# Boundary current

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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.

An ocean current is a continuous, directed movement of sea water generated by a number of forces acting upon the water, including wind, the Coriolis effect, breaking waves, cabbeling, and temperature and salinity differences. Depth contours, shoreline configurations, and interactions with other currents influence a current's direction and strength. Ocean currents are primarily horizontal water movements.

The coast, also known as the coastline or seashore, is the area where land meets the sea or ocean, or a line that forms the boundary between the land and the ocean or a lake. A precise line that can be called a coastline cannot be determined due to the coastline paradox.

## Eastern boundary currents

Eastern boundary currents are relatively shallow, broad and slow-flowing. They are found on the eastern side of oceanic basins (adjacent to the western coasts of continents). Subtropical eastern boundary currents flow equatorward, transporting cold water from higher latitudes to lower latitudes; examples include the Benguela Current, the Canary Current, the Humboldt Current, and the California Current. Coastal upwelling often brings nutrient-rich water into eastern boundary current regions, making them productive areas of the ocean.

In hydrology, an oceanic basin may be anywhere on Earth that is covered by seawater but geologically ocean basins are large geologic basins that are below sea level. Geologically, there are other undersea geomorphological features such as the continental shelves, the deep ocean trenches, and the undersea mountain ranges which are not considered to be part of the ocean basins; while hydrologically, oceanic basins include the flanking continental shelves and shallow, epeiric seas.

The Benguela Current is the broad, northward flowing ocean current that forms the eastern portion of the South Atlantic Ocean gyre. The current extends from roughly Cape Point in the south, to the position of the Angola-Benguela front in the north, at around 16°S. The current is driven by the prevailing south easterly trade winds. Inshore of the Benguela Current proper, the south easterly winds drive coastal upwelling, forming the Benguela Upwelling System. The cold, nutrient rich waters that upwell from around 200–300 m depth in turn fuel high rates of phytoplankton growth, and sustain the productive Benguela ecosystem.

The Canary Current is a wind-driven surface current that is part of the North Atlantic Gyre. This eastern boundary current branches south from the North Atlantic Current and flows southwest about as far as Senegal where it turns west and later joins the Atlantic North Equatorial Current. The current is named after the Canary Islands. The archipelago partially blocks the flow of the Canary Current.

## Western boundary currents

Western boundary currents are warm, deep, narrow, and fast flowing currents that form on the west side of ocean basins due to western intensification. They carry warm water from the tropics poleward. Examples include the Gulf Stream, the Agulhas Current, and the Kuroshio.

The Gulf Stream, together with its northern extension the North Atlantic Drift, is a warm and swift Atlantic ocean current that originates in the Gulf of Mexico and stretches to the tip of Florida, and follows the eastern coastlines of the United States and Newfoundland before crossing the Atlantic Ocean. The process of western intensification causes the Gulf Stream to be a northward accelerating current off the east coast of North America. At about 40°0′N30°0′W, it splits in two, with the northern stream, the North Atlantic Drift, crossing to Northern Europe and the southern stream, the Canary Current, recirculating off West Africa.

The Agulhas Current is the western boundary current of the southwest Indian Ocean. It flows down the east coast of Africa from 27°S to 40°S. It is narrow, swift and strong. It is suggested that it is the largest western boundary current in the world ocean, with an estimated net transport of 70 Sverdrups, as western boundary currents at comparable latitudes transport less — Brazil Current, Gulf Stream, Kuroshio.

The Kuroshio (黒潮), also known as the Black or Japan Current or the Black Stream, is a north-flowing ocean current on the west side of the North Pacific Ocean. It is similar to the Gulf Stream in the North Atlantic and is part of the North Pacific ocean gyre. Like the Gulf stream, it is a strong western boundary current.

### Western intensification

Western intensification is the intensification of the western arm of an oceanic current, particularly a large gyre in an ocean basin. The trade winds blow westward in the tropics, and the westerlies blow eastward at mid-latitudes. This wind pattern applies a stress to the subtropical ocean surface with negative curl in the northern hemisphere and a positive curl in the southern hemisphere. The resulting Sverdrup transport is equatorward in both cases. Because of conservation of mass and potential vorticity conservation, that transport is balanced by a narrow, intense poleward current, which flows along the western boundary of the ocean basin, allowing the vorticity introduced by coastal friction to balance the vorticity input of the wind. Western intensification also occurs in the polar gyres, where the sign of the wind stress curl and the direction of the resulting currents are reversed. It is because of western intensification that the currents on the western boundary of a basin (such as the Gulf Stream, a current on the western side of the Atlantic Ocean) are stronger than those on the eastern boundary (such as the California Current, on the eastern side of the Pacific Ocean). Western intensification was first explained by the American oceanographer Henry Stommel.

The trade winds are the permanent east-to-west prevailing winds that flow in the Earth's equatorial region. They are also called easterlies. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Trade winds have been used by captains of sailing ships to cross the world's oceans for centuries and enabled colonial expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans.

