Lee waves
In meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

, lee waves are atmospheric
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

 standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...

s. The most common form is mountain waves, which are atmospheric internal gravity wave
Gravity wave
In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media which has the restoring force of gravity or buoyancy....

s. These were discovered in 1933 by two German glider pilots, Hans Deutschmann and Wolf Hirth
Wolf Hirth
Wolfram Kurt Erhard Hirth was a German gliding pioneer and sailplane designer. He was a co-founder of Schempp-Hirth, still a renowned glider manufacturer....

, above the Riesengebirge.
They are periodic
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 changes of atmospheric pressure
Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

, temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 and orthometric height
Orthometric height
The orthometric height is the distance H along a line of force from a given point P at the physical surface of an object to the geoid.Orthometric heights are what are usually used in the US for ordinary engineering work. Values for measured points can be obtained from the National Geodetic Survey...

 in a current
Air current
Air currents may be caused by differences in temperature, pressure, or impurity concentration. Temperature differences can cause air currents because warmer air is less dense than cooler air, causing the warmer air to appear "lighter." Thus, if the warm air is under the cool air, air currents will...

 of air caused by vertical displacement, for example orographic lift
Orographic lift
Orographic lift occurs when an air mass is forced from a low elevation to a higher elevation as it moves over rising terrain. As the air mass gains altitude it quickly cools down adiabatically, which can raise the relative humidity to 100% and create clouds and, under the right conditions,...

 when the wind
Wind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space...

 blows over a mountain
Image:Himalaya_annotated.jpg|thumb|right|The Himalayan mountain range with Mount Everestrect 58 14 160 49 Chomo Lonzorect 200 28 335 52 Makalurect 378 24 566 45 Mount Everestrect 188 581 920 656 Tibetan Plateaurect 250 406 340 427 Rong River...

 or mountain range
Mountain range
A mountain range is a single, large mass consisting of a succession of mountains or narrowly spaced mountain ridges, with or without peaks, closely related in position, direction, formation, and age; a component part of a mountain system or of a mountain chain...

. They can also be caused by the surface wind blowing over an escarpment
An escarpment is a steep slope or long cliff that occurs from erosion or faulting and separates two relatively level areas of differing elevations.-Description and variants:...

 or plateau
In geology and earth science, a plateau , also called a high plain or tableland, is an area of highland, usually consisting of relatively flat terrain. A highly eroded plateau is called a dissected plateau...

, or even by upper winds deflected over a thermal
A thermal column is a column of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation, and are an example of convection. The sun warms the ground, which in turn warms the air directly above it...

 updraft or cloud street.

The vertical motion forces periodic changes in speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

 and direction
Boxing the compass
Boxing the compass is the action of naming all thirty-two points of the compass in clockwise order. Such names are formed by the initials of the cardinal directions and their intermediate ordinal directions, and are very handy to refer to a heading in a general or colloquial fashion, without...

 of the air within this air current. They always occur in groups on the lee
Windward and leeward
Windward is the direction upwind from the point of reference. Leeward is the direction downwind from the point of reference. The side of a ship that is towards the leeward is its lee side. If the vessel is heeling under the pressure of the wind, this will be the "lower side"...

 side of the terrain
Terrain, or land relief, is the vertical and horizontal dimension of land surface. When relief is described underwater, the term bathymetry is used...

 that triggers them. Usually a turbulent vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...

, with its axis of rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

 parallel to the mountain range, is generated around the first trough
Crest (physics)
A crest is the point on a wave with the maximum value or upward displacement within a cycle. A trough is the opposite of a crest, so the minimum or lowest point in a cycle.-Interference:...

; this is called a rotor. The strongest lee waves are produced when the lapse rate
Lapse rate
The lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is temperature unless specified otherwise. The terminology arises from the word lapse in the sense of a decrease or decline; thus, the lapse rate is the rate of decrease with height and...

 shows a stable layer above the obstruction, with an unstable layer above and below.


Both lee waves and the rotor may be indicated by specific wave cloud
Wave cloud
A wave cloud is a cloud form created by atmospheric internal waves.-Formation:The atmospheric internal waves that form wave clouds are created as stable air flows over a raised land feature such as a mountain range, and can form either directly above or in the lee of the feature. As an air mass...

 formations if there is sufficient moisture in the atmosphere, and sufficient vertical displacement to cool the air to the dew point
Dew point
The dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapor to condense into liquid water. The condensed water is called dew when it forms on a solid surface. The dew point is a saturation temperature.The dew point is...

