Gradient force

This article deals with the gradient force, which in meteorology describes the gradient field for pressure. For other forces that are gradients of scalar fields, see Gradient (Math) #Applications .

The air moves, following the gradient force , from high above the equator to low above the pole

The gradient force , also called pressure gradient force , is the geophysical cause of the wind as a balancing flow of the air between a high and a low pressure area .

Due to an air pressure gradient ( gradient means something like slope ), i.e. a difference in air pressure between high and low pressure areas, a force acts on the air along the pressure gradient . This is proportional to the difference in pressure and not to the absolute value of the pressure itself. As a result, equalizing currents (winds) are formed, which are always directed from the high to the low pressure area, i.e. from the location of the higher to the location of the lower air pressure. So while the air converges ( converges ) in the low pressure area, it diverges in the high pressure area (it diverges ).

The gradient force plays a role in the formation of most winds, e.g. Sometimes together with other influences that deflect the movement of the air masses :

• Euler wind : gradient force only
• geostrophic wind : gradient force and Coriolis force
• Cyclostrophic wind : gradient force and centrifugal force
• Gradient wind : gradient force, Coriolis force and centrifugal force.

The Coriolis force acts:

• deflecting to the right in the northern hemisphere , so that the air always turns to the right ( clockwise - in a mathematically negative sense) from the high and to the left (counterclockwise - in the mathematically positive sense) "turns in" into the low.
• deflecting left in the southern hemisphere , and the air rotates accordingly around the pressure areas.

Additional influences on the development of real winds are ground friction and topographical factors.

Horizontal and vertical component

The pressure gradient force on an air parcel with a mass and the density in a pressure field is calculated according to: ${\displaystyle {\vec {F}}_{p}}$ ${\displaystyle m}$ ${\displaystyle \rho }$ ${\displaystyle p}$

${\displaystyle {\vec {F}}_{p}=-{\frac {m}{\rho }}\left({\frac {\partial p}{\partial x}}{\vec {e}}_{x}+{\frac {\partial p}{\partial y}}{\vec {e}}_{y}+{\frac {\partial p}{\partial z}}{\vec {e}}_{z}\right)=-{\frac {m}{\rho }}{\vec {\nabla }}p}$

In the analysis of the air movements within the atmosphere of the horizontal component is and the vertical component considered separately, as a rule, said vertical coordinate z ${\displaystyle {\vec {F}}_{p,{\text{horizontal}}}}$ ${\displaystyle {\vec {F}}_{p,{\text{vertikal}}}}$

${\displaystyle {\vec {F}}_{p,{\text{horizontal}}}=-{\frac {m}{\rho }}\left({\frac {\partial p}{\partial x}}{\vec {e}}_{x}+{\frac {\partial p}{\partial y}}{\vec {e}}_{y}\right)}$

and

${\displaystyle {\vec {F}}_{p,{\text{vertikal}}}=-{\frac {m}{\rho }}{\frac {\partial p}{\partial z}}{\vec {e}}_{z}\ .}$

The vertical pressure gradient force is directed upwards because the air pressure decreases with increasing altitude. With hydrostatic equilibrium , the vertical component is compensated for by the weight of the air parcel. ${\displaystyle {\vec {F}}_{p,{\text{vertikal}}}}$

The pressure gradient force is directed perpendicular to the surfaces of equal pressure. Two such surfaces between which there is a pressure difference of 5 hPa have a vertical distance of about 40 m near the ground. In contrast, their distance in the horizontal direction is at typical values ​​of more than 400 km; the surfaces of the same pressure are thus almost parallel to the horizontal plane. This means that the vertical pressure gradient force is about 10,000 times greater than the horizontal one. Because of the compensation by the vertically acting force of gravity, it is precisely the much smaller horizontal pressure gradient force that causes the horizontal air mass displacement in winds . Typical amounts of the horizontal pressure gradient force on a 1 kg air parcel are approximately . ${\displaystyle {\vec {F}}_{p,{\text{horizontal}}}}$ ${\displaystyle 10^{-3}N}$

Illustration in weather maps

The horizontal pressure gradient forces can be visualized in weather maps as "arrows" which are perpendicular to the isobars and point from the higher to the lower pressure. The arrows become larger the closer the isobars are.

literature

• Gösta H. Liljequist, Konrad Cehak: General Meteorology . Springer-Verlag, 2013, ISBN 978-3-322-83675-5 ( limited preview in Google book search).
• Hans Häckel : Meteorology . UTB, 2016, ISBN 978-3-8252-4603-7 ( limited preview in Google Book Search).

Web links

• Pressure gradient and pressure gradient force in the online lexicon of the German Weather Service.
• WEBGEO module: pressure gradient, gradient force, gradient acceleration - WEBGEO - e-learning portal for geography and related sciences at the University of Freiburg ; requires flash plugin

Individual evidence

1. ^ Feynman lectures on physics , Vol. 2, pp. 40-1 (German), Online, Section 40-1, Fig. 40.3 (English)
2. ↑ ^{a b} German Weather Service (Ed.): General Meteorology (=  guidelines for training in the German Weather Service . No. 1 ). 3. Edition. Self-published DWD, Offenbach am Main 1987, 5.2 Die Druckgradientkraft, p. 41 .