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. Acous3c 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 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 moZon causes chanGes in the balance between planetary anD relave vorZcity Atmospheric Waves 5. Forced Sta3onary 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 equator 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 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 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 VerZcal 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 Atmosphere First Order Approxima0on stratosphere J troposphere Pole Eq General Circ is the atmospheric response to DifferenZal solar heanG at the surface à There woulD be no circulaon in the stratosphere, à There woulD be no troposphere-stratosphere couplinG è Momentum 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)!!!! .