. 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
    Crest (physics)
    A crest is the point on a wave with the maximum value or upward displacement within a cycle. A trough is the opposite of a crest, so the minimum or lowest point in a cycle.-Interference:...

     of the wave, adiabatic expansion cooling can form a cloud in shape
    The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...

     of a lens
    Lens (geometry)
    In geometry, a lens is a biconvex shape comprising two circular arcs, joined at their endpoints. If the arcs have equal radii, it is called a symmetric lens.A concave-convex shape is called a lune...

    Lenticular cloud
    Lenticular clouds are stationary lens-shaped clouds that form at high altitudes, normally aligned perpendicular to the wind direction. Lenticular clouds can be separated into altocumulus standing lenticularis , stratocumulus standing lenticular , and cirrocumulus standing lenticular...

    ). 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 cumulus
    Cumulus cloud
    Cumulus clouds are a type of cloud with noticeable vertical development and clearly defined edges. Cumulus means "heap" or "pile" in Latin. They are often described as "puffy" or "cotton-like" in appearance. Cumulus clouds may appear alone, in lines, or in clusters...

     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
    Pileus (meteorology)
    A pileus , also called scarf cloud or cap cloud, is a small, horizontal cloud that can appear above a cumulus or cumulonimbus cloud, giving the parent cloud a characteristic "hoodlike" appearance. Pilei tend to change shape rapidly. They are formed by strong updrafts acting upon moist air at lower...

     or 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 cumulus
    Cumulus cloud
    Cumulus clouds are a type of cloud with noticeable vertical development and clearly defined edges. Cumulus means "heap" or "pile" in Latin. They are often described as "puffy" or "cotton-like" in appearance. Cumulus clouds may appear alone, in lines, or in clusters...

     or stratus cloud
    Stratus cloud
    A stratus cloud is a cloud belonging to a class characterized by horizontal layering with a uniform base, as opposed to convective clouds that are as tall or taller than wide . More specifically, the term stratus is used to describe flat, hazy, featureless clouds of low altitude varying in color...

    s in the airmass
    In astronomy, air mass is the optical path length through Earth’s atmosphere for light from a celestial source. As it passes through the atmosphere, light is attenuated by scattering and absorption; the more atmosphere through which it passes, the greater the attenuation. Consequently, celestial...

    , creating a "wave window" or "Foehn gap".


Lee waves provide a possibility for gliders
Glider (sailplane)
A glider or sailplane is a type of glider aircraft used in the sport of gliding. Some gliders, known as motor gliders are used for gliding and soaring as well, but have engines which can, in some cases, be used for take-off or for extending a flight...

 to gain altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...

 or fly long distances when soaring
Gliding is a recreational activity and competitive air sport in which pilots fly unpowered aircraft known as gliders or sailplanes using naturally occurring currents of rising air in the atmosphere to remain airborne. The word soaring is also used for the sport.Gliding as a sport began in the 1920s...

. World record wave flight performances for speed, distance or altitude have been made in the lee of the Sierra Nevada, Alps
The Alps is one of the great mountain range systems of Europe, stretching from Austria and Slovenia in the east through Italy, Switzerland, Liechtenstein and Germany to France in the west....

, Patagonic
Patagonia is a region located in Argentina and Chile, integrating the southernmost section of the Andes mountains to the southwest towards the Pacific ocean and from the east of the cordillera to the valleys it follows south through Colorado River towards Carmen de Patagones in the Atlantic Ocean...

The Andes is the world's longest continental mountain range. It is a continual range of highlands along the western coast of South America. This range is about long, about to wide , and of an average height of about .Along its length, the Andes is split into several ranges, which are separated...

, and Southern Alps
Southern Alps
The Southern Alps is a mountain range extending along much of the length of New Zealand's South Island, reaching its greatest elevations near the island's western side...

 mountain ranges. The Perlan Project
Perlan Project
The Perlan Project is a current research project to fly a sailplane to an altitude of 100,000 feet .-Meteorological Basis of the Project:Standing Mountain waves are a source of rising air used in the sport of soaring...

 is working to demonstrate the viability of climbing above the tropopause
The tropopause is the atmospheric boundary between the troposphere and the stratosphere.-Definition:Going upward from the surface, it is the point where air ceases to cool with height, and becomes almost completely dry...

 in an unpowered glider using lee waves, making the transition into stratospheric
The stratosphere is the second major layer of Earth's atmosphere, just above the troposphere, and below the mesosphere. It is stratified in temperature, with warmer layers higher up and cooler layers farther down. This is in contrast to the troposphere near the Earth's surface, which is cooler...

 standing waves. They did this for the first time on August 30, 2006 in Argentina
Argentina , officially the Argentine Republic , is the second largest country in South America by land area, after Brazil. It is constituted as a federation of 23 provinces and an autonomous city, Buenos Aires...

