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

Abstract

[1] 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 (r′), pressure (p′), and temperature (T ′) perturbations. We show how GWs with large vertical wavelengths l z have dramatically different phase and amplitude relations than those with small l z . For zero viscosity, as jl z j increases, the phase between u H ′ and w′ decreases from 0 to $À90 , the phase between u H ′ and T′ decreases from $90 to 0 , and the phase between T ′ and r′ decreases from $180 to 0 for l H ≫ jl z j, where l H 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) r′, T′, w′, and the cross-track wind, can be used to infer a GW's l H , l z , propagation direction, and intrinsic frequency w 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 /r′ 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.Citation: Vadas, S. L., and M. J. Nicolls (2012), The phases and amplitudes of gravity waves propagating and dissipating in the thermosphere: Theory,

Numerical modeling study of the momentum deposition of small amplitude gravity waves in the thermosphere

“…Only GWs with large λ z can propagate deep into the thermosphere ). Eventually, every GW dissipates in the thermosphere (Pitteway and Hines, 1963;Hines, 1973;Richmond, 1978;Hickey and Cole, 1988;Zhang and Yi, 2002;VF05;Walterscheid and Hickey, 2011;Vadas and Nicolls, 2012;Nicolls et al, 2012).…”

Dissipation of acoustic-gravity waves: An asymptotic approach

“…For instance, kinematic viscosity is often assumed to be constant in derivations of dispersion equations of atmospheric waves. [7][8][9][10][11] It is a dubious approach since the kinematic viscosity changes by 5 orders of magnitude between ground level and 200 km altitude. While the assumption of constant shear viscosity would be much more realistic, it does not lead to plane-wave solutions.…”

“…(9) and (10)] should be satisfied, when x 2 d ¼ kg and im þ 1=2h ¼ k; B 2 and B 3 in Eq. (11) should vanish under these conditions. An inspection shows that Eqs.…”

“…Equation (9) relates the wave frequency and wave vector to the material parameters in the background state of the atmosphere and has the meaning of the dispersion equation of AGWs. In alternative derivations [7][8][9][10][11] of the AGW dispersion equations, the kinematic viscosity g 0 /q 0 and the ratios f 0 /q 0 and j 0 /q 0 are assumed to be constant. To reveal the consequences of such an assumption, we now suppose that g 0 /q 0 , f 0 /q 0 , and j 0 /q 0 are slowly varying in the sense that the gradients of these quantities are O(L À1 ).…”

Penetration of internal gravity waveguide modes into the upper atmosphere

“…Notice that waveguide modes have been studied before [Francis, 1973a, b], and the results are being widely used for theoretical works and for interpreting observation of various disturbances, including those in the upper atmosphere [Shibata, Okuzawa, 1983;Afraimovich et al, 2001;Vadas, Liu, 2009;Vadas, Nicolls, 2012;Idrus et al, 2013;Heale et al, 2014;Hedlin, Drob, 2014 et al]. Francis [Francis, 1973a, b] defined dispersion characteristics and vertical structures of waveguide modes.…”