Intro to Atmospheric Wave Dynamics
ATM 525 Fall 2013 Shallow Water Wave: • h p://www.acs.psu.edu/drussell/Demos/waves/Water-v8.gif
Dispersive vs. Non-dispersive AND Phase vs. Group Velocity • h p://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/Web- further-dispersive.htm
Group velocity vs Phase Speed
Group velocity (solid) phase speed (dashed) Atmospheric Waves
1. Acous c Waves:
Longitudinal Waves à compression/expansion of a fluid e.g., Sound waves Atmospheric Waves
2. Gravity Waves
Restoring force à Buoyancy/stability Assume à Hydrosta c Balance
19 Dec 2005, NASA/MODIS. Gravity waves forming off of Amsterdam Island in the southern Indian Ocean. Atmospheric Waves
3. Interio-Gravity Waves
Gravity waves with sufficiently long periods that allow them to “feel” the rota on of the earth. Atmospheric Waves
4. Rossby Waves Restoring force à N-S gradient of PV Meridional mo on causes changes in the balance between planetary and rela ve vor city Atmospheric Waves
5. Forced Sta onary Planetary Waves Wavelengths > 10,000 km Generated by sta onary features à Mountains, land/ sea contrasts
6. Free Traveling Planetary Waves Wavelengths ~ 10,000 km Generated in the atm, occur at “natural frequencies” Propagate around a la tude band à period ~ days Atmospheric Waves
7. Equatorial Waves Mixed Rossby-Gravity Waves Propagate: • eastward @ frequencies similar to iner o-gravity waves • Westward @ frequencies similar to Rossby waves
Driven by change in sign of COR at the equator e.g., Kelvin waves
Thanks to Kyle MacRitchie h p://www.kylemacritchie.com/equatorial- wave-background/equatorial-wave-theory/
Waves: Barotropic Rossby Waves
δy
ζ’>0 ζ’<0 Φo
d/dt (ζ+f) = 0 meaning (ζ+f)t=0 = (ζ+f)t=1
For a barotropic Rossby Wave ζt=0 = 0 ζ = ?? on a β-plane (f = fo + βy) t=1 ft=0 = fo ft=1 = fo + βδy
ζt=1 = -βδy Waves: Barotropic Rossby Waves
Dispersion rela onship and phase speed Speed with respect to zonal mean wind βk ν ν = uk − where c = β _____(+) 2 2 c − u = − è(-) k + l k k 2 + l2 (+)
2 β If you know beta and the zonal mean wind, you find the sta onary wave k = − s u Waves: Baroclinic Rossby Waves
Baroclinic Rossby Waves on a β–plane conserve QGPV 2 dq d # 2 f ∂ # ∂ψ && = %∇ ψ + f + o %ρ (( = 0 Charney-Drazin Criteria dt dt ρ N 2 ∂z $ ∂z ' $ o ' β 0 < u < f 2 Ver cal propaga on of k 2 + l2 + o sta onary baroclinic Rossby waves only occurs if: ( ) 4N 2H 2 -1 Uc = 28 ms (wave 1) -1 Uc = 16 ms (wave 2) Seasonal Climatology - Lower & Middle Atm
JJA DJF U>U wave 1
U<0 U<0
From the ECMWF/ERA-40 Atlas Lets Consider the Zonal Mean Atmosphere First Order Approxima on
stratosphere J troposphere
Pole Eq General Circ is the atmospheric response to differen al solar hea ng at the surface à There would be no circula on in the stratosphere, à There would be no troposphere-stratosphere coupling è Momentum transfer by waves is an important part of the stratospheric circula on Lets Consider the Zonal Mean Atmosphere
Radia vely determined T for Jan 15 Zonal Mean T for DJF à Actual T difference between the two poles is much smaller ß Departure from radia ve equilibrium in the zonal mean à maintained by eddies (waves)!!!!