In meteorology, lee waves are atmospheric stationary waves. The most common form is mountain waves, which are atmospheric internal gravity waves. These were discovered in 1933 by two German glider pilots, Hans Deutschmann and Wolf Hirth, above the Giant Mountains. They are periodic changes of atmospheric pressure, temperature and orthometric height in a current of air caused by vertical displacement, for example orographic lift when the wind blows over a mountain or mountain range. They can also be caused by the surface wind blowing over an escarpment or plateau, or even by upper winds deflected over a thermal updraft or cloud street. The vertical motion forces periodic changes in speed and direction of the air within this air current. They always occur in groups on the lee side of the terrain that triggers them. Sometimes, mountain waves can help to enhance precipitation amounts downwind of mountain ranges. Usually a turbulent vortex, with its axis of rotation parallel to the mountain range, is generated around the first trough; this is called a rotor. The strongest lee waves are produced when the lapse rate shows a stable layer above the obstruction, with an unstable layer above and below. Strong winds (with wind gusts over 100 mph) can be created in the foothills of large mountain ranges by mountain waves. These strong winds can contribute to unexpected wildfire growth and spread (including the 2016 Great Smoky Mountains wildfires when sparks from a wildfire in the Smoky Mountains were blown into the Gatlinburg and Pigeon Forge areas).

Basic theory

Lee waves are a form of internal gravity waves produced when a stable, 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 a vertical oscillation of the perturbed air parcels at the Brunt-Väisäla frequency, which for the atmosphere is: , where \theta_0(z) is the vertical profile of potential temperature. Oscillations tilted off the vertical axis at an angle of \phi will occur at a lower frequency of N\cos{\phi}. These air parcel oscillations occur in concert, parallel to the wave fronts (lines of constant phase). These wave fronts represent extrema in the perturbed pressure field (i.e., lines of lowest and highest pressure), while the areas between wave fronts represent extrema in the perturbed buoyancy field (i.e., areas most rapidly gaining or losing buoyancy). Energy is transmitted along the wave fronts (parallel to air parcel oscillations), which is the direction of the wave group velocity. In contrast, the phase propagation (or phase speed) of the waves points perpendicular to energy transmission (or group velocity).

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.

Aviation

Lee waves provide a possibility for gliders to gain altitude or fly long distances when soaring. World record wave flight performances for speed, distance or altitude have been made in the lee of the Sierra Nevada, Alps, Patagonic Andes, and Southern Alps mountain ranges. The Perlan Project is working to demonstrate the viability of climbing above the tropopause in an unpowered glider using lee waves, making the transition into stratospheric standing waves. They did this for the first time on August 30, 2006 in Argentina, climbing to an altitude of 15460 m. The Mountain Wave Project of the Organisation Scientifique et Technique du Vol à Voile focusses on analysis and classification of lee waves and associated rotors. The conditions favoring strong lee waves suitable for soaring are: 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 Mount Fuji, Japan in 1966, and the in-flight separation of an engine on an Evergreen International Airlines Boeing 747 cargo 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, stall or loss of control.

Other varieties of atmospheric waves

There are a variety of distinctive types of waves which form under different atmospheric conditions.