Mountain waves Mountaininduced clouds Hydraulic jump or rotor

Mountain waves (Mountain-induced clouds)

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

Lenticular clouds http: //www. photolib. noaa. gov/historic/nws/wea 00108. htm

Lenticular clouds over Lake Tahoe (photo by RGF)

Lenticular clouds http: //www. photolib. noaa. gov/historic/nws/wea 00010. htm

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

Lee waves forced by the Appalachians 13 April 2007

Lee waves downwind of Rockies 17 March 2005

Lee waves in Nevada 17 March 2005

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

Background on gravity waves and pendulum equations

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

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

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

DTDM animation input_strfcn_isolated_nowind. txt

Westward wave tilts westward with height; Eastward wave tilts eastward Tilt implies vertical propagation

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

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

Mountain wave equation l 2 = Scorer parameter

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

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

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

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