mountain waves (mountain-induced clouds). hydraulic jump or rotor clouds in the owens valley looking...
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![Page 1: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/1.jpg)
Mountain waves(Mountain-induced clouds)
![Page 2: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/2.jpg)
![Page 3: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/3.jpg)
Hydraulic jump or rotor clouds in the Owens ValleyLooking south on east side of Sierras;
photo by glider pilot Robert Symons
![Page 4: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/4.jpg)
Lenticular clouds http://www.photolib.noaa.gov/historic/nws/wea00108.htm
![Page 5: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/5.jpg)
Lenticular clouds over Lake Tahoe (photo by RGF)
![Page 6: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/6.jpg)
Lenticular clouds http://www.photolib.noaa.gov/historic/nws/wea00010.htm
![Page 7: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/7.jpg)
Lenticular/cap/banner clouds over Mt. Rainierhttp://www.phototripusa.com/images/rwarfield/rw_3843_12.html
![Page 8: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/8.jpg)
Lee waves forced by the Appalachians13 April 2007
![Page 9: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/9.jpg)
Lee waves downwind of Rockies17 March 2005
![Page 10: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/10.jpg)
Lee waves in Nevada17 March 2005
![Page 11: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/11.jpg)
Lee waves on Marshttp://www.solarviews.com/raw/mars/leewave.gif
![Page 12: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/12.jpg)
Background on gravity wavesand pendulum equations
![Page 13: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/13.jpg)
An oscillating parcel in a stable environment
z’ = parcel vertical displacementN = Brunt-Vaisalla frequency
Assumed solution:wavy in time…
Result:
where
![Page 14: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/14.jpg)
Environmental response to oscillating parcels
Assumed solution wavy in time & space
where
![Page 15: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/15.jpg)
Gravity wave frequency equation
Two waves - opposite directionsPeriod shorter in more stable environment
Horizontal phase speeds
Still proportionalto N
![Page 16: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/16.jpg)
DTDM animation
input_strfcn_isolated_nowind.txt
![Page 17: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/17.jpg)
Westward wave tilts westwardwith height;
Eastward wave tilts eastwardTilt implies vertical propagation
![Page 18: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/18.jpg)
Adding a mean flow (constant w/ height)
Owing to mean flow,one wave speeds up, one slows down
Mountain waves are horizontally stationary gravity waves
![Page 19: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/19.jpg)
Mountain wave analysis
• Adiabatic, Boussinesq, inviscid– But linearize about a mean state with wind, as
well as vertical shear and even curvature shear, so
– Assume locally steady state
![Page 20: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/20.jpg)
Mountain wave equation
l2 = Scorer parameter
![Page 21: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/21.jpg)
Cases to be examined
• Sinusoidal terrain – l2 constant with height – flow with constant
stability and mean wind– l2 variable with height
• Isolated mountain
• Conditions for wave trapping leading to lenticular clouds
![Page 22: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/22.jpg)
l2 < k2
Narrow mountain
Waves decay w/ z
l2 > k2
Wide mountain
Waves preserved w/ z, mimic mountain shape
Sinusoidal mountain
![Page 23: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/23.jpg)
Isolated ridgeNarrow mountain wide mountain
l2 < k2 l2 > k2
![Page 24: Mountain waves (Mountain-induced clouds). Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e4e5503460f94b441f7/html5/thumbnails/24.jpg)
More stable layer below - trapped lee waves& lenticular/lee wave clouds