The Froude Number

The Froude number establishes a relation between wind speed and atmospheric stability.

When an air stream hits an obstacle like a mountain chain, it has the possibility to either flow over it without being decelerated or to split and circle around both sides of the obstacle with the formation of an upstream decelerated area which propagates continuously upstream over time. The flow behavior depends largely on atmospheric stability and wind speed. The Froude number (here in the non-classical form) describes this behavior:

where U is the mean wind speed [m/s], H is the height of the barrier [m] relative to the height of the air stream and N the Brunt-Väisälä frequency [s-1]. When the Froude number Fr >> 1, the air tends to stream over the mountain chain, and in the opposite case (Fr << 1) it tends to contour the obstacle.

In the lower levels the wind needs more kinetic energy to crest the mountain than in levels slightly below the mountain top. Lower winds are therefore either blocked or deflected around the barrier, while higher up winds tend to pass over the mountain peaks. Typically, the wind will pass over the smallest elevations which in turn leads to a channeling effect as can be observed at many mountain passes in the Alps.

Figure 10: Airstream overflowing or bypassing a mountain.