Lee waves are a form of internal gravity waves produced when stably stratified flow is forced over an obstacle. This disturbance elevates air parcels above their level of neutral buoyancy. Buoyancy restoring forces therefore act to excite vertical oscillation of the perturbed air parcels at the Brunt-Väisäla frequency, which for the atmosphere is: , where is the vertical profile of potential temperature. Oscillations tilted off the vertical axis at an angle of will occur at a lower frequency of. These air parcel oscillations occur in concert, parallel to the wave fronts. These wave fronts represent extrema in the perturbed pressure field, while the areas between wave fronts represent extrema in the perturbed buoyancy field. Energy is transmitted along the wave fronts, which is the direction of the wave group velocity. In contrast, the phase propagation of the waves points perpendicular to energy transmission.
Clouds
Both lee waves and the rotor may be indicated by specific wave cloud formations if there is sufficient moisture in the atmosphere, and sufficient vertical displacement to cool the air to the dew point. Waves may also form in dry air without cloud markers. Wave clouds do not move downwind as clouds usually do, but remain fixed in position relative to the obstruction that forms them.
The rotor may generate cumulus or cumulus fractus in its upwelling portion, also known as a "roll cloud". The rotor cloud looks like a line of cumulus. It forms on the lee side and parallel to the ridge line. Its base is near the height of the mountain peak, though the top can extend well above the peak and can merge with the lenticular clouds above. Rotor clouds have ragged leeward edges and are dangerously turbulent.
A foehn wall cloud may exist at the lee side of the mountains, however this is not a reliable indication of the presence of lee waves.
A pileus or cap cloud, similar to a lenticular cloud, may form above the mountain or cumulus cloud generating the wave.
The rotor turbulence may be harmful for other small aircraft such as balloons, hang gliders and paragliders. It can even be a hazard for large aircraft; the phenomenon is believed responsible for many aviation accidents and incidents, including the in-flight breakup of BOAC Flight 911, a Boeing 707, near Mt. Fuji, Japan in 1966, and the in-flight separation of an engine on an Evergreen International AirlinesBoeing 747cargo jet near Anchorage, Alaska in 1993. The rising air of the wave, which allows gliders to climb to great heights, can also result in high altitude upset in jet aircraft trying to maintain level cruising flight in lee waves. Rising, descending or turbulent air in or above the lee waves can cause overspeed or stall, resulting in mach tuck and loss of control, especially when the aircraft is operated near the "coffin corner".
Other varieties of atmospheric waves
There are a variety of distinctive types of waves which form under different atmospheric conditions.
Wind shear can also create waves. This occurs when an atmospheric inversion separates two layers with a marked difference in wind direction. If the wind encounters distortions in the inversion layer caused by thermals coming up from below, it will create significant shear waves in the lee of the distortions that can be used for soaring.
Hydraulic jump induced waves are a type of wave that forms when there exists a lower layer of air which is dense, yet thin relative to the size of the mountain. After flowing over the mountain, a type of shock wave forms at the trough of the flow, and a sharp vertical discontinuity called the hydraulic jump forms which can be several times higher than the mountain. The hydraulic jump is similar to a rotor in that it is very turbulent, yet it is not as spatially localized as a rotor. The hydraulic jump itself acts as an obstruction for the stable layer of air moving above it, thereby triggering wave. Hydraulic jumps can distinguished by their towering roll clouds, and have been observed on the Sierra Nevada range as well as mountain ranges in southern California.
Hydrostatic waves are vertically propagating waves which form over spatially large obstructions. In hydrostatic equilibrium, the pressure of a fluid can depend only on altitude, not on horizontal displacement. Hydrostatic waves get their name from the fact that they approximately obey the laws of hydrostatics, i.e. pressure amplitudes vary primarily in the vertical direction instead of the horizontal. Whereas conventional, non-hydrostatic waves are characterized by horizontal undulations of lift and sink, largely independent of altitude, hydrostatic waves are characterized by undulations of lift and sink at different altitudes over the same ground position.
Kelvin–Helmholtz instability can occur when velocity shear is present within a continuous fluid or when there is sufficient velocity difference across the interface between two fluids.
Rossby waves are large-scale motions in the atmosphere whose restoring force is the variation in Coriolis effect with latitude.