The westerlies, anti-trades, or prevailing westerlies, are prevailing winds from the west toward the east in the middle latitudes between 30 and 60 degrees latitude. They originate from the high-pressure areas in the horse latitudes and trend towards the poles and steer extratropical cyclones in this general manner. Tropical cyclones which cross the subtropical ridge axis into the westerlies recurve due to the increased westerly flow. The winds are predominantly from the southwest in the Northern Hemisphere and from the northwest in the Southern Hemisphere.

In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space. At every point in the field, the curl of that point is represented by a vector. The attributes of this vector characterize the rotation at that point.

In 1948, Henry Stommel published a paper in Transactions, American Geophysical Union titled "The Westward Intensification of Wind-Driven Ocean Currents", [1] in which he used a simple, homogeneous, rectangular ocean model to examine the streamlines and surface height contours for an ocean at a non-rotating frame, an ocean characterized by a constant Coriolis parameter and finally, a real-case ocean basin with a latitudinally-varying Coriolis parameter. In this simple, modeling setting, the principal factors that were accounted for influencing the oceanic circulation were surface wind stress, bottom friction, a variable surface height leading to horizontal pressure gradients, and finally, the Coriolis effect.

In his simplified model, [2] he assumed an ocean of constant density and depth ${\displaystyle D+h}$ in the presence of ocean currents; he also introduced a linearized, frictional term to account for the dissipative effects that prevent the real ocean from accelerating. He starts, thus, from the steady-state momentum and continuity equations:

${\displaystyle f(D+h)v-F\cos \left({\frac {\pi y}{b}}\right)-Ru-g(D+h){\frac {\partial h}{\partial x}}=0\qquad (1)}$

${\displaystyle \quad -f(D+h)u-Rv-g(D+h){\frac {\partial h}{\partial y}}=0\qquad \qquad (2)}$

${\displaystyle \qquad \qquad {\frac {\partial [(D+h)u]}{\partial x}}+{\frac {\partial [(D+h)v]}{\partial y}}=0\qquad \qquad \qquad (3)}$

Here ${\displaystyle f}$ is the strength of the Coriolis force, ${\displaystyle R}$ is the bottom-friction coeffecient, ${\displaystyle g\,\,}$ is gravity, and ${\displaystyle -F\cos \left({\frac {\pi y}{b}}\right)}$ is the wind forcing. The wind is blowing towards the west at ${\displaystyle y=0}$ and towards the east at ${\displaystyle y=b}$.

Acting on (1) with ${\displaystyle {\frac {\partial }{\partial y}}}$ and on (2) with ${\displaystyle {\frac {\partial }{\partial x}}}$, subtracting, and then using (3), gives

${\displaystyle v(D+h)\left({\frac {\partial f}{\partial y}}\right)+{\frac {\pi F}{b}}\sin \left({\frac {\pi y}{b}}\right)+R\left({\frac {\partial v}{\partial x}}-{\frac {\partial u}{\partial y}}\right)=0\quad (4)}$

If we introduce a Stream function ${\displaystyle \psi }$ and linearize by assuming that ${\displaystyle D>>h}$, equation (4) reduces to

${\displaystyle \nabla ^{2}\psi +\alpha \left({\frac {\partial \psi }{\partial x}}\right)=\gamma \sin \left({\frac {\pi y}{b}}\right)\qquad (5)}$

Here

${\displaystyle \alpha =\left({\frac {D}{R}}\right)\left({\frac {\partial f}{\partial y}}\right)}$

and

${\displaystyle \gamma ={\frac {\pi F}{Rb}}}$

The solutions of (5) with boundary condition that ${\displaystyle \psi }$ be constant on the coastlines, and for different values of ${\displaystyle \alpha }$, emphasize the role of the variation of the Coriolis parameter with latitude in inciting the strengthening of western boundary currents. Such currents are observed to be much faster, deeper, narrower and warmer than their eastern counterparts.

For a non-rotating state (zero Coriolis parameter) as well as an ocean state at which the Coriolis parameter is a constant, the ocean circulation does not demonstrate any preference toward intensification/acceleration near the western boundary. The streamlines exhibit a symmetric behavior in all directions, with the height contours demonstrating a nearly parallel relation to the streamlines, in the case of the homogeneously rotating ocean. Finally, for the case of interest - the one in which the Coriolis force is latitudinally variant - a distinct tendency for an asymmetrical streamline diagram is noted, with an observed, intense clustering toward the western part of the modeled ocean. A nice set of figures depicting the distribution of streamlines and height contours for the cases of a uniformly-rotating ocean and an ocean where the Coriolis force is linearly dependent on latitude can be found in Stommel's 1948 paper.

### Sverdrup Balance and Physics of Western Intensification

The physics of western intensification can be understood through a mechanism that helps maintain the vortex balance along an ocean gyre. Harald Sverdrup was the first one, preceding Henry Stommel, to attempt to explain the mid-ocean vorticity balance by looking at the relationship between surface wind forcings and the mass transport within the upper ocean layer. He assumed a geostrophic interior flow, while neglecting any frictional or viscosity effects and presuming that the circulation vanishes at some depth in the ocean. This prohibited the application of his theory to the western boundary currents, since some form of dissipative effect (bottom Ekman layer) would be later shown to be necessary to predict a closed circulation for an entire ocean basin and to counteract the wind-driven flow.

