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

• Published in: Journal of Geophysical Research: Space Physics Vol. 117; no. A5
• Main Authors: Vadas, S. L., Nicolls, M. J.
• Format: Journal Article
• Language: English
• Published: Washington, DC Blackwell Publishing Ltd 01.05.2012; American Geophysical Union
• Subjects: acoustic-gravity waves; Acoustics; Atmospheric sciences; dissipation; Earth sciences; Earth, ocean, space; Exact sciences and technology; Gravity waves; Theoretical physics; thermosphere; Wave crest; Wavelengths; United States; Alaska; USA, Alaska; altitude; North America; acoustical waves; amplitude; Neutral wind; temperature; Height; polarization; wavelength; density; high frequency; satellite measurements; Satellite observation; Perturbation; pressure; velocity; trajectory; in situ; phase shift; viscosity; propagation; Gravity wave; Wave packet; three-dimensional models; dispersion; theory
• ISSN: 0148-0227; 2169-9380; 2156-2202; 2169-9402
• DOI: 10.1029/2011JA017426

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 (uH′) and vertical (w′) velocity, density (ρ′), pressure (p′), and temperature (T′) perturbations. We show how GWs with large vertical wavelengths λz have dramatically different phase and amplitude relations than those with small λz. For zero viscosity, as ∣λz∣ increases, the phase between uH′ and w′ decreases from 0 to ∼−90°, the phase between uH′ and T′ decreases from ∼90 to 0°, and the phase between T′ and ρ′ decreases from ∼180 to 0° for λH ≫ ∣λz∣, where λH is the horizontal wavelength. This effect lessens substantially with increasing altitudes, primarily because the density scale height H 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 λH, λz, propagation direction, and intrinsic frequency ωIr. 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. Key Points Determine the polarization and dispersion relations of dissipating gravity waves Show how the phases and amplitudes change as a gravity wave dissipates Delineate the method for use with in situ satellite measurements