There are two possibilities for air to flow past a mountain ridge. Either the air parcels go round the mountain or is forced to rise over the mountain: Which of these cases occurs, is dependant on several parameters:
The static stability (N), the height of the mountain or mountain ridge (h) and the wind component perpendicular to the mountain (U). The term Nh/U combining these parameters gives an idea whether there is a flow across the mountain or not: If U is small the mountain is difficult to cross; also if N increases (i.e. the atmosphere becomes more stable) the mountain will be more difficult to cross.

But even in the case of air partially streaming around the mountain, those streamlines approaching a greater height will cross the mountains.

When the wind has a component perpendicular to a mountain chain the air accumulation due to deceleration of wind speed by the obstacle on the upwind side creates high pressure. Part of the air is deflected upward giving rise to mountain waves. According to the theory of internal gravity waves, an air parcel within a stable stratified atmosphere will start to oscillate, as long as the waves are damped by friction.

Waves can only occur in a stable atmosphere. An air parcel which is removed from its original place cannot oscillate if there is no returning force. Lee Cloudiness will form where there is a sufficient supply of humidity near the wave crests and where there is upward motion. In the regions with downward motion the clouds will evaporate. The result is the pattern of parallel cloud lines perpendicular to the mountains.

One parameter to describe the state of the atmosphere in this situation is the Brunt - Vaisala frequency N² which is defined by the following formula:

where

T	temperature
θ	potential vorticity
g	gravity constant
cp	specific heat at constant pressure

N2>0	stable atmosphere
N2 = 0.02 -0.03	inversions
N2 = 0	neutral atmosphere

Another important parameter is the Scorer parameter (symbolised by l) which combines stability and characteristics of the wind field; it is approximated by following formula:

where

U(z)	profile of the wind speed on the windward side of the mountains
N(z)	Brunt-Vaisala frequency

The typical profile of the Scorer parameter shows a high gradient in low levels due to increasing wind speeds. Higher levels often show values of about 0.0005/m, rarely exceeding 0.001/m. The smaller the Scorer parameter the easier waves are formed.

This parameter and the dimension of the mountain (L) determines if Lee Waves can be formed. The broader the mountain the easier waves can be formed. This relation can be expressed (assuming N and U are constant with height) by:

no Lee Waves are formed, but there are perturbations decreasing with height

Lee Waves are formed

The dimension of a critical width (L) is several kilometres, increasing with wind speed, but decreasing with increasing stability. If a mountain is not wide enough, Lee Waves will not develop.

Lee Waves are a form of vertical energy propagation. At higher levels the density of the air is less, that means the amplitude has to increase. Therefore the wavelength increases with height, which clearly is reflected in the more extended area of High Lee Cloudiness.

The wavelengths also depend on the shape of the mountains. There often is a dominating wave length.

The example from 18 January 2000 shows some of the parameters mentioned above. The image shows a region with Lee Cloudiness extending from the South Alps to the Adriatic Sea. The nearest available radiosonde was Milan which is indicated on the image. The Lee Cloud is quite high in this case and can be found just below 200 hPa.

The air column above Milan shows two conditionally unstable layers (yellow) restricted by inversions (green). The Lee Cloudiness under consideration is within a stable layer (blue) just below the upper inversion. This is in agreement with the above mentioned statement that Lee Cloud can only develop in a stable atmosphere.

• Whilst the wind direction varies between NW and NE in the whole troposphere, it is NW at the relevant height, which is parallel to the High Lee Cloud plume.

• There are two wind speed maxima: a lower one at about 650 hPa and a higher one around 200 hPa which correspond to the Lee Cloudiness under consideration. The vertical increase of wind speed is interrupted in a layer between 650 and 450 hPa. As can be seen in the stability columns above, at 650 hPa there is an inversion in the temperature distribution.

• In this case the Scorer parameter is around 0.0005m^-1; a value in agreement with the limits discussed above.

• The Brunt - Vaisälä - frequency is in aggreement with theory summarised above. The dashed curve represents the Brunt-Vaisala frequency for saturation. In this case values above 400 hPa are also positve.