Sverdrup introduced a potential vorticity argument to connect the net, interior flow of the oceans to the surface wind stress and the incited planetary vorticity perturbations. For instance, Ekman convergence in the sub-tropics (related to the existence of the trade winds in the tropics and the westerlies in the mid-latitudes) was suggested to lead to a downward vertical velocity and therefore, a squashing of the water columns, which subsequently forces the ocean gyre to spin more slowly (via angular momentum conservation). This is accomplished via a decrease in planetary vorticity (since relative vorticity variations are not significant in large ocean circulations), a phenomenon attainable through an equator-wardly[ check spelling ] directed, interior flow that characterizes the subtropical gyre. [3] The opposite is applicable when Ekman divergence is induced, leading to Ekman absorption (suction) and a subsequent, water column stretching and poleward return flow, a characteristic of sub-polar gyres.

This return flow, as shown by Stommel, [1] occurs in a meridional current, concentrated near the western boundary of an ocean basin. To balance the vorticity source induced by the wind stress forcing, Stommel introduced a linear frictional term in the Sverdrup equation, functioning as the vorticity sink. This bottom ocean, frictional drag on the horizontal flow allowed Stommel to theoretically predict a closed, basin-wide circulation, while demonstrating the west-ward intensification of wind-driven gyres and its attribution to the Coriolis variation with latitude (beta effect). Walter Munk (1950) further implemented Stommel's theory of western intensification by using a more realistic frictional term, while emphasizing "the lateral dissipation of eddy energy." [4] In this way, not only did he reproduce Stommel's results, recreating thus the circulation of a western boundary current of an ocean gyre resembling the Gulf stream, but he also showed that sub-polar gyres should develop northward of the subtropical ones, spinning in the opposite direction.

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In continuum mechanics, the vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point, as would be seen by an observer located at that point and traveling along with the flow.

Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Carl-Gustaf Arvid Rossby. They are observed in the atmospheres and oceans of planets owing to the rotation of planet. Atmospheric Rossby waves on Earth are giant meanders in high-altitude winds that have a major influence on weather. These waves are associated with pressure systems and the jet stream. Oceanic Rossby waves move along the thermocline: the boundary between the warm upper layer and the cold deeper part of the ocean.

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In oceanography, a gyre is any large system of circulating ocean currents, particularly those involved with large wind movements. Gyres are caused by the Coriolis effect; planetary vorticity along with horizontal and vertical friction, determine the circulation patterns from the wind stress curl (torque).

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The Equatorial Counter Current is an eastward flowing, wind-driven current which extends to depths of 100-150m in the Atlantic, Indian, and Pacific Oceans. More often called the North Equatorial Countercurrent (NECC), this current flows west-to-east at about 3-10°N in the Atlantic, Indian Ocean and Pacific basins, between the North Equatorial Current (NEC) and the South Equatorial Current (SEC). The NECC is not to be confused with the Equatorial Undercurrent (EUC) that flows eastward along the equator at depths around 200m in the western Pacific rising to 100m in the eastern Pacific.

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## References

• Thurman, Harold V., Trujillo, Alan P. Introductory Oceanography Tenth Edition. ISBN   0-13-143888-3
• AMS glossary
• Professor Raphael Kudela, UCSC, lectures OCEA1 Fall 2007
• H. Stommel, The Westward Intensification of Wind-Driven Ocean Currents, Transactions American Geophysical Union: Vol. 29, 1948
• Munk, W. H., On the wind-driven ocean circulation, J. Meteorol., Vol. 7,1950
• Stewart, R. "11". Wind Driven Ocean Circulation. ocianworld.tamu.edu. Archived from the original on 2011-11-21. Retrieved 2011-12-08.
• John H. Steele; et al. Ocean Currents: A Derivative of the Encyclopedia of Ocean Sciences.
• Sverdrup, Harald (1947). "Wind-Driven Currents in a Baroclinic Ocean; with Application to the Equatorial Currents of the Eastern Pacific". Proceedings of the National Academy of Sciences of the United States of America. JSTOR   87657.Missing or empty |url= (help)

## Footnotes

1. Stommel, Henry (April 1948). "The Westward Intensification of Wind-Driven Ocean Currents" (PDF). Transactions, American Geophysical Union. 29 (2): 202–206. doi:10.1029/tr029i002p00202 . Retrieved 27 August 2012.
2. H. Stommel, The Westward Intensification of Wind-Driven Ocean Currents, Transactions American Geophysical Union: Vol. 29, 1948
3. Lynne D Talley; et al. Descriptive Physical Oceanography.
4. Berger, Wolfgang H.; Noble Shor, Elizabeth. Ocean: reflections on a century of exploration.