# Geostrophic wind > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Geostrophic_wind > Markdown URL: https://mediated.wiki/source/Geostrophic_wind.md > Source: https://en.wikipedia.org/wiki/Geostrophic_wind > Source revision: 1348566470 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Concept in atmospheric science}} {{Redirect|Geostrophic flow|oceanic wind|Geostrophic current}} {{More citations needed|dare=August 2018|date=August 2018}} In [atmospheric science](/source/atmospheric_science), '''geostrophic flow''' ({{IPAc-en|ˌ|dʒ|iː|ə|ˈ|s|t|r|ɒ|f|ɪ|k|,_|ˌ|dʒ|iː|oʊ|-|,_|-|ˈ|s|t|r|oʊ|-}}{{refn|{{Dictionary.com|access-date=2016-01-22|geostrophic}}}}{{refn|{{Cite dictionary |url=http://www.lexico.com/definition/geostrophic |archive-url=https://web.archive.org/web/20211223131345/https://www.lexico.com/definition/geostrophic |url-status=dead |archive-date=2021-12-23 |title=geostrophic |dictionary=[Lexico](/source/Lexico) UK English Dictionary |publisher=[Oxford University Press](/source/Oxford_University_Press)}} }}{{refn|{{MerriamWebsterDictionary|access-date=2016-01-22|geostrophic}}}}) is the theoretical [wind](/source/wind) that would result from an exact balance between the [Coriolis force](/source/Coriolis_effect) and the [pressure gradient](/source/pressure_gradient) force. This condition is called ''[geostrophic equilibrium](/source/geostrophic_equilibrium)'' or ''geostrophic balance'' (also known as ''geostrophy''). The geostrophic wind is directed [parallel](/source/Parallel_(geometry)) to [isobar](/source/isobar_(meteorology))s (lines of constant [pressure](/source/Atmospheric_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](/source/friction) from the ground. Thus, the actual wind would equal the geostrophic wind only if there were no friction (e.g. above the [atmospheric boundary layer](/source/atmospheric_boundary_layer)) and the isobars were perfectly straight. The geostrophic wind merely reflects the horizontal pressure gradient as the driving force of atmospheric motion, while the actual near-surface wind requires the synergistic modulation of multiple factors including the frictional force, vertical atmospheric stratification and thermal wind. As a result, the ratio between actual wind speed and geostrophic wind speed, and the wind direction angle difference between the actual wind and the geostrophic wind vary significantly with environmental conditions.{{Cite journal |last=Brümmer |first=Burghard |date=2023-09-11 |title=Actual versus geostrophic wind: statistics from 12‑year measurements at the 280 m high Hamburg Weather Mast |url=https://www.schweizerbart.de/papers/metz/detail/32/102606/Actual_versus_geostrophic_wind_statistics_from_12y |journal=Meteorologische Zeitschrift |language=en |pages=245–258 |doi=10.1127/metz/2023/1097|doi-access=free }} Despite this, much of the atmosphere outside the [tropics](/source/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 wave](/source/inertial_waves). ==Origin== A useful heuristic is to imagine [air](/source/air) starting from rest, experiencing a force directed from areas of high [pressure](/source/pressure) toward areas of low pressure, called the [pressure gradient](/source/pressure_gradient) force. If the air began to move in response to that force, however, the [Coriolis force](/source/Coriolis_force) would deflect it, to the right of the motion in the [Northern Hemisphere](/source/Northern_Hemisphere) or to the left in the [Southern Hemisphere](/source/Southern_Hemisphere). As the air accelerated, the deflection would increase until the Coriolis force's strength and direction balanced the pressure gradient force, a state called geostrophic balance. At this point, the flow is no longer moving from high to low pressure, but instead moves along [isobar](/source/isobar_(meteorology))s. Geostrophic balance helps to explain why, in the Northern Hemisphere, [low-pressure system](/source/low-pressure_system)s (or ''[cyclone](/source/cyclone)s'') spin counterclockwise and [high-pressure systems](/source/High-pressure_area) (or ''[anticyclone](/source/anticyclone)s'') spin clockwise, and the opposite in the Southern Hemisphere. ==Geostrophic currents== {{main|Geostrophic current}} 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 altimeters](/source/satellite_altimetry) are also used to measure sea surface height [anomaly](/source/anomaly_(natural_sciences)), which permits a calculation of the geostrophic current at the surface. ==Limitations of the geostrophic approximation== 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. The geostrophic wind neglects [friction](/source/friction)al effects, which is usually a good [approximation](/source/approximation) for the [synoptic scale](/source/synoptic_scale_meteorology) instantaneous flow in the midlatitude mid-[troposphere](/source/troposphere).