A geostrophic current is an oceanic flow in which the pressure gradient
Pressure gradient
In atmospheric sciences , the pressure gradient is a physical quantity that describes in which direction and at what rate the pressure changes the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pressure per unit length...

 force is balanced by the Coriolis
Coriolis may refer to:* Gaspard-Gustave Coriolis , French mathematician, mechanical engineer and scientist* Coriolis effect, the apparent deflection of moving objects from a straight path when viewed from a rotating frame of reference...

 force. The direction of geostrophic flow is parallel to the isobars, with the high pressure to the right of the flow in the Northern Hemisphere
Northern Hemisphere
The Northern Hemisphere is the half of a planet that is north of its equator—the word hemisphere literally means “half sphere”. It is also that half of the celestial sphere north of the celestial equator...

, and the high pressure to the left in the Southern Hemisphere
Southern Hemisphere
The Southern Hemisphere is the part of Earth that lies south of the equator. The word hemisphere literally means 'half ball' or "half sphere"...

. This concept is familiar from weather maps, whose isobars show the direction of geostrophic flow in the atmosphere. Geostrophic flow may be either barotropic
In meteorology, a barotropic atmosphere is one in which the pressure depends only on the density and vice versa, so that isobaric surfaces are also isopycnic surfaces . The isobaric surfaces will also be isothermal surfaces, hence the geostrophic wind is independent of height...

 or baroclinic. A geostrophic current may also be thought of as a rotating shallow water wave with a frequency of zero. The principal of geostrophy is useful to oceanographers because it allows them to infer ocean current
Ocean current
An ocean current is a continuous, directed movement of ocean water generated by the forces acting upon this mean flow, such as breaking waves, wind, Coriolis effect, cabbeling, temperature and salinity differences and tides caused by the gravitational pull of the Moon and the Sun...

s from measurements of the sea surface height (by satellite altimeters) or from vertical profiles of seawater density taken by ships or autonomous buoys. The major currents of the world's ocean
An ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas.More than half of this area is over 3,000...

s, such as the Gulf Stream
Gulf Stream
The Gulf Stream, together with its northern extension towards Europe, the North Atlantic Drift, is a powerful, warm, and swift Atlantic ocean current that originates at the tip of Florida, and follows the eastern coastlines of the United States and Newfoundland before crossing the Atlantic Ocean...

, the Kuroshio Current
Kuroshio Current
The Kuroshio 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...

, the Agulhas Current
Agulhas Current
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...

, and the Antarctic Circumpolar Current
Antarctic Circumpolar Current
The Antarctic Circumpolar Current is an ocean current that flows from west to east around Antarctica. An alternative name for the ACC is the West Wind Drift. The ACC is the dominant circulation feature of the Southern Ocean and, at approximately 125 Sverdrups, the largest ocean current...

, are all approximately in geostrophic balance and are examples of geostrophic currents.

Simple explanation

Sea water naturally wants to move from a region of high pressure (or high sea level) to a region of low pressure (or low sea level). The force pushing the water towards the low pressure region is called the pressure gradient force. In a geostrophic flow, instead of water moving from a region of high pressure (or high sea level) to a region of low pressure (or low sea level), it moves along the lines of equal pressure (isobars). This occurs because the earth is rotating. The rotation of the earth results in a "force" being felt by the water moving from the high to the low, known as Coriolis force. The Coriolis force acts at right angles to the flow, and when it balances the pressure gradient force, the resulting flow is known as geostrophic.

As stated above, the direction of flow is with the high pressure to the right of the flow in the Northern Hemisphere, and the high pressure to the left in the Southern Hemisphere. The direction of the flow depends on the hemisphere, because the direction of the Coriolis force is opposite in the different hemispheres.

Geostrophic Equations

The geostrophic equations are a simplified form of the Navier Stokes equations. In particular, it is assumed that there is no acceleration (steady-state), that there is no viscosity, and that the pressure is hydrostatic. The resulting balance is (Gill, 1982):

One special property of the geostrophic equations, is that they satisfy the steady-state version of the continuity equation. That is:

Rotating Waves of zero frequency

The equations governing a linear, rotating shallow water wave are:

The assumption of steady-state made above (no acceleration) is:

Alternatively, we can assume a wave-like, periodic, dependence in time:

In this case, if we set , we have reverted to the geostrophic equations above. Thus a geostrophic current
can be thought of as a rotating shallow water wave with a frequency of zero.
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