Acoustic-Gravity Waves

Figure 2.1: Acoustic-gravity dispersion diagram (courtesy of Paul Cally). Waves are propagating in the acoustic and gravity dominated regimes. Between these, waves are evanescent.

Under the combined forces of pressure and gravity, the two modes remain distinct. Figure 2.1 shows the dispersion relation for waves propagating in the vertical direction (i.e., along the z axis). Acoustic waves propagate for ω > ω_ac, with group and phase velocity greater and less than the sound speed respectively, and approaching zero and infinity at ω_ac respectively. At high frequencies, the waves are purely acoustic. Gravity waves are propagating for ω < ω_ac, with phase and group velocity less than the sound speed. For large k_x, the waves are purely gravitational. The acoustic cut-off is larger than the Brunt-Väisälä frequency by a factor,

which is ~ 1.02 for γ = 5/3. Between the acoustic and gravity dominated regimes, waves are evanescent.