Ageostrophic current is anoceanic current in which thepressure gradient force is balanced by theCoriolis effect. The direction of geostrophic flow is parallel to theisobars, with the high pressure to the right of the flow in theNorthern Hemisphere, and the high pressure to the left in theSouthern Hemisphere. The concept is familiar fromweather maps, whose isobars show the direction ofgeostrophic winds. Geostrophic flows may bebarotropic orbaroclinic. A geostrophic current may also be thought of as a rotating shallow water wave with a frequency of zero.

The principle ofgeostrophy orgeostrophic balance is useful to oceanographers because it allows them to inferocean currents from measurements of thesea surface height (by combinedsatellite altimetry andgravimetry) or from vertical profiles ofseawater density taken by ships or autonomous buoys. The major currents of the world'soceans including theGulf Stream, theKuroshio Current, theAgulhas Current, and theAntarctic Circumpolar Current, are approximately in geostrophic balance and examples of geostrophic currents.

Seawater naturally tends 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). That occurs because theEarth rotates. The rotation of the earth results in a "force" being felt by the water moving from the high to the low, known as aCoriolis 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 mentioned, the direction of flow is with the high pressure to the right of the flow in theNorthern Hemisphere, and the high pressure to the left in theSouthern Hemisphere. The direction of the flow depends on the hemisphere, because the direction of the Coriolis force is opposite in the different hemispheres.

The geostrophic equations are a simplified form of theNavier–Stokes equations in a rotating reference frame. In particular, it is assumed that there is no acceleration (steady-state), no viscosity, and that the pressure ishydrostatic. The resulting balance is (Gill, 1982):

${\displaystyle fv=\frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }x}}$

${\displaystyle fu=-\frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }y}}$

where${\displaystyle f}$ is theCoriolis parameter,${\displaystyle \rho }$ is the density,${\displaystyle p}$ is the pressure and${\displaystyle u,v}$ are the velocities in the${\displaystyle x,y}$-directions respectively.

One special property of the geostrophic equations, is that they satisfy theincompressible version of the continuity equation. That is:$${\displaystyle \mathrm{\nabla }\cdot \mathbf{u}=0}$$

${\displaystyle \frac{\mathrm{\partial }u}{\mathrm{\partial }x}+\frac{\mathrm{\partial }v}{\mathrm{\partial }y}=0}$

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

${\displaystyle \frac{\mathrm{\partial }u}{\mathrm{\partial }t}-fv=-\frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }x}}$

${\displaystyle \frac{\mathrm{\partial }v}{\mathrm{\partial }t}+fu=-\frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }y}}$

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

${\displaystyle \frac{\mathrm{\partial }u}{\mathrm{\partial }t}=\frac{\mathrm{\partial }v}{\mathrm{\partial }t}=0}$

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

${\displaystyle u\propto v\propto e^{i\omega t}}$

In this case, if we set${\displaystyle \omega =0}$, 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.

• Geostrophic wind

• Gill, Adrian E. (1982),Atmosphere-Ocean Dynamics, International Geophysics Series, vol. 30, Oxford: Academic Press,ISBN 0-12-283522-0

• Ocean currents

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• Short description matches Wikidata