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 Unauthenticated | Downloaded 09/23/21 05:09 PM UTC VOL. 37, No. 3, MARCH, 1956 97 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<p, and the values according to A. ence gains anticyclonic vorticity due to the varia- Defant [2] are indicated by circles. tion of the Coriolis parameter with latitude, and when moving from b2 to b1 it gains cyclonic vor- A successful attempt to determine the depth ticity.