Geostrophy

The articles Geostrophischer_Wind and Geostrophie overlap thematically. Help me to better differentiate or merge the articles (→  instructions ) . To do this, take part in the relevant redundancy discussion . Please remove this module only after the redundancy has been completely processed and do not forget to include the relevant entry on the redundancy discussion page{{ Done | 1 = ~~~~}}to mark. FloLoBonn ( discussion ) 20:11, 20 Mar. 2014 (CET)

Right third of the image: balance between pressure gradient force and Coriolis force , the resulting flow (yellow) runs parallel to the isobars .
The geostrophic adjustment can be seen on the left.

In physics and meteorology, geostrophy is the equilibrium between Coriolis force and pressure gradient force . This horizontal equilibrium is often referred to as geostrophic equilibrium . Geostrophy is the stationary end state of the geostrophic adjustment of pressure and flow fields that are initially not in geostrophic equilibrium. The resulting wind of a geostrophic equilibrium is called geostrophic wind .

Geostrophy is a simplification that can be assumed when a system is frictionless . In the case of the ocean , this applies approximately inside, between the turbulent boundary layers on the sea floor and on the surface of the sea, and in the case of the earth's atmosphere for regions above the planetary boundary layer .

Equations

In equations, geostrophy is represented as follows:

${\displaystyle {\vec {F}}_{\mathrm {C} }=-{\vec {F}}_{\mathrm {p} }}$

With

• the Coriolis force ${\displaystyle {\vec {F}}_{\mathrm {C} }=2\cdot m\cdot ({\vec {v}}\times {\vec {\omega }})}$
  • the mass of the considered water or air parcel ${\displaystyle m}$
  • its speed ${\displaystyle {\vec {v}}}$
  • the angular velocity of the earth ${\displaystyle \omega ={\frac {2\pi }{24\;\mathrm {h} }}={\frac {2\pi }{86164\;\mathrm {s} }}}$

${\displaystyle \,}$

• the pressure gradient force ${\displaystyle {\vec {F}}_{\mathrm {p} }=-{\frac {m}{\rho }}\cdot {\vec {\nabla }}_{h}\,p=-V\cdot {\frac {\Delta p}{\Delta x}}}$
  • the density (of water or air) ${\displaystyle \rho }$
  • the Nabla operator in the horizontal direction ${\displaystyle {\vec {\nabla }}_{h}}$
  • the pressure ${\displaystyle p}$
  • the volume ${\displaystyle V}$
  • the pressure difference between two points ${\displaystyle \Delta p}$
  • the horizontal distance between these two points. ${\displaystyle \Delta x}$

Geostrophic wind speed

The above equations give the speed of the geostrophic wind (in m / s) by transforming:

${\displaystyle {\begin{aligned}\Rightarrow \mid {\vec {v}}_{\mathrm {g} }\mid &={\frac {1}{\rho \cdot f}}\cdot \mid {\vec {\nabla }}_{h}\,p\mid \\&={\frac {1}{\rho \cdot f}}\cdot \left|{\frac {\Delta p}{\Delta x}}\right|\end{aligned}}}$

With

• the density of the air ( ) ${\displaystyle \rho _{L}\approx 1\,\mathrm {kg} /\mathrm {m} ^{3}}$
• the Coriolis parameter ${\displaystyle f=2\cdot \omega \cdot \sin \varphi }$
  • the latitude . ${\displaystyle \phi }$

In addition to meteorology, this wind formula is also used in flight navigation , see Single Heading Flight .

literature

• German Weather Service : Guide for training in the German Weather Service - General Meteorology . Self-published by DWD, Offenbach am Main 1987