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| [[File:Geostrophic current.pdf|right|400px|An example of a geostrophic flow in the Northern Hemisphere.]]
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| A '''geostrophic current''' is an oceanic flow in which the [[pressure gradient]] force is balanced by the [[Coriolis effect]]. The direction of geostrophic flow is parallel to the [[isobar (meteorology)|isobars]], 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]]. This concept is familiar from weather maps, whose isobars show the direction of geostrophic flow in the atmosphere. Geostrophic flow may be either [[barotropic]] or [[baroclinic]]. A geostrophic current may also be thought of as a rotating shallow water wave with a frequency of zero. The principle of geostrophy is useful to oceanographers because it allows them to infer [[ocean current]]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]]s, such as the [[Gulf Stream]], the [[Kuroshio Current]], the [[Agulhas Current]], and the [[Antarctic Circumpolar Current]], are all approximately in geostrophic balance and are examples of geostrophic currents.
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| == Simple explanation ==
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| [[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 ([[Contour line#Barometric 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.
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| 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.
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| == Geostrophic equations ==
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| 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):
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| :<math> fv = \frac{1}{\rho} \frac{\partial p}{\partial x}</math> | |
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| :<math> fu = -\frac{1}{\rho} \frac{\partial p}{\partial y}</math>
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| One special property of the geostrophic equations, is that they satisfy the steady-state version of the continuity equation. That is:
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| :<math> \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0 </math>
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| === Rotating waves of zero frequency ===
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| The equations governing a linear, rotating shallow water wave are:
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| :<math> \frac{\partial u}{\partial t} - fv = -\frac{1}{\rho} \frac{\partial p}{\partial x}</math>
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| :<math> \frac{\partial v}{\partial t} + fu = -\frac{1}{\rho} \frac{\partial p}{\partial y}</math>
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| The assumption of steady-state made above (no acceleration) is:
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| :<math> \frac{\partial u}{\partial t} = \frac{\partial v}{\partial t} =0 </math>
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| Alternatively, we can assume a wave-like, periodic, dependence in time:
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| :<math> u \propto v \propto e^{i \omega t} </math>
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| In this case, if we set <math> \omega = 0 </math>, we have reverted to the geostrophic equations above. Thus a geostrophic current
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| can be thought of as a rotating shallow water wave with a frequency of zero.
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| ==See also==
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| *[[geostrophic wind]]
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| ==References==
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| *{{citation |title=Atmosphere-Ocean Dynamics |series=International Geophysics Series |volume=30 |first=Adrian E. |last=Gill | year=1982 |publisher=Academic Press |location=Oxford |isbn=0-12-283522-0 }}
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| {{physical oceanography}}
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| [[Category:Geology]]
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| [[fr:Vent géostrophique#Équilibre géostrophique]]
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