{{cite book |first1=James R. |last1=Holton |first2=Gregory J. |last2=Hakim |chapter=2.4.1 Geostrophic Approximation and Geostrophic Wind |title=An Introduction to Dynamic Meteorology |chapter-url=https://books.google.com/books?id=hcxcqQp7XOsC&pg=PA42 |date=2012 |publisher=Academic Press |isbn=978-0-12-384867-3 |pages=42–43 |edition=5th |series=International Geophysics |volume=88}} Although [ageostrophic](/source/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](/source/Quasi-geostrophic_equations) and semi geostrophic theory are used to model flows in the atmosphere more widely. These theories allow for a divergence to take place and for weather systems to then develop. ==Formulation== {{See also|Geostrophic current#Formulation}} [Newton's second law](/source/Newton's_second_law) can be written as follows if only the pressure gradient, gravity, and friction act on an air parcel, where bold symbols are vectors: :{D\boldsymbol{U} \over Dt} = - {1 \over \rho} \nabla p - 2\boldsymbol{\Omega} \times \boldsymbol{U} + \boldsymbol{g} + \boldsymbol{F}_r Here '''''U''''' is the velocity field of the air, '''Ω''' is the angular velocity vector of the planet, ''ρ'' is the density of the air, P is the air pressure, '''F'''r is the friction, '''g''' is the [acceleration vector due to gravity](/source/standard_gravity) and {{sfrac|D|D''t''}} is the [material derivative](/source/material_derivative). Locally this can be expanded in [Cartesian coordinates](/source/Cartesian_coordinates), with a positive ''u'' representing an eastward direction and a positive ''v'' representing a northward direction. Neglecting friction and vertical motion, as justified by the [Taylor–Proudman theorem](/source/Taylor%E2%80%93Proudman_theorem), we have: :{Du \over Dt} = -{1 \over \rho}{\partial P \over \partial x} + fv + 0 + 0 : :{Dv \over Dt} = -{1 \over \rho}{\partial P \over \partial y} - fu + 0 + 0 : :{D w \over Dt}=-{1 \over \rho}{\partial P \over \partial z}+0-g+0 With {{nowrap|1=''f'' = 2Ω sin ''φ''}} the [Coriolis parameter](/source/Coriolis_frequency) (approximately {{val|e=-4|u=s−1}}, varying with latitude). Assuming geostrophic balance, the system is stationary and the first two equations become: :fv = {1 \over \rho}{\partial P \over \partial x} : :fu = -{1 \over \rho}{\partial P \over \partial y} : : -g -{1 \over \rho}{\partial P \over \partial z}=0 By substituting using the third equation above, we have: :\begin{align} fv &= \frac{\; -g \;}{\; \frac{\partial P}{\partial z} \;} \frac{\partial P}{\partial x} := \frac{\; -g \;}{\; c \;} a \\[5px] fu &= - \frac{\; -g \;}{\; \frac{\partial P}{\partial z} \;} \frac{\partial P}{\partial y} := + \frac{\; g \;}{\; c \;}b \end{align} with ''z'' the [geopotential height](/source/geopotential_height) of the constant pressure surface, satisfying :{\rm d}P={\partial P \over \partial x}{\rm d}x + {\partial P \over \partial y}{\rm d} y + {\partial P \over \partial z}{\rm d}z := a{\rm d} x+b{\rm d} y+c{\rm d} z = 0 Further simplify those formulae above: \begin{align} fv & = \frac{\; -g \;}{\; c \;} a = +g\biggl( \frac{{\rm d } z}{ {\rm d} x}\biggr)_{{\rm d}y=0} \\[5px] fu &= + \frac{\; g \;}{\; c \;}b = -g\biggl(\frac{{\rm d} z}{{\rm d} y}\biggr)_{{\rm d} x=0} \end{align} This leads us to the following result for the geostrophic wind components: v_g = {g \over f} {{\rm d}z \over {\rm d} x} u_g = - {g \over f} {{\rm d} z \over {\rm d} y} The validity of this approximation depends on the local [Rossby number](/source/Rossby_number). It is invalid at the equator, because ''f'' is equal to zero there, and therefore generally not used in the [tropics](/source/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](/source/geopotential_height) Φ on a surface of constant pressure: :\mathbf{V}_\mathrm{g} = \frac\hat\mathbf{k}{f} \times \nabla_p \Phi == See also == * [Geostrophic current](/source/Geostrophic_current) * [Thermal wind](/source/Thermal_wind) * [Gradient wind](/source/Gradient_wind) * [Prevailing winds](/source/Prevailing_winds) ==References== {{Reflist}} == External links == * [http://atmos.nmsu.edu/education_and_outreach/encyclopedia/geostrophic.htm Geostrophic approximation] * [http://nsidc.org/cryosphere/glossary/term/geostrophic-wind Definition of geostrophic wind] * [https://web.archive.org/web/20110726123313/http://atmo.tamu.edu/class/atmo203/tut/windpres/wind8.html Geostrophic wind description] {{Authority control}} {{DEFAULTSORT:Geostrophic Wind}} Category:Fluid dynamics Category:Atmospheric dynamics --- Adapted from the Wikipedia article [Geostrophic wind](https://en.wikipedia.org/wiki/Geostrophic_wind) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Geostrophic_wind?action=history)). 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