An atmospheric gravity wave, formed when stable air flow passes over a mountain or mountain barrier. Mountain waves are often standing or nearly so, at least to the extent that upstream environmental conditions (and diurnal forcing) are stationary. Two divisions of mountain wave are recognized, vertically propagating and trapped lee waves. Vertically propagating mountain waves over a barrier may have horizontal wavelengths of many tens of kilometers or more, usually extend upward into the lower stratosphere, and in pure form, tilt upwind with height. They can accompany foehn, chinook, or bora wind conditions. They have the capability to concentrate momentum on the lee slopes, sometimes in structures resembling a hydraulic jump, leading to occasionally violent downslope windstorms. When sufficient moisture is present in the upstream flow, vertically propagating mountain waves produce interesting cloud forms, including altocumulus standing lenticular (ACSL) and other foehn clouds. Intense waves can present a significant hazard to aviation by producing severe or even extreme clear air turbulence. Trapped lee waves generally have horizontal wavelengths of 5–35 km. They occur within or beneath a layer of high static stability and moderate wind speeds at low levels of the troposphere (the lowest 1–5 km) lying beneath a layer of low stability and strong winds in the middle and upper troposphere. These conditions are often diagnosed using a vertical profile of the Scorer parameter, a sharp decrease in midtroposphere indicating conditions favorable to trapped lee wave formation. Trapped lee waves assume the form of a series of waves running parallel to the ridges, and the crests of these waves often contain altocumulus, stratocumulus, wave clouds, or rotor clouds in parallel bands that can be very striking in satellite pictures. Because wave energy is trapped within the stable layer, these waves (and accompanying cloud bands) may dissipate only very slowly downwind, and they can continue downstream for many wavelengths spanning many tens of kilometers. Flow beneath the wave crests, occasionally made visible by rotor clouds, is often turbulent, thus presenting a significant hazard to low-level aviation. Vertically propagating mountain waves and trapped lee waves can coexist, and sometimes lee waves are incompletely trapped or “leaky,” leading to a variety of complex rotor interactions. This complexity of rotor patterns often produces interesting variations in cloud forms. As mountain waves propagate upward, the rotor's amplitude can grow to the point that the rotor “breaks,” that is, the rotor becomes convectively unstable and overturns. Wave breaking can have an important role in vertically redistributing horizontal atmospheric momentum, as it slows the atmosphere by turbulent transport of the earth's momentum upward.