1. Mountain waves (Mountain-induced clouds)

3. Hydraulic jump or rotor clouds in the Owens Valley Looking south on east side of Sierras; photo by glider pilot Robert Symons

4. Lenticular clouds http://www.photolib.noaa.gov/historic/nws/wea00108.htm

5. Lenticular clouds over Lake Tahoe (photo by RGF)

6. Lenticular clouds http://www.photolib.noaa.gov/historic/nws/wea00010.htm

7. Lenticular/cap/banner clouds over Mt. Rainier http://www.phototripusa.com/images/rwarfield/rw_3843_12.html

8. Lee waves forced by the Appalachians 13 April 2007

9. Lee waves downwind of Rockies 17 March 2005

10. Lee waves in Nevada 17 March 2005

11. Lee waves on Mars http://www.solarviews.com/raw/mars/leewave.gif

12. Background on gravity waves and pendulum equations

13. An oscillating parcel in a stable environment z’ = parcel vertical displacement N = Brunt-Vaisalla frequency Assumed solution: wavy in time… Result: where

14. Environmental response to oscillating parcels Assumed solution wavy in time & space where

15. Gravity wave frequency equation Two waves - opposite directions Period shorter in more stable environment Horizontal phase speeds Still proportional to N

16. DTDM animation input_strfcn_isolated_nowind.txt

17. Phase line tilt with height Westward wave tilts westward with height; Eastward wave tilts eastward Tilt implies vertical propagation

18. 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

19. 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

20. Mountain wave equation l 2 = Scorer parameter

21. Cases to be examined Sinusoidal terrain –l 2 constant with height – flow with constant stability and mean wind –l 2 variable with height Isolated mountain Conditions for wave trapping leading to lenticular clouds

22. l 2 < k 2 Narrow mountain Waves decay w/ z l 2 > k 2 Wide mountain Waves preserved w/ z, mimic mountain shape Sinusoidal mountain

23. Isolated ridge Narrow mountain wide mountain l 2 < k 2 l 2 > k 2

24. More stable layer below - trapped lee waves & lenticular/lee wave clouds