Sverdrup balance

The Sverdrup balance, or Sverdrup relation, is a theoretical relationship between the wind stress exerted on the surface of the open ocean and the vertically integrated meridional (north-south) transport of ocean water.


Aside from the oscillatory motions associated with tidal flow, there are two primary causes of large scale flow in the ocean: (1) thermohaline processes, which induce motion by introducing changes at the surface in temperature and salinity, and therefore in seawater density, and (2) wind forcing. In the 1940s, when Harald Sverdrup was thinking about calculating the gross features of ocean circulation, he chose to consider exclusively the wind stress component of the forcing. As he says in his 1947 paper, in which he presented the Sverdrup relation, this is probably the more important of the two. After making the assumption that frictional dissipation is negligible, Sverdrup obtained the simple result that the meridional mass transport (the Sverdrup transport) is proportional to the curl of the wind stress. This is known as the Sverdrup relation;



is the rate of change of the Coriolis parameter, f, with meridional distance;
V is the vertically integrated meridional mass transport including the geostrophic interior mass transport and the Ekman mass transport;
k is the unit vector in the z (vertical) direction;
is the wind stress vector.

Physical interpretation

Sverdrup balance may be thought of as a consistency relationship for flow which is dominated by the Earth's rotation. Such flow will be characterized by weak rates of spin compared to that of the earth. Any parcel at rest with respect to the surface of the earth must match the spin of the earth underneath it. Looking down on the earth at the north pole, this spin is in a counterclockwise direction, which is defined as positive rotation or vorticity. At the south pole it is in a clockwise direction, corresponding to negative rotation. Thus to move a parcel of fluid from the south to the north without causing it to spin, it is necessary to add sufficient (positive) rotation so as to keep it matched with the rotation of the earth underneath it. The left-hand side of the Sverdrup equation represents the motion required to maintain this match between the absolute vorticity of a water column and the planetary vorticity, while the right represents the applied force of the wind.


The Sverdrup relation can be derived from the linearized barotropic vorticity equation for steady motion:


Here is the geostrophic interior y-component (northward) and is the z-component (upward) of the water velocity. In words, this equation says that as a vertical column of water is squashed, it moves toward the Equator; as it is stretched, it moves toward the pole. Assuming, as did Sverdrup, that there is a level below which motion ceases, the vorticity equation can be integrated from this level to the base of the Ekman surface layer to obtain:


where is seawater density, is the geostrophic meridional mass transport and is the vertical velocity at the base of the Ekman layer.

The driving force behind the vertical velocity is the Ekman transport, which in the Northern (Southern) hemisphere is to the right (left) of the wind stress; thus a stress field with a positive (negative) curl leads to Ekman divergence (convergence), and water must rise from beneath to replace the old Ekman layer water. The expression for this Ekman pumping velocity is


which, when combined with the previous equation and adding the Ekman transport, yields the Sverdrup relation.

Further development

In 1948 Henry Stommel proposed a circulation for the entire ocean depth by starting with the same equations as Sverdrup but adding bottom friction, and showed that the variation in Coriolis parameter with latitude results in a narrow western boundary current in ocean basins. Walter Munk in 1950 combined the results of Rossby (eddy viscosity), Sverdrup (upper ocean wind driven flow) and Stommel (western boundary current flow) and proposed a complete solution for the ocean circulation.


  • Sverdrup, H.U. (November 1947). "Wind-Driven Currents in a Baroclinic Ocean; with Application to the Equatorial Currents of the Eastern Pacific". Proc. Natl. Acad. Sci. U.S.A. 33 (11): 318–26. doi:10.1073/pnas.33.11.318. PMC 1079064. PMID 16588757.
  • Gill, A.E. (1982). Atmosphere-Ocean Dynamics. Academic Press.

External links

Bahama Banks

The Bahama Banks are the submerged carbonate platforms that make up much of the Bahama Archipelago. The term is usually applied in referring to either the Great Bahama Bank around Andros Island, or the Little Bahama Bank of Grand Bahama Island and Great Abaco, which are the largest of the platforms, and the Cay Sal Bank north of Cuba. The islands of these banks are politically part of the Bahamas. Other banks are the three banks of the Turks and Caicos Islands, namely the Caicos Bank of the Caicos Islands, the bank of the Turks Islands, and wholly submerged Mouchoir Bank. Further southeast are the equally wholly submerged Silver Bank and Navidad Bank north of the Dominican Republic.

