Billows are the most common form of dynamic instability in the free air where the air is stably stratified. They occur mainly in layers where the static stability is much larger than average and therefore where there are already large gradients of temperature and humidity. They are produced predominantly by the tilting of these very stable layers in the wavy airflow produced by hills. The billows form a cat's-eye pattern of motion that becomes statically unstable in the closed circulations. Consequently, the gradients inside are destroyed by the buoyancy-induced mixing, and large gradients are produced at the boundary of the circulations. The original stable layer is thus replaced by two stable layers at a distance apart of the order of 5 times the depth of the original layer. During the overturning, large gradients of temperature are produced at the wavy boundary, which is itself corrugated by the internal mixing motions.