Atmospheric Gravity Waves

1. Atmospheric Gravity Waves References: 1 “Atmospheric Physics” Andrews, Chapter 5 (5.5) 2 “Introduction to Dynamic Meteorology”, Holton, Chapter 7

2. Examples for Waves http://science.nasa.gov/headlines/y2008/19mar_grits.htm

3. Atmospheric Waves

4. 1200 1000 800 600 0 4e+10 8e+10 360 320 280 240 -4 0 4 8 12 1200 1000 800 600 400 200 300 500 700 900 Evidence for GW in the Thermosphere of Jupiter • Electron density profile • Galileo probe T-profile 1400 T Ne Altitude [km] [m-3] [K] • High stratospheric T-profile • In situ measurements dT/dz • Radio occultations Altitude [km] • Stellar occultations [K/km]

5. Longitudinal wave Compression The oscillation is perpendicular the phase lines Example: Sound wave Transverse wave No compression The oscillation is along the phase lines Example: Gravity wave Transverse and Longitudinal Waves Wave propagation Wave propagation Particle oscillation Particle oscillation

6. Basic parameters • General oscillation: • A – amplitude • lx, ly, lz – wavelength in x, y, z direction respectively • k, l, m - wavenumbers • w=2p/T – frequency of the wave • f – phase of the oscillation • f=constant – phase line (plane)

7. Phase lines • Consider 2D motion (xz-plane). z x,z2 x,z1 x,z0

8. Atmospheric Oscillations Environmental Lapse Rate Colder Altitude Air parcel z0 Adiabatic Lapse Rate Warmer Temperature

9. Simple gravity wave model • Consider a corrugated sheet pulled horizontally at a speed c through a stratified fluid. z q

10. Example: • Wind, c, is blowing over a mountain. • Wave motion will be expected in the air. It is a stationary wave (cp=0 wrt the mountain). • The horizontal phase speed of the wave with respect to the wind will be -c. • The horizontal wavelength of the wave is lx and is set by the wavelength of the topography (mountain). • The horizontal and the vertical wavenumbers of the wave are:

11. General solution and some properties • Displacement eq.: • General solution: • Wave frequency: • Large frequency - small q • Short periods - small q • The largest w is for a vertical phase line (infinitely large vertical wavelength lz) • These waves are stationary with respect to the mountain (cp=0)

12. Particle motion Altitude [km] Distance from the source [km] Propagation of AGW Alexander 2002 - CEDAR

13. Dependence on the wind speed Strong wind Week wind

14. Dependence on horizontal scale of the topography Short wavelengths (large k) q Long wavelengths (small k)

15. lx l q lz Dispersion relation • For a vertically propagating wave m needs to be real. • Therefore w<N. • Internal GW have periods longer than ~5 min in the Earth troposphere.

16. Phase and Group velocity • Dispersion relation Phase velocities: Group velocity:

17. Phase and group velocity • Phase velocity shows the speed and the direction of phase propagation. • Group velocity shows the speed and the direction of energy propagation. • The AGW are dispersive: the phase speed is a function of the wavenumber and the phase speed is equal the group velocity. • In contrast, sound waves are not dispersive. All sound waves propagate at the speed of sound independent of their wavelengths or frequencies and the phase and group velocities are equal.

18. Direction of energy propagation • Homework problem: show that the group velocity vector is perpendicular to the wavenumber vector. • Downward propagating phase lines correspond to upward propagating energy! Energy flow Phase propagation

19. Why Do We Care About GW? • Verticalmomentum and energy transport; • Meridional circulation and heat transport; • Transport of chemical species; • Atmospheric mixing end eddy diffusion; • Quasi-biennial oscillations; • Traveling ionospheric disturbances (TID); • Sporadic ionospheric instabilities: communications; • Air-breaking of satellites - Mars; …

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