Mountain waves(Mountain-induced clouds)

Hydraulic jump or rotor clouds in the Owens ValleyLooking south on east side of Sierras;

photo by glider pilot Robert Symons

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

Lenticular clouds over Lake Tahoe (photo by RGF)

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

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

Lee waves forced by the Appalachians13 April 2007

Lee waves downwind of Rockies17 March 2005

Lee waves in Nevada17 March 2005

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

Background on gravity wavesand pendulum equations

An oscillating parcel in a stable environment

z’ = parcel vertical displacementN = 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 directionsPeriod shorter in more stable environment

Horizontal phase speeds

Still proportionalto N

DTDM animation

input_strfcn_isolated_nowind.txt

Westward wave tilts westwardwith height;

Eastward wave tilts eastwardTilt 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

l2 = Scorer parameter

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

l2 < k2

Narrow mountain

Waves decay w/ z

l2 > k2

Wide mountain

Waves preserved w/ z, mimic mountain shape

Sinusoidal mountain

Isolated ridgeNarrow mountain wide mountain

l2 < k2 l2 > k2

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