Linear Acoustic-gravity Waves Research Articles

Caustics of waves in the thermally conducting, viscous atmosphere

This paper considers waves in the atmospheric as linear acoustic-gravity waves, in which fluid’s buoyancy and compressibility simultaneously serve as restoring forces. Atmosphere is modeled as an inhomogeneous, moving fluid with nearly horizontal winds and gradual variation of its composition, sound speed and wind velocity having representative spatial scales that are large compared to the wavelength. Uniform short-wave asymptotic expansions of the wave field in the presence of a simple caustic are derived and utilized to quantify and compare the effects of wave diffraction and dissipation. Unlike acoustic waves, the geometric, or Berry, phase plays an important role in the caustic asymptotics of acoustic-gravity waves. The uniform asymptotic expansion of acoustic-gravity wave field in the presence of a caustic agrees with known results in the acoustic limit. Away from the caustic on its insonified side, the uniform asymptotic solution reduces to ray-theoretical results. When the source and receiver are located sufficiently far from the caustic, ray-theoretical calculations of the wave absorption are found to be applicable for rays that approach and leave the caustic.

Wentzel–Kramers–Brillouin approximation for atmospheric waves

Ray and Wentzel–Kramers–Brillouin (WKB) approximations have long been important tools in understanding and modelling propagation of atmospheric waves. However, contradictory claims regarding the applicability and uniqueness of the WKB approximation persist in the literature. Here, we consider linear acoustic–gravity waves (AGWs) in a layered atmosphere with horizontal winds. A self-consistent version of the WKB approximation is systematically derived from first principles and compared toad hocapproximations proposed earlier. The parameters of the problem are identified that need to be small to ensure the validity of the WKB approximation. Properties of low-order WKB approximations are discussed in some detail. Contrary to the better-studied cases of acoustic waves and internal gravity waves in the Boussinesq approximation, the WKB solution contains the geometric, or Berry, phase. The Berry phase is generally non-negligible for AGWs in a moving atmosphere. In other words, knowledge of the AGW dispersion relation is not sufficient for calculation of the wave phase.

Verifications of the high-resolution numerical model and polarization relations of atmospheric acoustic-gravity waves

Abstract. Comparisons of amplitudes of wave variations of atmospheric characteristics obtained using direct numerical simulation models with polarization relations given by conventional theories of linear acoustic-gravity waves (AGWs) could be helpful for testing these numerical models. In this study, we performed high-resolution numerical simulations of nonlinear AGW propagation at altitudes 0–500 km from a plane wave forcing at the Earth's surface and compared them with analytical polarization relations of linear AGW theory. After some transition time te (increasing with altitude) subsequent to triggering the wave source, the initial wave pulse disappears and the main spectral components of the wave source dominate. The numbers of numerically simulated and analytical pairs of AGW parameters, which are equal with confidence of 95 %, are largest at altitudes 30–60 km at t > te. At low and high altitudes and at t < te, numbers of equal pairs are smaller, because of the influence of the lower boundary conditions, strong dissipation and AGW transience making substantial inclinations from conditions, assumed in conventional theories of linear nondissipative stationary AGWs in the free atmosphere. Reasonable agreements between simulated and analytical wave parameters satisfying the scope of the limitations of the AGW theory prove the adequacy of the used wave numerical model. Significant differences between numerical and analytical AGW parameters reveal circumstances when analytical theories give substantial errors and numerical simulations of wave fields are required. In addition, direct numerical AGW simulations may be useful tools for testing simplified parameterizations of wave effects in the atmosphere.

Consistent Wentzel-Kramers-Brillouin (WKB) approximation for acoustic-gravity waves in the atmosphere

The ray and WKB approximations have long been important tools of understanding and modeling propagation of atmospheric waves. However, contradictory claims regarding applicability and uniqueness of the WKB approximation persist in the literature. Here, linear acoustic-gravity waves (AGWs) in a layered atmosphere with horizontal winds are considered, and a self-consistent version of the WKB approximation is systematically derived from first principles and compared to ad hoc approximations proposed earlier. Parameters of the problem that need to be small to ensure validity of the WKB approximation are identified. Properties of low-order WKB approximations are discussed in some detail. Contrary to familiar cases of acoustic waves and internal gravity waves in the Boussinesq approximation, the WKB solution contains the geometric, or Berry, phase. Put differently, knowledge of the AGW dispersion relation is not sufficient for calculation of the wave phase. Significance of the Berry phase is illustrated by its effect on resonant frequencies of the atmosphere for vertically propagating waves.

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 (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 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.

Waves in Sunspots: Resonant Transmission and the Adiabatic Coefficient

We investigate linear acoustic-gravity waves in three different semi-empirical model atmospheres of large sunspot umbrae. The sunspot filter theory is applied, that is, the resonant transmission of vertically propagating waves is modelled. The results are compared with observed linear sunspot oscillations. For three umbral models we present the transmission coefficients and the energy density of the oscillations with the maxima of transmission. The height dependence of the adiabatic coefficient (the ratio of specific heats) γ strongly influences the calculated resonance frequencies. The variable γ can explain the observed closely spaced resonance period peaks. The first resonance in the 3 min range is interpreted as a resonance of the upper chromosphere only, while the higher order peaks are resonances of the whole chromosphere.

On three-dimensional acoustic-gravity waves in model non-isothermal atmospheres

The propagation of acoustic-gravity waves is studied in a family of model non-isothermal atmospheres, including temperature profiles with any initial and asymptotic temperature and adjustable maximum temperature gradient. The equation for the vertical velocity of linear acoustic-gravity waves is solved exactly in terms of hypergeometric functions, the wave field being described to all orders in the scattering parameter kL, at all frequencies and distances, including wavelengths comparable to the scale of temperature change and atmospheric layers with a large temperature gradient. It is found that since the temperature is bounded, in the asymptotic regime waves grow in amplitude exponentially and phase increases linearly with altitude. The growth in amplitude is larger than exponential and the phase increases faster than linearly for atmospheres whose temperature increases with altitude, the effect being more marked for high frequency waves in regions of large temperature gradients. The accumulation of these effects leads to a wave field which is equivalent to the isothermal case at asymptotic temperature modified by a constant amplitude factor and phase shift which account for the history of propagation of the wave through the temperature gradients.