Wentzel–Kramers–Brillouin approximation for atmospheric waves

Godin, Oleg A.

doi:10.1017/jfm.2015.367

Cited by 17 publications

(38 citation statements)

References 67 publications

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“…The terms with d u /d z are inversely proportional to the spatial scale of the altitude dependence of wind velocity. This spatial scale serves as a large parameter in the asymptotic expansions that lead to the ray and Wentzel‐Kramers‐Brillouin (WKB) approximations [ Godin , , ]. Therefore, the terms with d u /d z have no effect on the AGW dispersion relation but will affect the Berry phase and wave amplitude in the ray and WKB approximations [see Godin , , ].…”

Section: Effects Of Earth Rotationmentioning

confidence: 99%

Resonance vibrations of the Ross Ice Shelf and observations of persistent atmospheric waves

Godin

Zabotin

2016

JGR Space Physics

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Recently reported lidar observations have revealed a persistent wave activity in the Antarctic middle and upper atmosphere that has no counterpart in observations at midlatitude and low‐latitude locations. The unusual wave activity suggests a geographically specific source of atmospheric waves with periods of 3–10 h. Here we investigate theoretically the hypothesis that the unusual atmospheric wave activity in Antarctica is generated by the fundamental and low‐order modes of vibrations of the Ross Ice Shelf (RIS). Simple models are developed to describe basic physical properties of resonant vibrations of large ice shelves and their coupling to the atmosphere. Dispersion relation of the long surface waves, which propagate in the floating ice sheet and are responsible for its low‐order resonances, is found to be similar to the dispersion relation of infragravity waves in the ice‐free ocean. The phase speed of the surface waves and the resonant frequencies determine the periods and wave vectors of atmospheric waves that are generated by the RIS resonant oscillations. The altitude‐dependent vertical wavelengths and the periods of the acoustic‐gravity waves in the atmosphere are shown to be sensitive to the physical parameters of the RIS, which can be difficult to measure by other means. Predicted properties of the atmospheric waves prove to be in a remarkable agreement with the key features of the observed persistent wave activity.

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Section: Effects Of Earth Rotationmentioning

confidence: 99%

Resonance vibrations of the Ross Ice Shelf and observations of persistent atmospheric waves

Godin

Zabotin

2016

JGR Space Physics

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“…Equation 1was derived using the WKB approximation, and therefore is appropriate for use in ray tracing when the parameters vary slowly enough [Godin, 2015]. The residue, R, can be used to indicate when ray tracing is valid [Einaudi and Hines, 1970;VF05]:…”

Section: Gw Dissipative Dispersion Relation and Amplitude Decay In Timementioning

confidence: 99%

Neutral wind and density perturbations in the thermosphere created by gravity waves observed by the TIDDBIT sounder

Vadas

Crowley

2017

JGR Space Physics

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In this paper, we study the 10 traveling ionospheric disturbances (TIDs) observed at zobs∼283 km by the TIDDBIT ionospheric sounder on 30 October 2007 at 0400–0700 UT near Wallops Island, USA. These TIDs propagated northwest/northward and were previously found to be secondary gravity waves (GWs) from tropical storm Noel. An instrumented sounding rocket simultaneously measured a large neutral wind peak uH′ with a similar azimuth at z ∼ 325 km. Using the measured TID amplitudes and wave vectors from the TIDDBIT system, together with ion‐neutral theory, GW dissipative polarization relations and ray tracing, we determine the GW neutral horizontal wind and density perturbations as a function of altitude from 220 to 380 km. We find that there is a serious discrepancy between the GW dissipative theory and the observations unless the molecular viscosity, μ, decreases with altitude in the middle to upper thermosphere. Assuming that μ∝trueρ̄q, where trueρ̄ is the density, we find using GW dissipative theory that the GWs could have been observed at zobs and that one or more of the GWs could have caused the uH′ wind peak at z≃325 km if q ∼ 0.67 for z≥220 km. This implies that the kinematic viscosity, ν=μ/trueρ̄, increases less rapidly with altitude for z≥220 km: ν∝1/trueρ̄0.33. This dependence makes sense because as trueρ̄→0, the distance between molecules goes to infinity, which implies no molecular collisions and therefore no molecular viscosity μ.

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“…The resonances are manifested as narrow frequency bands of greatly amplified oscillations and have periods of 3-5 min. Although the resonances are referred to as acoustic resonances, buoyancy effects are not negligible at such frequencies (Gossard and Hooke 1975;Jones and Georges 1976;Godin 2015). In addition to transient responses of the atmosphere to an impulsive excitation, acoustic resonances are prominent in long-term averages of the seismic noise spectrum (Nishida 2014).…”

Section: Introductionmentioning

confidence: 99%

“…Analytic and semi-analytic approaches (Jones and Georges 1976;Tahira 1995;Matsumura et al 2009) to prediction of acoustic resonances often assume vertical propagation of AGWs in the atmosphere and relate occurrence of the resonances to waves reaching an altitude, where their frequency equals the acoustic cutoff frequency (Gossard and Hooke 1975). Any upward propagating atmospheric wave with a finite speed of propagation along the ground surface reaches a turning point, where it travels horizontally, before reaching the cutoff (Hines 1965;Godin 2015). This makes the assumption of vertical propagation questionable.…”

Section: Introductionmentioning

confidence: 99%

“…The sources are modeled as vibrations of the lower boundary of the atmosphere. We apply the consistent Wentzel-Kramers-Brillouin (WKB) approximation (Godin 2015) to study atmospheric resonances, their geographic and temporal variability, and the atmospheric properties that lead to occurrence of the resonances. The asymptotic theory is supplemented by direct numerical solution of the wave equation when necessary.…”

Section: Introductionmentioning

confidence: 99%

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Atmospheric resonances and their coupling to vibrations of the ground and waves in the ocean

Godin

Zabotin

Zabotina

2020

Earth Planets Space

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Observations of the ionosphere with the airglow, GPS-TEC, and HF radar techniques reveal a resonant response of the middle and upper atmosphere to broad-band excitation by earthquakes, volcano eruptions, and convective storms. The resonances occur at such frequencies that an atmospheric wave, which is radiated at the ground level and is reflected from a turning point in the middle or upper atmosphere, upon return to the ground level satisfies boundary conditions on the ground. Using asymptotic and numerical models of atmospheric waves, this paper investigates atmospheric resonances and their excitation by seismic waves and infragravity waves in the ocean. It is found that "buoyancy" resonances with periods up to several hours arise in addition to "acoustic" resonances with periods of about 3-5 min. The acoustic and buoyancy resonances occur, respectively, on the acoustic and gravity branches of the dispersion curve of acoustic-gravity waves. Buoyancy of the atmosphere is important for the resonances of both kinds. Acoustic resonances are found to be sensitive to the temperature profile, especially around mesopause and tropopause, and are predicted to be a seasonal phenomenon in polar atmosphere. Unlike acoustic resonances, buoyancy resonances exhibit high sensitivity to the wind velocity profile and its variations. The resonances correspond to most efficient coupling between the atmosphere and its lower boundary and are promising for detection of such coupling.

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Wentzel–Kramers–Brillouin approximation for atmospheric waves

Cited by 17 publications

References 67 publications

Resonance vibrations of the Ross Ice Shelf and observations of persistent atmospheric waves

Resonance vibrations of the Ross Ice Shelf and observations of persistent atmospheric waves

Neutral wind and density perturbations in the thermosphere created by gravity waves observed by the TIDDBIT sounder

Atmospheric resonances and their coupling to vibrations of the ground and waves in the ocean

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