- Lee waves
meteorology, lee waves, are atmospheric standing 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 Riesengebirge. [cite journal
title=Modeling and Classification of Mountain Waves
coauthors=Rasulov, M.; Aslan, Z.
issn=0744-8996] [cite web
url = http://www.nateferguson.com/glider.html
title = Article about wave lift
accessdate = 2006-09-28] They are periodic changes of
atmospheric pressure, temperatureand orthometric heightin a current of aircaused by vertical displacement, for example orographic liftwhen the windblows over a mountainor mountain range. They can also be caused by the surface wind blowing over an escarpmentor plateau, or even by upper winds deflected over a thermal updraftor cloud street.
The vertical motion forces periodic changes in
speedand directionof the air within this air current. They always occur in groups on the lee side of the terrainthat triggers them. Usually a turbulent horizontal vortexis generated around the first trough, the so called rotor. The strongest lee waves are produced when the lapse rateshows a stable layer above the obstruction, with an unstable layer above and below.cite book | last = Pagen | first = Dennis | title = Understanding the Sky | publisher = Sport Aviation Pubns | location = City | year = 1992 | isbn = 0936310103 | pages= pp.169-175 | quote= This is the ideal case, for an unstable layer below and above the stable layer create what can be described as a springboard for the stable layer to bounce on once the mountain begins the oscillation.]
Both lee waves and the rotor may be indicated by specific
wave cloudformations if there is sufficient moisture in the atmosphere, and sufficient vertical displacement to cool the air below 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.
* Around the crest of the wave, Adiabatic expansion cooling can form a cloud in
shapeof a lens (lenticularis). Multiple lenticular clouds can be stacked on top of each other if there are alternating layers of relatively dry and moist air aloft.
* The rotor may generate
cumulusor cumulus fractusin 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.
foehnwall cloud may exist at the lee side of the mountains, however this is not a reliable indication of the presence of lee waves.
Pileusor Cap Cloud, similar to a lenticular cloud, may form above the mountain or cumulus cloud generating the wave.
* Adiabatic compression heating in the trough of each wave oscillation may also
evaporate cumulusor stratusclouds in the airmass, creating a "wave window" or "Foehn gap".ImageStackLeft|280
Lee waves provide a possibility for
gliders to gain altitudeor 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 Alpsmountain ranges. [ [http://records.fai.org/gliding/ FAI gliding records] ] The Perlan Projectis working to demonstrate the viability of climbing above the tropopausein 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 50,671 feet (15,447 m). [ [http://www.perlanproject.com/ Perlan Project] ] The Mountain Wave Projectof the Organisation Scientifique et Technique du Vol à Voilefocusses on analysis and classification of lee waves and associated rotors. [http://126.96.36.199/Defaultengl.htm Mountain Wave Project] - accessed 2008-02-17]
The conditions favoring strong lee waves suitable for soaring are:
* A gradual increase in windspeed with altitude
* Wind direction within 30° of perpendicular to the mountain ridgeline
* Strong low-altitude winds in a stable atmosphere
* Ridgetop winds of at least 20 knots
The rotor turbulence may be harmful for other small
aircraftsuch as balloons, hang gliders and para gliders. It can even be a hazard for large aircraft; the phenomenon is believed responsible for many aviation accidents and incidentsincluding the in-flight break up of BOAC Flight 911, a Boeing 707, near Mt. Fuji, Japanin 1966, and the in-flight separation of an engine on an Evergreen International Airlines Boeing 747cargo jet near Anchorage, Alaskain 1993. [ [http://www.ntsb.gov/ntsb/brief.asp?ev_id=20001211X11963&key=1 NTSB Accident brief 20001211X11963] ]
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 tuckand 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. Some less commonly known types are as follows:
* "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 jumpforms 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 [http://ams.confex.com/ams/pdfpapers/40363.pdf Observations of Mountain-Induced Rotors and Related Hypotheses: a Review] by Joachim Kuettner and Rolf F. Hertenstein] as well as mountain ranges in southern California.
* "Hydrostatic waves". These 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" (or planetary waves) are large-scale motions in the atmosphere whose restoring force is the variation in Coriolis effect with latitude.
*Grimshaw, R., (2002). "Environmental Stratified Flows". Boston: Kluwer Academic Publishers.
*Jacobson, M., (1999). "Fundamentals of Atmospheric Modeling". Cambridge: Cambridge University Press.
*Nappo, C., (2002). "An Introduction to Atmospheric Gravity Waves". Boston: Academic Press.
*Pielke, R., (2002). "Mesoscale Meteorological Modeling". Boston: Academic Press.
*Turner, B., (1979). "Buoyancy Effects in Fluids". Cambridge: Cambridge University Press.
*Whiteman, C., (2000). "Mountain Meteorology". Oxford Oxfordshire: Oxford University Press.
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