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

Lenticular clouds over Lake Tahoe (photo by RGF)

Lenticular clouds

Lenticular/cap/banner clouds over Mt. Rainier

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

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

DTDM animation input_strfcn_isolated_nowind.txt

Phase line tilt with height 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

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

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