, climbing to an altitude of 50,671 ft (15,447 m). The Mountain Wave Project
Mountain Wave Project
The Mountain Wave Project pursues global scientific research of gravity waves and associated turbulence. MWP seeks to develop new scientific insights and knowledge through high altitude and record seeking glider flights with the goal of increasing overall flight safety and improving pilot...

 of the Organisation Scientifique et Technique du Vol à Voile
Organisation Scientifique et Technique du Vol à Voile
Organisation Scientifique et Technique du Vol à Voile is a body associated with the FAI Gliding Commission . The FAI IGC oversees the sport of gliding worldwide and is a department of the Fédération Aéronautique Internationale ....

 focusses on analysis and classification of lee waves and associated rotors.

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 aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

 such as balloons, hang gliders and para glider
Paragliding is the recreational and competitive adventure sport of flying paragliders: lightweight, free-flying, foot-launched glider aircraft with no rigid primary structure...

s. It can even be a hazard for large aircraft; the phenomenon is believed responsible for many aviation accidents and incidents
Aviation accidents and incidents
An aviation accident is defined in the Convention on International Civil Aviation Annex 13 as an occurrence associated with the operation of an aircraft which takes place between the time any person boards the aircraft with the intention of flight and all such persons have disembarked, in which a...

 including the in-flight break up of BOAC Flight 911
BOAC flight 911
BOAC Flight 911 was a round-the-world flight operated by British Overseas Airways Corporation.On 5 March 1966, the Boeing 707-436 operating this flight was commanded by Captain Bernard Dobson, 45, from Dorset, an experienced 707 pilot who had been flying these aircraft since November 1960.The...

, a Boeing 707
Boeing 707
The Boeing 707 is a four-engine narrow-body commercial passenger jet airliner developed by Boeing in the early 1950s. Its name is most commonly pronounced as "Seven Oh Seven". The first airline to operate the 707 was Pan American World Airways, inaugurating the type's first commercial flight on...

, near Mt. Fuji, Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

 in 1966, and the in-flight separation of an engine on an Evergreen International Airlines
Evergreen International Airlines
Evergreen International Airlines is a cargo airline based in McMinnville, Oregon, USA. It operates contract freight services, offering charters and scheduled flights, as well as wet lease services. It operates services for the U.S. military and the United States Postal Service, as well as ad hoc...

 Boeing 747
Boeing 747
The Boeing 747 is a wide-body commercial airliner and cargo transport, often referred to by its original nickname, Jumbo Jet, or Queen of the Skies. It is among the world's most recognizable aircraft, and was the first wide-body ever produced...

 cargo jet near Anchorage, Alaska
Anchorage, Alaska
Anchorage is a unified home rule municipality in the southcentral part of the U.S. state of Alaska. It is the northernmost major city in the United States...

 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
Overspeed (aircraft)
Overspeed is the aircraft flight condition when the airspeed or ground speed is greater than a maximum speed, e.g.;*never exceed speed*maximum speed for stability characteristics*maximum operating limit speed*maximum flap extended speed...

 or stall
Stall (flight)
In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases. This occurs when the critical angle of attack of the foil is exceeded...

, resulting in mach tuck
Mach tuck
Mach tuck is an aerodynamic effect, whereby the nose of an aircraft tends to pitch downwards as the airflow around the wing reaches supersonic speeds...

 and loss of control, especially when the aircraft is operated near the "coffin corner
Coffin corner (aviation)
The coffin corner is the altitude at or near which a fast fixed-wing aircraft's stall speed is equal to the critical Mach number, at a given gross weight and G-force loading. At this altitude the airplane becomes nearly impossible to keep in stable flight...


Other varieties of atmospheric waves

There are a variety of distinctive types of waves which form under different atmospheric conditions.
  • Wind shear
    Wind shear
    Wind shear, sometimes referred to as windshear or wind gradient, is a difference in wind speed and direction over a relatively short distance in the atmosphere...

    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 thermal
    A thermal column is a column of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation, and are an example of convection. The sun warms the ground, which in turn warms the air directly above it...

    s 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
    Hydraulic jump
    A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface...

     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 wave
    Rossby wave
    Atmospheric Rossby waves are giant meanders in high-altitude winds that are a major influence on weather.They are not to be confused with oceanic Rossby waves, which move along the thermocline: that is, the boundary between the warm upper layer of the ocean and the cold deeper part of the...

    (or planetary waves) are large-scale motions in the atmosphere whose restoring force is the variation in Coriolis effect with latitude.

Further reading

  • 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.

External links

  • http://www.inglaner.com/meteorologia_onda.htm chronological collection of meteorological data, satpics and cloud images of mountain waves in Bariloche, Argentina. In spanish
  • http://www.mountain-wave-project.com official website
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