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The '''geostrophic wind''' ({{IPAc-en|icon|dʒ|iː|ɵ|ˈ|s|t|r|ɒ|f|ɨ|k}} or {{IPAc-en|dʒ|iː|ɵ|ˈ|s|t|r|oʊ|f|ɨ|k}}) is the [[theoretical]] [[wind]] that would result from an exact balance between the [[Coriolis effect]] and the [[pressure gradient]] force.  This condition is called ''geostrophic balance.'' The geostrophic wind is directed [[Parallel (geometry)|parallel]] to [[isobar (meteorology)|isobar]]s (lines of constant [[Atmospheric pressure|pressure]] at a given height). This balance seldom holds exactly in nature.  The true wind almost always differs from the geostrophic wind due to other forces  such as [[friction]] from the ground. Thus, the actual wind would equal the geostrophic wind only if there were no friction and the isobars were perfectly straight. Despite this, much of the atmosphere outside the [[tropics]] is close to geostrophic flow much of the time and it is a valuable first approximation. Geostrophic flow in air or water is a zero-frequency [[inertial waves|inertial wave]].
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[[Air]] naturally moves from areas of high [[pressure]] to areas of low pressure, due to the [[pressure gradient]] force.  As soon as the air starts to move, however, the [[Coriolis effect|Coriolis "force"]] deflects it.  The {{wict|deflection}} is to the right in the [[northern hemisphere]], and to the left in the [[southern hemisphere]].  As the air moves from the high pressure area, its speed increases, and so does its Coriolis deflection.  The deflection increases until the Coriolis and pressure gradient forces are in geostrophic balance: at this point, the air flow is no longer moving from high to low pressure, but instead moves along an {{wict|isobar}}. (Note that this explanation assumes that the atmosphere starts in a geostrophically unbalanced state and describes how such a state would evolve into a balanced flow. In practice, the flow is nearly always balanced.) The geostrophic balance helps to explain why, in the northern hemisphere, [[low pressure system]]s (or ''[[cyclone]]s'') spin counterclockwise and [[High pressure area|high pressure systems]] (or ''[[anticyclone]]s'') spin clockwise, and the opposite in the southern hemisphere.
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==Geostrophic currents==
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


Flow of ocean water is also largely geostrophic. Just as multiple weather balloons that measure pressure as a function of height in the atmosphere are used to map the atmospheric pressure field and infer the geostrophic wind, measurements of density as a function of depth in the ocean are used to infer geostrophic currents.  [[satellite altimetry|Satellite altimeters]] are also used to measure sea surface height anomaly, which permits a calculation of the geostrophic current at the surface.
<!--'''PNG''' (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


==Limitations of the Geostrophic approximation==
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


The effect of friction, between the air and the land, breaks the geostrophic balance. Friction slows the flow, lessening the effect of the Coriolis force. As a result, the pressure gradient force has a greater effect and the air still moves from high pressure to low pressure, though with great deflection. This explains why high pressure system winds radiate out from the center of the system, while low pressure systems have winds that spiral inwards.
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The geostrophic wind neglects [[friction]]al effects, which is usually a good [[approximation]] for the [[synoptic scale meteorology|synoptic scale]] instantaneous flow in the midlatitude mid-[[troposphere]].<ref>Holton, J.R., 'An Introduction to Dynamic Meteorology', International Geophysical Series, Vol 48 Academic Press.</ref> Although [[ageostrophic]] terms are relatively small, they are essential for the time evolution of the flow and in particular are necessary for the growth and decay of storms. Quasigeostrophic and Semigeostrophic theory are used to model flows in the atmosphere more widely. These theories allow for divergence to take place and for weather systems to then develop.
==Demos==


==Governing formula==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
Newton's Second law can be written as follows if only the pressure gradient, gravity, and friction act on an air parcel, where the bold symbolizes a vector.