Boundary current

Boundary currents are ocean currents with dynamics determined by the presence of a coastline, and fall into two distinct categories: western boundary currents and eastern boundary currents.

Carbonate platform

A carbonate platform is a sedimentary body which possesses topographic relief, and is composed of autochthonic calcareous deposits. Platform growth is mediated by sessile organisms whose skeletons build up the reef or by organisms (usually microbes) which induce carbonate precipitation through their metabolism. Therefore, carbonate platforms can not grow up everywhere: they are not present in places where limiting factors to the life of reef-building organisms exist. Such limiting factors are, among others: light, water temperature, transparency and pH-Value. For example, carbonate sedimentation along the Atlantic South American coasts takes place everywhere but at the mouth of the Amazon River, because of the intense turbidity of the water there. Spectacular examples of present-day carbonate platforms are the Bahama Banks under which the platform is roughly 8 km thick, the Yucatan Peninsula which is up to 2 km thick, the Florida platform, the platform on which the Great Barrier Reef is growing, and the Maldive atolls. All these carbonate platforms and their associated reefs are confined to tropical latitudes. Today's reefs are built mainly by scleractinian corals, but in the distant past other organisms, like archaeocyatha (during the Cambrian) or extinct cnidaria (tabulata and rugosa) were important reef builders.

Coriolis force

In physics, the Coriolis force is an inertial or fictitious force that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

Newton's laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference. When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal accelerations appear. When applied to massive objects, the respective forces are proportional to the masses of them. The Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to the square of the rotation rate. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation). The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are termed inertial forces, fictitious forces or pseudo forces. They "allow" the application of Newton's laws to a rotating system. They are correction factors that do not exist in a non-accelerating or inertial reference frame.In popular (non-technical) usage of the term "Coriolis effect", the rotating reference frame implied is almost always the Earth. Because the Earth spins, Earth-bound observers need to account for the Coriolis force to correctly analyze the motion of objects. The Earth completes one rotation per day, so for motions of everyday objects the Coriolis force is usually quite small compared to other forces; its effects generally become noticeable only for motions occurring over large distances and long periods of time, such as large-scale movement of air in the atmosphere or water in the ocean. Such motions are constrained by the surface of the Earth, so only the horizontal component of the Coriolis force is generally important. This force causes moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the Northern Hemisphere and to the left in the Southern Hemisphere. The horizontal deflection effect is greater near the poles, since the effective rotation rate about a local vertical axis is largest there, and decreases to zero at the equator. Rather than flowing directly from areas of high pressure to low pressure, as they would in a non-rotating system, winds and currents tend to flow to the right of this direction north of the equator and to the left of this direction south of it. This effect is responsible for the rotation of large cyclones (see Coriolis effects in meteorology).

For an intuitive explanation of the origin of the Coriolis force, consider an object, constrained to follow the Earth's surface and moving northward in the northern hemisphere. Viewed from outer space, the object does not appear to go due north, but has an eastward motion (it rotates around toward the right along with the surface of the Earth). The further north it travels, the smaller the "diameter of its parallel" (the minimum distance from the surface point to the axis of rotation, which is in a plane orthogonal to the axis), and so the slower the eastward motion of its surface. As the object moves north, to higher latitudes, it has a tendency to maintain the eastward speed it started with (rather than slowing down to match the reduced eastward speed of local objects on the Earth's surface), so it veers east (i.e. to the right of its initial motion).Though not obvious from this example, which considers northward motion, the horizontal deflection occurs equally for objects moving eastward or westward (or in any other direction).The theory that the effect influences draining water to rotate clockwise in the northern hemisphere and anti-clockwise in the southern hemisphere has been repeatedly disproven by modern-day scientists.

Ekman transport

Ekman transport, part of Ekman motion theory first investigated in 1902 by Vagn Walfrid Ekman. Winds are the main source of energy for ocean circulation, and Ekman Transport is a component of wind-driven ocean current.. Ekman transport occurs when ocean surface waters are influenced by the friction force acting on them via the wind. As the wind blows it casts a friction force on the ocean surface that drags the upper 10-100m of the water column with it.. However, due to the influence of the Coriolis effect, the ocean water moves at a 90° angle from the direction of the surface wind.. The direction of transport is dependent on the hemisphere: in the northern hemisphere, transport occurs at 90° clockwise from wind direction, while in the southern hemisphere it occurs at a 90° counterclockwise.. This phenomenon was first noted by Fridtjof Nansen, who recorded that ice transport appeared to occur at an angle to the wind direction during his Arctic expedition during the 1890s.. Ekman transport has significant impacts on the biogeochemical properties of the world’s oceans. This is because they lead to upwelling (Ekman suction), downwelling (Ekman pumping) in order to obey mass conservation laws. Mass conservation, in reference to Ekman transfer, requires that any water displaced within an area must be replenished, this can be done by either Ekman suction or Ekman pumping depending on wind patterns..

