Intro to Atmospheric Dynamics

ATM 525 Fall 2013 Shallow Water Wave: • hp://www.acs.psu.edu/drussell/Demos/waves/Water-v8.gif

Dispersive vs. Non-dispersive AND Phase vs. Group Velocity • hp://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

1. Acousc Waves:

Longitudinal Waves à compression/expansion of a fluid e.g., waves Atmospheric Waves

2. Gravity Waves

Restoring à Buoyancy/stability Assume à Hydrostac 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 rotaon of the earth. Atmospheric Waves

4. Rossby Waves Restoring force à N-S gradient of PV Meridional moon causes changes in the balance between planetary and relave vorcity Atmospheric Waves

5. Forced Staonary Planetary Waves Wavelengths > 10,000 km Generated by staonary 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 latude band à period ~ days Atmospheric Waves

7. Equatorial Waves Mixed Rossby-Gravity Waves Propagate: • eastward @ frequencies similar to inero-gravity waves • Westward @ frequencies similar to Rossby waves

Driven by change in sign of COR at the e.g., Kelvin waves

Thanks to Kyle MacRitchie hp://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 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 relaonship 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 staonary 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 Vercal propagaon of k 2 + l2 + o staonary 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 First Order Approximaon

J troposphere

Pole Eq General Circ is the atmospheric response to differenal solar heang at the surface à There would be no circulaon in the stratosphere, à There would be no troposphere-stratosphere coupling è transfer by waves is an important part of the stratospheric circulaon Lets Consider the Zonal Mean Atmosphere

Radiavely determined T for Jan 15 Zonal Mean T for DJF à Actual T difference between the two poles is much smaller ß Departure from radiave equilibrium in the zonal mean à maintained by eddies (waves)!!!!