Coriolis param- between the isobars and the lines of equal den- eter with latitude, that is, the planetary vorticity sity is destroyed (and it must be destroyed with effect, is cancelled in the large scale circulation friction and austausch), it is important to realize by the "topographic" vorticity effect due to the that a fraction of Vh may remain uncompensated poleward increase of the depth of the layer of no by the density distribution (Vp). This fraction motion, the question arises again as to what of gpVh represents a horizontal pressure gradient mechanism causes the strong currents along the which is constant throughout the vertical column east coast of North America and along the east of water above the level d. coast of Asia. In the South Atlantic Ocean, With frictionally driven currents, a vertical and probably in the South Pacific Ocean, it shear can also be the result of the friction, and seems that the discussed effect of the variable the concept of the level of no motion is connected depth of the layer of no motion balances com- with the baroclinity and the friction of the fluid. pletely the planetary vorticity effect, and that It is therefore possible that the level d may still the still unknown mechanism which makes the be maintained as a stationary level where the Gulf Stream and the Kuro Shio the swiftest velocities vanish. It must be remembered that currents in the oceans does not apply to the the level d as well as the whole model is sta- corresponding current systems in the Southern tionary by supposition. The stationary hori- Hemisphere. zontal mass transport in the model is then the result of a proper adjustment of all the terms APPENDIX in the complete equation. By such reasons it The following may help the reader understand would be very critical to make the cross product the present model better, without going into the VpXVd exactly equal to zero without any restric- details of the theory. In the complete analysis, tion. This may be possible only with a pure geo- the crucial term which may produce an effect of strophic flow. However, in this case, the den- the variable depth d is a cross product Vpd X Vd. sity stratification (Vp) and the level d must Here, Vpd means the gradient of the pressure p fulfill very special requirements. If it is ac- along the surface d(x,y), and Vd the gradient of d. cepted (and most oceanographers will agree) If this cross product vanishes exactly, the effect that the wind driven circulation extends into of the varying depth d is completely cancelled much greater depths in polar regions than near out. the equator, the pure geostrophic flow which We may ask for the conditions which must should fulfill these requirements in zonal and be fulfilled if this cross product should vanish meridional direction is impossible. Those re- identically. With Vd 0, it is obvious that quirements are in contradiction with a continu- this term vanishes either if Vpd is exactly equal ous slope of d in meridional direction, which in to zero, or if Vpd is exactly parallel to Vd. Since turn is connected with the large scale density Pd = gp(d + h), where g is the acceleration of distribution (strong vertical gradients in low gravity, p the average density of a water column latitudes, and almost homogeneity in polar above d, and h the elevation of the sea surface regions). Unauthenticated | Downloaded 09/23/21 05:09 PM UTC 100 BULLETIN AMERICAN METEOROLOGICAL SOCIETY As to the order of magnitude of the cross search under contract No. Nonr 285(12). The product, a rough estimate can be made. In reproduction in whole or in part is permitted for order to make this term comparable to the plane- any purpose of the United States Government. tary vorticity, it is found that a relatively small value of Vpd is required. In the South Atlantic, REFERENCES approximately 20 Mill-m3 water may circulate [1] Defant, A., 1931: "Bericht uber die ozeanogr. Un- tersuchungen des Vermessungsschiffes 'Meteor' in per second in the whole gyre. This figure may der Danemarkstrasse und in der Irmingersee." II. be too high, but the exact value is unimportant Ber. Sits. ber. Preuss. Akad. d. Wiss., Phys- for this estimate. The magnitude of V df/dy Math. Kl. XIX, Berlin. 8 [2] Defant, A., 1941: "Die absolute Topographie des is, approximately, 10~ , or less. Since dd/dy physikalischen Meeresniveaus und der Druck- -4 ~ 5 • 10 , according to A. Defant [2], dpd/dx flachen, sowie die Wasserbewegungen im Atlanti- must be approximately 2-10~5, or less, in order schen Ozean." Deutsche Atlant. Exped. "Meteor," 1925-1927, Wiss. Erg. Bd. VI, 2, Teil, 5, pp. 191- to make the cross product of the same order of 260. magnitude as the planetary vorticity. This [3] Stommel, H., 1948: "The Westward Intensification pressure gradient would compare to a geostrophic of Wind Driven Ocean Currents." Trans. Amer. Geophys. Union, 29, pp. 202-206. velocity of 0.2 cm/sec in middle latitudes. [4] Stommel, H., 1951 : "An Elementary Explanation of Why Currents are Strongest in the West." Bull. Amer. Met. Soc., v. 32, no. 1, January 1951. ACKNOWLEDGMENT [5] Neumann, G., 1955: "On the Dynamics of Wind- Driven Ocean Currents." Meteorological Papers, The subject of this paper is part of a research Vol. 2, No. 4, Aug., 1955. University Series, New project sponsored by the Office of Naval Re- York University Press. Instrumental in the establishment of professional mete- orology training at Massachusetts Institute of Tech- NEWS AND NOTES nology and The University of Chicago, he has also held the positions of Assistant Chief for research and educa- tion, United States Weather Bureau, and Research Asso- Professor Rossby Cited as ciate at the Woods Hole Oceanographic Institution. Outstanding Scientist Born in Sweden in 1898, the distinguished meteorolo- gist was educated at the University of Stockholm, the Professor Carl-Gustaf Arvid Rossby, past President of Geophysical Institute in Bergen, Norway, and the Uni- AMS and internationally renowned meteorologist, has versity of Leipzig. He came to this country in 1926 on been named one of "the world's 100 most important a Scandinavian-American Foundation scholarship, and people" by Look magazine. The article comprised a list later became a United States citizen. Under the spon- of men and women outstanding for 1955 in the fields of sorship of the Daniel Guggenheim Fund for the Promo- public affairs, the military, economics, philosophy, the tion of Aeronautics, he established in California in 1927 press, science, arts and letters, health, the church. the first model airways weather service on this side of Chiefly noted were Professor Rossby's pioneering ac- the Atlantic. During his following years at MIT Pro- complishments in long-range weather forecasts. fessor Rossby was largely responsible for the general Resulting from a long and impressive career in scien- acceptance in America of the Norwegian methods of tific achievement, this latest honor comes as no surprise synoptic weather analysis. At the same time he made to AMS members who are familiar with the brilliant important contributions in the fields of atmospheric ther- work of Professor Rossby in research and teaching as modynamics and the mechanics of turbulent motion in well as within AMS activities. the atmosphere and ocean. In Sweden, where he now lives, Professor Rossby is Kenyon College awarded him an honorary Ph.D. de- Director of the Institute of Meteorology and Professor gree in 1939. In addition to his work in AMS, Professor of Meteorology at the University of Stockholm. He for- Rossby is a member of the Royal Meteorological Society merly taught as Professor of Meteorology at The Uni- and holds honorary membership in the Institute of the versity of Chicago, where he was recipient of the Andrew Aeronautical Sciences. MacLeish Distinguished Service Professorship. During As President of AMS in 1944-45, he was active in World War II he served as expert consultant to the Sec- creating a professional status of membership, in establish- retary of War and consultant on weather problems to ing a national headquarters for the first time in the his- the Commanding General of the Army Air Force, as well tory of the Society, and in developing the publication,. as chairman of the University Meteorological Committee, Journal of Meteorology. charged with the responsibility of wartime training of meteorologists for military service. (Continued on page 107) Unauthenticated | Downloaded 09/23/21 05:09 PM UTC