Wind Regimes - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 14

some of them. Nearly always, the terms containing f* are discarded because they
are very small compared to all other terms in the same equation. In larger-scale
motions term VI is always neglected as well. Term VI is only important in whirl
winds and close to the centre of high and low pressure systems. Looking at the
vertical acceleration only (Eq. ( 2.4 )), terms III and IV are dominating. Equating
these two terms in ( 2.4 ) leads to the hydrostatic equation ( 2.1 ) above.
There is only one driving force in Eqs. ( 2.2 - 2.4 ): the abovementioned pressure
force which is expressed by term III. The constant outer force due to the gravity of
the Earth (term IV) prevents the atmosphere from escaping into space. The only
braking force is the frictional force in term VII. The other terms (II, V, and VI) just
redistribute the momentum between the three different wind components.
Thus, sometimes terms V and VI are named ''apparent forces''. In the special case
when all terms II to VII would disappear simultaneously or would cancel each
other perfectly, the air would move inertially at constant speed. This is the reason
why term I is often called inertial term.

2.3 Geostrophic Winds and Gradient Winds

The easiest and most fundamental balance of forces is found in the free tropo-
sphere above the atmospheric boundary layer, because frictional forces are neg-
ligible there. Therefore, our analysis is started here for large-scale winds in the free
troposphere. The frictional forces in term VII in Eqs. ( 2.2 - 2.4 ) can be neglected
above the atmospheric boundary layer. Term VI is also very small and negligible
away from pressure maxima and minima. The same applies to term II for large-
scale motions with small horizontal gradients in the wind field. A scale analysis
shows that the equilibrium of pressure and Coriolis forcess is the dominating
feature and the inertial term I can be neglected as well. This leads to the following
two equations:

qfu g ¼ o p
oy

ð 2 : 5 Þ

qfv g ¼ o p
ox

ð 2 : 6 Þ

with u g and v g being the components of this equilibrium wind, which is usually
called geostrophic wind in meteorology. The geostrophic wind is solely deter-
mined by the large-scale horizontal pressure gradient and the latitude-dependent
Coriolis parameter, the latter being in the order of 0.0001 s -1 (see Table 2.1 for
some sample values). Because term VII had been neglected in the definition of the
geostrophic wind, surface friction and the atmospheric stability of the atmospheric
boundary layer has no influence on the magnitude and direction of the geostrophic
wind. The modulus of the geostrophic wind reads: