Gradient wind

The gradient wind designates in meteorology the wind that is made up

• the gradient force (due to the pressure differences between a high and a low pressure area ),
• the Coriolis force (due to the rotation of the earth ) and
• the centrifugal force (due to the rotation of a high or low pressure area)

composed. Local effects, for example from mountains or ground friction , are not taken into account.

The gradient wind is an extension of the geostrophic wind and the cyclostrophic wind , so that the term geostrophic-cyclostrophic wind is also used. It represents the best approximation of the real wind, which can still be predicted relatively precisely from weather maps and altitude wind measurements.

The strength of the gradient wind depends on the path forced on it:

• with anti-cyclonic movements (movement around a high pressure area) the gradient force results as a vectorial difference from the Coriolis force and the centrifugal force, i.e. H. the pressure gradient is greater than in the geostrophic wind (supergeostrophic).
• on cyclonic orbits (movement around a low pressure area), on the other hand, the gradient force results from the sum of centrifugal force and Coriolis force, so that the pressure gradient is lower than in geostrophic winds (subgeostrophic).

With the same pressure gradient, the wind therefore blows more strongly around a high pressure area than around a low pressure area.

Critical curvature

In particularly small high-pressure areas, the high centrifugal force means that the gradient wind does not achieve an equilibrium between the Coriolis force and the sum of the centrifugal and compressive forces . From this it can be seen that high pressure areas below a certain minimum radius , equivalent to a large curvature , become unstable and are therefore not possible in the atmosphere. The critical curvature follows from the quadratic equation for solving the equilibrium of forces of the gradient wind: ${\displaystyle R_{krit}}$ ${\displaystyle \kappa _{krit}}$

${\displaystyle \kappa _{krit}={\frac {1}{R_{krit}}}={\frac {1}{4\cdot v_{g}}}\cdot f_{c}}$

With

• the speed in the geostrophic wind ${\displaystyle v_{g}}$
• the Coriolis parameter ${\displaystyle f_{c}=2\cdot \Omega \cdot \sin \varphi }$
  • the angular velocity of the earth ${\displaystyle \Omega ={\frac {2\pi }{24\;\mathrm {h} }}={\frac {2\pi }{86400\;\mathrm {s} }}}$
  • the latitude . ${\displaystyle \varphi }$

Because the Coriolis parameter increases with increasing geographical latitude , ever greater curvatures and thus ever smaller peaks are possible towards the poles .

literature

• Andreas Bott: Synoptic Meteorology: Methods of Weather Analysis and Forecast . Springer, Berlin, Heidelberg 2012.

Web links

• Gradient wind - diplomet.info