<math>{D\boldsymbol{U} \over Dt} = -2\boldsymbol{\Omega} \times \boldsymbol{U} - {1 \over \rho} \nabla p + \boldsymbol{g} + \boldsymbol{F}_r</math>


Where F<sub>r</sub> is the friction and ''g'' is the [[standard gravity|acceleration due to gravity]] (9.81 m.s<sup>−2</sup>).
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Locally this can be expanded in cartesian coordinates, with a positive u representing an eastward direction and a positive v representing a northward direction. Neglecting friction and vertical motion, we have:
==Test pages ==


<math>{Du \over Dt} = -{1 \over \rho}{\partial P \over \partial x} + f \cdot v</math>
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<math>{Dv \over Dt} = -{1 \over \rho}{\partial P \over \partial y} - f \cdot u</math>
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
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<math> 0 = -g -{1 \over \rho}{\partial P \over \partial z}</math>
==Bug reporting==
 
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With <math>f = 2 \Omega \sin{\phi}</math> the [[Coriolis effect|Coriolis parameter]] (approximately 10<sup>&minus;4</sup> s<sup>&minus;1</sup>, varying with latitude).
 
Assuming geostrophic balance, the system is stationary and the first two equations become:
 
<math>f \cdot v = {1 \over \rho}{\partial P \over \partial x}</math>
 
<math>f \cdot u =  -{1 \over \rho}{\partial P \over \partial y}</math>
 
By substituting using the third equation above, we have:
 
<math>f \cdot v = g\frac{\partial P / \partial x}{\partial P / \partial z} = g{\partial Z \over \partial x}</math>
 
<math>f \cdot u = -g\frac{\partial P / \partial y}{\partial P / \partial z} = -g{\partial Z \over \partial y}</math>
 
with ''Z'' the height of the constant pressure surface (satisfying <math>{\partial P \over \partial x}dx + {\partial P \over \partial y}dy + {\partial P \over \partial z} dZ = 0 </math>).
 
This leads us to the following result for the geostrophic wind components <math>(u_g,v_g)</math>:
 
: <math> u_g = - {g \over f}  {\partial Z \over \partial y}</math>
 
<!-- extra blank line between two lines of "displayed" [[TeX]], for legiblity -->
 
: <math> v_g = {g \over f}  {\partial Z \over \partial x}</math>
 
The validity of this approximation depends on the local [[Rossby number]]. It is invalid at the equator, because ''f'' is equal to zero there, and therefore generally not used in the [[tropics]].
 
Other variants of the equation are possible; for example, the geostrophic wind vector can be expressed in terms of the gradient of the [[geopotential height]] Φ on a surface of constant pressure:
 
: <math> \overrightarrow{V_g} = {\hat{k} \over f} \times \nabla_p \Phi </math>
 
== See also ==
*[[Geostrophic current]]
*[[Thermal wind]]
*[[Gradient wind]]
*[[Prevailing winds]]
 
==References==
{{Reflist}}
 
== External links ==
* [http://atmos.nmsu.edu/education_and_outreach/encyclopedia/geostrophic.htm  Geostrophic approximation]
* [http://nsidc.org/arcticmet/glossary/geostrophic_winds.html Definition of geostrophic wind]
*[http://atmo.tamu.edu/class/atmo203/tut/windpres/wind8.html Geostrophic wind description]
 
{{DEFAULTSORT:Geostrophic Wind}}
[[Category:Geophysics]]
[[Category:Fluid dynamics]]
[[Category:Atmospheric dynamics]]
 
[[ar:رياح جيوستروفيك]]
[[ca:Equilibri geostròfic]]
[[de:Geostrophischer Wind]]
[[es:Viento geostrófico]]
[[fr:Vent géostrophique]]
[[it:Vento geostrofico]]
[[nl:Geostrofische wind]]
[[ja:地衡風]]
[[no:Geostrofisk vind]]
[[nn:Geostrofisk vind]]
[[pl:Wiatr geostroficzny]]
[[pt:Vento geostrófico]]
[[ru:Геострофический ветер]]
[[fi:Geostrofinen tuuli]]
[[sv:Geostrofisk vind]]
[[uk:Геострофічний вітер]]
[[zh:地轉風]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

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