Geophysical fluid dynamics

Geophysical fluid dynamics, in its broadest meaning, refers to the fluid dynamics of naturally occurring flows, such as lava flows, oceans, and planetary atmospheres, on Earth and other planets.Two physical features that are common to many of the phenomena studied in geophysical fluid dynamics are rotation of the fluid due to the planetary rotation and stratification (layering). The applications of geophysical fluid dynamics do not generally include the circulation of the mantle, which is the subject of geodynamics, or fluid phenomena in the magnetosphere.

Harald Sverdrup (oceanographer)

Harald Ulrik Sverdrup (15 November 1888 – 21 August 1957) was a Norwegian oceanographer and meteorologist.

He was director of Scripps Institution of Oceanography and director of the Norwegian Polar Institute.

List of submarine volcanoes

A list of active and extinct submarine volcanoes and seamounts located under the world's oceans. There are estimated to be 40,000 to 55,000 seamounts in the global oceans. Almost all are not well-mapped and many may not have been identified at all. Most are unnamed and unexplored. This list is therefore confined to seamounts that are notable enough to have been named and/or explored.

Oceanic plateau

An oceanic or submarine plateau is a large, relatively flat elevation that is higher than the surrounding relief with one or more relatively steep sides.There are 184 oceanic plateaus covering an area of 18,486,600 km2 (7,137,700 sq mi), or about 5.11% of the oceans. The South Pacific region around Australia and New Zealand contains the greatest number of oceanic plateaus (see map).

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Plateaus formed by large igneous provinces were formed by the equivalent of continental flood basalts such as the Deccan Traps in India and the Snake River Plain in the United States.

In contrast to continental flood basalts, most igneous oceanic plateaus erupt through young and thin (6–7 km (3.7–4.3 mi)) mafic or ultra-mafic crust and are therefore uncontaminated by felsic crust and representative for their mantle sources.

These plateaus often rise 2–3 km (1.2–1.9 mi) above the surrounding ocean floor and are more buoyant than oceanic crust. They therefore tend to withstand subduction, more-so when thick and when reaching subduction zones shortly after their formations. As a consequence, they tend to "dock" to continental margins and be preserved as accreted terranes. Such terranes are often better preserved than the exposed parts of continental flood basalts and are therefore a better record of large-scale volcanic eruptions throughout Earth's history. This "docking" also means that oceanic plateaus are important contributors to the growth of continental crust. Their formations often had a dramatic impact on global climate, such as the most recent plateaus formed, the three, large, Cretaceous oceanic plateaus in the Pacific and Indian Ocean: Ontong Java, Kerguelen, and Caribbean.

Outline of oceanography

The following outline is provided as an overview of and introduction to Oceanography.

Physical oceanography

Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters.

Physical oceanography is one of several sub-domains into which oceanography is divided. Others include biological, chemical and geological oceanography.

Physical oceanography may be subdivided into descriptive and dynamical physical oceanography.Descriptive physical oceanography seeks to research the ocean through observations and complex numerical models, which describe the fluid motions as precisely as possible.

Dynamical physical oceanography focuses primarily upon the processes that govern the motion of fluids with emphasis upon theoretical research and numerical models. These are part of the large field of Geophysical Fluid Dynamics (GFD) that is shared together with meteorology. GFD is a sub field of Fluid dynamics describing flows occurring on spatial and temporal scales that are greatly influenced by the Coriolis force.

Undersea mountain range

Undersea mountain ranges are mountain ranges that are mostly or entirely underwater, and specifically under the surface of an ocean. If originated from current tectonic forces, they are often referred to as a mid-ocean ridge. In contrast, if formed by past above-water volcanism, they are known as a seamount chain. The largest and best known undersea mountain range is a mid-ocean ridge, the Mid-Atlantic Ridge. It has been observed that, "similar to those on land, the undersea mountain ranges are the loci of frequent volcanic and earthquake activity".

Wave base

The wave base, in physical oceanography, is the maximum depth at which a water wave's passage causes significant water motion. For water depths deeper than the wave base, bottom sediments and the seafloor are no longer stirred by the wave motion above.

Ocean zones
Sea level


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