Lee wave

In

Strong winds (with wind gusts over 100 miles per hour (160 km/h)) can be created in the foothills of large mountain ranges by mountain waves.[6]^[7][8][9] 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).^[10]

Basic theory

Lee waves are a form of

${\displaystyle N={\sqrt {{g \over \theta _{0}}{d\theta _{0} \over dz}}}}$, where ${\displaystyle \theta _{0}(z)}$ is the vertical profile of potential temperature.

Oscillations tilted off the vertical axis at an angle of ${\displaystyle \phi }$ will occur at a lower frequency of ${\displaystyle N\cos {\phi }}$. 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).^[11][12]

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.^[4] 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 shape of 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
  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.^[4]
• 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.
• airmass
  , creating a "wave window" or "Foehn gap".

Aviation

Lee waves provide a possibility for

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.^[19]

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

Other varieties of atmospheric waves

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

• 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.^[20]

• 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
  Sierra Nevada range^[21]
  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 (or planetary waves) are large-scale motions in the atmosphere whose restoring force is the variation in Coriolis effect with latitude.

See also

• Gravity wave
• Nor'west arch

References

1. ^ On 10 March 1933, German glider pilot Hans Deutschmann (1911–1942) was flying over the Giant Mountains in Silesia when an updraft lifted his plane by a kilometre. The event was observed, and correctly interpreted, by German engineer and glider pilot Wolf Hirth (1900–1959), who wrote about it in: Wolf Hirth, Die hohe Schule des Segelfluges [The advanced school of glider flight] (Berlin, Germany: Klasing & Co., 1933). The phenomenon was subsequently studied by German glider pilot and atmospheric physicist Joachim P. Küttner (1909 -2011) in: Küttner, J. (1938) "Moazagotl und Föhnwelle" (Lenticular clouds and foehn waves), Beiträge zur Physik der Atmosphäre, 25, 79–114, and Kuettner, J. (1959) "The rotor flow in the lee of mountains." GRD [Geophysics Research Directorate] Research Notes No. 6, AFCRC[Air Force Cambridge Research Center]-TN-58-626, ASTIA [Armed Services Technical Information Agency] Document No. AD-208862.
2. ISSN 0744-8996
   .
3. ^ "Article about wave lift". Retrieved 2006-09-28.
4. ^
   ISBN 978-0-936310-10-7
   . 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.
5. doi:10.1175/1520-0434(2003)018<0224:AUHACS>2.0.CO;2
   .
6. doi:10.1175/2008WAF2007096.1
   .
7. doi:10.1175/1087-3562(2003)007<0001:TSAWOC>2.0.CO;2
   .
8. doi:10.1175/1520-0434(1998)013<0702:TSWOSB>2.0.CO;2
   .
9. doi:10.1175/1520-0469(1978)035<0059:ASDWAA>2.0.CO;2
   .
10. ^ Ryan Shadbolt; Joseph Charney; Hannah Fromm (2019). "A mesoscale simulation of a mountain wave wind event associated with the Chimney Tops 2 fire (2016)" (Special Symposium on Mesoscale Meteorological Extremes: Understanding, Prediction, and Projection). American Meteorological Society: 5 pp. {{cite journal}}: Cite journal requires |journal= (help)
11. ISBN 9780122835223
    .
12. ISBN 9781935704256
    .
13. ^ FAI gliding records Archived 2006-12-05 at the Wayback Machine
14. ^ "Fai Record File". Archived from the original on 2015-04-13. Retrieved 2015-01-27.
15. ^ Perlan Project
16. ^ OSTIV-Mountain Wave Project
17. ^ [1] Archived 2016-03-03 at the Wayback Machine – accessed 2009-11-03
18. ISSN 0744-8996
    .
19. ^ NTSB Accident Report AAR-93-06
20. ISBN 978-3-9808838-2-5
    .
21. ^ Observations of Mountain-Induced Rotors and Related Hypotheses: a Review by Joachim Kuettner and Rolf F. Hertenstein

• Alexander, P.; Luna, D.; Llamedo, P.; de la Torre, A. (2010-02-19). "A gravity waves study close to the Andes mountains in Patagonia and Antarctica with GPS radio occultation observations". Annales Geophysicae. 28 (2): 587–595.
  ISSN 0992-7689
  .

Further reading

• Grimshaw, R., (2002). Environmental Stratified Flows. Boston: Kluwer Academic Publishers.
• Jacobson, M., (1999). Fundamentals of Atmospheric Modeling. Cambridge, UK: 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, UK: Cambridge University Press.
• Whiteman, C., (2000). Mountain Meteorology. Oxford, UK: Oxford University Press.

External links

Wikimedia Commons has media related to Orographic waves.

• Mountain Wave Project official website
• Chronological collection of meteorological data, satellite pics and cloud images of mountain waves in Bariloche, Argentina (in Spanish)
• On High Winds and Foehn Warming associated with Mountain-Wave Events in the Western Foothills of the Southern Appalachian Mountains
• An Examination of the Areal Extent of High Winds due to Mountain Waves along the Western Foothills of the Southern Appalachian Mountains
• SOUTHTRAC (Transport and Composition of the Southern Hemisphere Upper Troposphere and Lower Stratosphere) Campaign in Southern Argentina