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In atmospheric science, geostrophic flow () is the theoretical
wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few ...
that would result from an exact balance between the
Coriolis force In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
and the
pressure gradient In atmospheric science, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The ...
force. This condition is called ''
geostrophic equilibrium In atmospheric science, balanced flow is an idealisation of atmospheric motion. The idealisation consists in considering the behaviour of one isolated parcel of air having constant density, its motion on a horizontal plane subject to selected for ...
'' or ''geostrophic balance'' (also known as ''geostrophy''). The geostrophic wind is directed parallel to isobars (lines of constant
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
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 Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding (motion), sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative la ...
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 In meteorology, the planetary boundary layer (PBL), also known as the atmospheric boundary layer (ABL) or peplosphere, is the lowest part of the atmosphere and its behaviour is directly influenced by its contact with a planetary surface. On Ear ...
) and the isobars were perfectly straight. Despite this, much of the atmosphere outside the
tropics The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in the Southern Hemisphere at S. The tropics are also referred ...
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.


Origin

A useful heuristic is to imagine air starting from rest, experiencing a force directed from areas of high
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
toward areas of low pressure, called the
pressure gradient In atmospheric science, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The ...
force. If the air began to move in response to that force, however, the Coriolis "force" would deflect it, to the right of the motion in the northern hemisphere or to the left in the 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 isobars. Geostrophic balance helps to explain why, in the northern hemisphere,
low-pressure system In meteorology, a low-pressure area, low area or low is a region where the atmospheric pressure is lower than that of surrounding locations. Low-pressure areas are commonly associated with inclement weather (such as cloudy, windy, with possible ...
s (or '' cyclones'') spin counterclockwise and high-pressure systems (or ''
anticyclone An anticyclone is a weather phenomenon defined as a large-scale circulation of winds around a central region of high atmospheric pressure, clockwise in the Northern Hemisphere and counterclockwise in the Southern Hemisphere as viewed from abo ...
s'') spin clockwise, and the opposite in the southern hemisphere.


Geostrophic currents

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 are also used to measure sea surface height anomaly, 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 Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding (motion), sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative la ...
al effects, which is usually a good
approximation An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix '' ...
for the
synoptic scale The synoptic scale in meteorology (also known as large scale or cyclonic scale) is a horizontal length scale of the order of 1000 kilometers (about 620 miles) or more. This corresponds to a horizontal scale typical of mid-latitude depressions (e. ...
instantaneous flow in the midlatitude mid-
troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
. 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..


Formulation

Newton's Second Law Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
can be written as follows if only the pressure gradient, gravity, and friction act on an air parcel, where bold symbols are vectors: :\frac = -2\boldsymbol \times \boldsymbol - \frac \nabla P + \mathbf + \mathbf_\mathrm 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, Fr is the friction, g is the acceleration vector due to gravity and is the
material derivative In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material de ...
. Locally this can be expanded in
Cartesian coordinates A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured i ...
, 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, we have: :\begin \frac &= -\frac\frac + f \cdot v \\ px\frac &= -\frac\frac - f \cdot u \\ px0 &= -g -\frac\frac \end With the
Coriolis parameter The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the latitude \varphi. :f = 2 \Omega \sin \varphi.\, The rotation rate ...
(approximately , varying with latitude). Assuming geostrophic balance, the system is stationary and the first two equations become: :\begin f \cdot v &= \;\;\,\frac\frac \\ pxf \cdot u &= -\frac\frac \end By substituting using the third equation above, we have: :\begin f \cdot v &= -g\frac = g\frac \\ pxf \cdot u &= g\frac = -g\frac \end with ''Z'' the height of the constant pressure surface (
geopotential height Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level, an adjustment to geometric height (altitude above mean sea level) that accounts for the variation of gravity with latitude and altitude. Thu ...
), satisfying :\frac\mathrmx + \frac\mathrmy + \frac\mathrmZ = 0 This leads us to the following result for the geostrophic wind components (''u''g, ''v''g): :\begin u_\mathrm &= -\frac \frac \\ pxv_\mathrm &= \;\;\,\frac \frac \end The validity of this approximation depends on the local
Rossby number The Rossby number (Ro), named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow. The Rossby number is the ratio of inertial force to Coriolis force, terms , \mathbf \cdot \nabla \mathbf, \sim U^2 / L and \Omega ...
. It is invalid at the equator, because ''f'' is equal to zero there, and therefore generally not used in the
tropics The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in the Southern Hemisphere at S. The tropics are also referred ...
. Other variants of the equation are possible; for example, the geostrophic wind vector can be expressed in terms of the gradient of the
geopotential Geopotential is the potential of the Earth's gravity field. For convenience it is often defined as the ''negative'' of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of this potential, without the negati ...
Φ on a surface of constant pressure: :\mathbf_\mathrm = \frac\hat\mathbf \times \nabla_p \Phi


See also

*
Balanced wind In telecommunications and professional audio, a balanced line or balanced signal pair is a circuit consisting of two conductors of the same type, both of which have equal impedances along their lengths and equal impedances to ground and to other ...
* Geostrophic current * Thermal wind *
Gradient wind In atmospheric science, balanced flow is an idealisation of atmospheric motion. The idealisation consists in considering the behaviour of one isolated parcel of air having constant density, its motion on a horizontal plane subject to selected for ...
*
Prevailing winds In meteorology, prevailing wind in a region of the Earth's surface is a surface wind that blows predominantly from a particular direction. The dominant winds are the trends in direction of wind with the highest speed over a particular point on ...


References


External links


Geostrophic approximation

Definition of geostrophic wind


{{DEFAULTSORT:Geostrophic Wind Fluid dynamics Atmospheric dynamics