WKB approximation in application to acoustic-gravity waves

Einaudi, Franco; Hines, C. O.

doi:10.1029/gm018p0508

Cited by 39 publications

(102 citation statements)

References 13 publications

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“…In that particular study, the waves considered had shorter horizontal wavelengths than those considered here, and were therefore more likely to be ducted because their vertical wavelengths were not so large as those considered here. In contrast to the results discussed here, strong reflection was generally obtained for a range of wave parameters in the work of Hickey [Einaudi and Hines, 1971 ]. We obtain values of R (not shown) which never exceed 0.9 and 1.8 for the W2000 and Z93 waves, respectively (using our nominal winds profiles), implying that the WKB approximation may be a reasonable approximation for the W2000 wave and that it may be a bad approximation for the Z93 wave.…”

Section: Discussioncontrasting

confidence: 90%

Reflection of a long‐period gravity wave observed in the nightglow over Arecibo on May 8–9, 1989?

Hickey¹

2001

J. Geophys. Res.

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Section: Discussioncontrasting

confidence: 90%

Reflection of a long‐period gravity wave observed in the nightglow over Arecibo on May 8–9, 1989?

Hickey¹

2001

J. Geophys. Res.

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“…If the spectral characteristics of the GW source and the background state are known, ray tracing can be a useful tool for studying the propagation of GWs and their influence on the background atmosphere (Jones, 1969;Schoeberl, 1985;Marks and Eckermann, 1995;Ding et al, 2003;VF05;VF06;Broutman and Eckermann, 2012;. Ray tracing is applicable for nonbreaking, small amplitude GWs which propagate in slowly varying background atmospheres (Einaudi and Hines, 1970;VF05). Its can also be applied to the large-amplitude GWs after properly including a scheme to parameterize the effects of GW saturation and/or breaking (Marks and Eckermann, 1995;Vadas and Crowley, 2010;.…”

Section: Liu Et Al: the Momentum Deposition Of Small Amplitude Grmentioning

confidence: 99%

“…Its can also be applied to the large-amplitude GWs after properly including a scheme to parameterize the effects of GW saturation and/or breaking (Marks and Eckermann, 1995;Vadas and Crowley, 2010;. It is important to note that the theoretical basis for ray tracing is the WKB (Wentzel-Kramers-Brillouin) method, which requires the variation of the background atmosphere to be slow relative to the GW vertical wavelength (Pitteway and Hines, 1963;Einaudi and Hines, 1970;Nappo, 2002). For example, in a constant-wind (dissipative) thermosphere, the slowly varying background assumption requires λ z ≤ 4πH (VF05; Vadas, 2007).…”

Section: Liu Et Al: the Momentum Deposition Of Small Amplitude Grmentioning

confidence: 99%

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

Liu

Yue

et al. 2013

Ann. Geophys.

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Abstract. We study the momentum deposition in the thermosphere from the dissipation of small amplitude gravity waves (GWs) within a wave packet using a fully nonlinear two-dimensional compressible numerical model. The model solves the nonlinear propagation and dissipation of a GW packet from the stratosphere into the thermosphere with realistic molecular viscosity and thermal diffusivity for various Prandtl numbers. The numerical simulations are performed for GW packets with initial vertical wavelengths (λ z ) ranging from 5 to 50 km. We show that λ z decreases in time as a GW packet dissipates in the thermosphere, in agreement with the ray trace results of Vadas and Fritts (2005) (VF05). We also find good agreement for the peak height of the momentum flux (z diss ) between our simulations and VF05 for GWs with initial λ z ≤ 2πH in an isothermal, windless background, where H is the density scale height. We also confirm that z diss increases with increasing Prandtl number. We include eddy diffusion in the model, and find that the momentum deposition occurs at lower altitudes and has two separate peaks for GW packets with small initial λ z . We also simulate GW packets in a non-isothermal atmosphere. The net λ z profile is a competition between its decrease from viscosity and its increase from the increasing background temperature. We find that the wave packet disperses more in the non-isothermal atmosphere, and causes changes to the momentum flux and λ z spectra at both early and late times for GW packets with initial λ z ≥ 10 km. These effects are caused by the increase in T in the thermosphere, and the decrease in T near the mesopause.

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“…The gravity waves considered in the present study are within those wavelengths, and we found that a relaxation of the mid-frequency approximation does not change the results (not shown). In order to examine the validity of the WKB approximation, we checked whether the present gravity waves satisfy the criterion of δ ≡ m zz /2 m 3 − 3 m z /4 m 4 1 proposed by Einaudi and Hines (1970). For a dominant wave in our case (a zonal wave with a phase speed of 10 m s −1 ), the maximum value of δ is about 0.26, which is comfortably less than unity.…”

Section: Resultsmentioning

confidence: 86%

Gravity wave reflection and its influence on the consistency of temperature- and wind-based momentum fluxes simulated above Typhoon Ewiniar

Kim

Chun

Preusse³

et al. 2012

Atmos. Chem. Phys.

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Abstract. For a case study of Typhoon Ewiniar performed with a mesoscale model, we compare stratospheric gravity wave (GW) momentum flux determined from temperature variances by applying GW polarization relations and by assuming upward propagating waves, with GW momentum flux calculated from model winds which is considered as a reference. The temperature-based momentum-flux profile exhibits positive biases relative to the reference, which fluctuate significantly with altitude. The vertically-averaged magnitude of the positive biases is about 14 % of the reference momentum flux. We found that this deviation from the reference stems from the interference between upward and downward propagating waves. The downward propagating GWs are due mainly to partial reflections of upward propagating waves at altitudes where the background wind and stability change with height. When the upward and downward propagating waves are decomposed and their momentum fluxes are calculated separately from temperature perturbations, the fraction of the momentum flux arising from the downward propagating waves is about 4.5-8.2 % of that from the upward propagating waves. The net momentum flux of upward and downward propagating GWs agrees well with the reference from the model wind perturbations. The implications of this study for the GW momentum-flux observations from satellites are discussed.

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WKB approximation in application to acoustic-gravity waves

Cited by 39 publications

References 13 publications

Reflection of a long‐period gravity wave observed in the nightglow over Arecibo on May 8–9, 1989?

Reflection of a long‐period gravity wave observed in the nightglow over Arecibo on May 8–9, 1989?

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

Gravity wave reflection and its influence on the consistency of temperature- and wind-based momentum fluxes simulated above Typhoon Ewiniar

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