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

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

Atmospheric Waves

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

Transverse and Longitudinal Waves 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 Wave propagation Wave propagation Particle oscillation Particle oscillation

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)

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

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

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

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:

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)

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

Dependence on the wind speed Strong wind Week wind

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

Dispersion relation lx l lz q 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.

Phase and Group velocity Dispersion relation Phase velocities: Group velocity:

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.

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

Why Do We Care About GW? Vertical momentum 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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