The phases and amplitudes of gravity waves propagating and dissipating in the thermosphere: Theory

We derive the high‐frequency, compressible, dissipative dispersion and polarization relations for linear acoustic‐gravity waves (GWs) and acoustic waves (AWs) in a single‐species thermosphere. The wave amplitudes depend explicitly on time, consistent with a wave packet approach. We investigate the phase shifts and amplitude ratios between the GW components, which include the horizontal ( u H ′) and vertical ( w ′) velocity, density ( ρ ′), pressure ( p ′), and temperature ( T ′) perturbations. We show how GWs with large vertical wavelengths λ z have dramatically different phase and amplitude relations than those with small λ z . For zero viscosity, as ∣ λ z ∣ increases, the phase between u H ′ and w ′ decreases from 0 to ∼−90°, the phase between u H ′ and T ′ decreases from ∼90 to 0°, and the phase between T ′ and ρ ′ decreases from ∼180 to 0° for λ H ≫ ∣ λ z ∣, where λ H is the horizontal wavelength. This effect lessens substantially with increasing altitudes, primarily because the density scale height increases. We show how in‐situ satellite measurements of either (1) the 3D neutral wind or (2) ρ ′, T ′, w ′, and the cross‐track wind, can be used to infer a GW's λ H , λ z , propagation direction, and intrinsic frequency ω Ir . We apply this theory to a GW observed by the DE2 satellite. We find a significant region of overlap in parameter space for 5 independent constraints (i.e., T ′ 0 / ρ ′ 0 , the phase shift between T ′ and w ′, and the distance between wave crests), which provides a good test and validation of this theory. In a companion paper, we apply this theory to ground‐based observations of a GW over Alaska.