Time-Dependent Propagation of Tsunami-Generated Acoustic–Gravity Waves in the Atmosphere

Abstract Tsunami-generated linear acoustic–gravity waves in the atmosphere with altitude-dependent vertical stratification and horizontal background winds are studied with the long-term goal of real-time tsunami warning. The initial-value problem is examined using Fourier–Laplace transforms to investigate the time dependence and to compare the cases of anelastic and compressible atmospheres. The approach includes formulating the linear propagation of acoustic–gravity waves in the vertical, solving the vertical displacement of waves and pressure perturbations numerically as a set of coupled ODEs in the Fourier–Laplace domain, and employing den Iseger’s algorithm to carry out a fast and accurate numerical inverse Laplace transform. Results are presented for three cases with different atmospheric and tsunami profiles. Horizontal background winds enhance wave advection in the horizontal but hinder the vertical transmission of internal waves through the whole atmosphere. The effect of compressibility is significant. The rescaled vertical displacement of internal waves at 100-km altitude shows an arrival at the early stage of wave development due to the acoustic branch that is not present in the anelastic case. The long-term displacement also shows an O(1) difference between the compressible and anelastic results for the cases with uniform and realistic stratification. Compressibility hence affects both the speed and amplitude of energy transmitted to the upper atmosphere because of fast acoustic waves.

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Wentzel–Kramers–Brillouin approximation for atmospheric waves

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.367 ◽

2015 ◽

Vol 777 ◽

pp. 260-290 ◽

Cited By ~ 8

Author(s):

Oleg A. Godin

Keyword(s):

Gravity Waves ◽

Acoustic Waves ◽

Ad Hoc ◽

Berry Phase ◽

Boussinesq Approximation ◽

Internal Gravity Waves ◽

Wkb Approximation ◽

Approximation Properties ◽

Atmospheric Waves ◽

Acoustic Gravity 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 to ad hoc approximations 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.

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Transmission of acoustic-gravity waves through gas–liquid interfaces

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.336 ◽

2012 ◽

Vol 709 ◽

pp. 313-340 ◽

Cited By ~ 10

Author(s):

Oleg A. Godin ◽

Iosif M. Fuks

Keyword(s):

Gravity Waves ◽

Acoustic Waves ◽

Low Frequency ◽

Paper Analysis ◽

Liquid Interfaces ◽

Power Flux ◽

Acoustic Gravity Waves ◽

Restoring Forces ◽

Anomalous Transparency ◽

Diffraction Effects

AbstractIt was demonstrated recently that gas–liquid interfaces, which are usually almost perfect reflectors of acoustic waves, become anomalously transparent, and the power flux in the wave transmitted into the gas increases dramatically, when a compact sound source in the liquid approaches the interface within a fraction of the wavelength (Godin, Phys. Rev. Lett., vol. 97, 2006b, 164301). Powerful underwater explosions and certain natural sources, such as underwater landslides, generate very low-frequency waves in water and air, for which fluid buoyancy and compressibility simultaneously serve as restoring forces. In this paper, analysis of sound transmission through gas–liquid interfaces is extended to acoustic-gravity waves (AGWs) and applied to the air–water interface. It is found that, as for sound, the interface becomes anomalously transparent for sufficiently shallow compact sources of AGWs. Depending on the source type, the increase of a wave power flux into gas due to diffraction effects can reach several orders of magnitude. The physical mechanisms responsible for the anomalous transparency are discussed. Excitation of an interface wave by a point source in the liquid is shown to be an important channel of AGW transmission into the gas, which has no counterpart in the case of sound.

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Radiation of acoustic and gravity waves and propagation of boundary waves in the stratified fluid from a time-varying bottom boundary

Journal of Fluid Mechanics ◽

10.1017/s0022112009005953 ◽

2009 ◽

Vol 627 ◽

pp. 361-377 ◽

Cited By ~ 19

Author(s):

SHINGO WATADA

Keyword(s):

Gravity Waves ◽

Energy Flow ◽

Surface Deformation ◽

Fluid Pressure ◽

Vertical Displacement ◽

Bottom Surface ◽

Time Varying ◽

Bottom Boundary ◽

Acoustic Gravity Waves ◽

Propagating Waves

Energy flow and radiation of linearized acoustic–gravity waves and propagation of boundary waves in a gravitationally stratified isothermal compressible inviscid semi-infinite fluid from a time-varying bottom boundary are investigated in the frequency–wavenumber domain. Impedance Z, the ratio of the bottom vertical displacement to the fluid pressure above it, is a function of the frequency and horizontal wavenumber (ω, k) of the bottom boundary undulation. The amplitude and phase of Z at the bottom boundary divide the (ω, k) coordinates into wave-type regimes. In contrast to the pure acoustic or gravity wave case, the phase of Z is continuous but changes quickly across the regime boundaries between the propagating waves and trapped waves at the bottom, except for the Lamb wave branch along which the amplitude is infinite and across which the phase jumps by π. The phase of Z determines the efficiency of the work against the fluid by the deforming bottom boundary, showing reduced upward wave-energy flow from the bottom near the regime boundaries in which the phase of Z approaches ±π/2. For precise modelling of pressure waves and the energy flow of acoustic and gravity waves in the fluid originating from a time-dependent bottom-surface deformation with an apparent phase velocity comparable to the speed of sound in the fluid, it is necessary to include the dependency on (ω, k) of impedance Z.

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Ground-based acoustic parametric generator impact on the atmosphere and ionosphere in an active experiment

Annales Geophysicae ◽

10.5194/angeo-35-53-2017 ◽

2017 ◽

Vol 35 (1) ◽

pp. 53-70 ◽

Cited By ~ 4

Author(s):

Yuriy G. Rapoport ◽

Oleg K. Cheremnykh ◽

Volodymyr V. Koshovy ◽

Mykola O. Melnik ◽

Oleh L. Ivantyshyn ◽

...

Keyword(s):

Acoustic Wave ◽

Gravity Waves ◽

Acoustic Waves ◽

Difference Frequency ◽

Sound Waves ◽

Acoustic Gravity Waves ◽

Active Experiment ◽

The Difference ◽

The Impact ◽

Sound Generator

Abstract. We develop theoretical basics of active experiments with two beams of acoustic waves, radiated by a ground-based sound generator. These beams are transformed into atmospheric acoustic gravity waves (AGWs), which have parameters that enable them to penetrate to the altitudes of the ionospheric E and F regions where they influence the electron concentration of the ionosphere. Acoustic waves are generated by the ground-based parametric sound generator (PSG) at the two close frequencies. The main idea of the experiment is to design the output parameters of the PSG to build a cascade scheme of nonlinear wave frequency downshift transformations to provide the necessary conditions for their vertical propagation and to enable penetration to ionospheric altitudes. The PSG generates sound waves (SWs) with frequencies f1 = 600 and f2 = 625 Hz and large amplitudes (100–420 m s−1). Each of these waves is modulated with the frequency of 0.016 Hz. The novelty of the proposed analytical–numerical model is due to simultaneous accounting for nonlinearity, diffraction, losses, and dispersion and inclusion of the two-stage transformation (1) of the initial acoustic waves to the acoustic wave with the difference frequency Δf = f2 − f1 in the altitude ranges 0–0.1 km, in the strongly nonlinear regime, and (2) of the acoustic wave with the difference frequency to atmospheric acoustic gravity waves with the modulational frequency in the altitude ranges 0.1–20 km, which then reach the altitudes of the ionospheric E and F regions, in a practically linear regime. AGWs, nonlinearly transformed from the sound waves, launched by the two-frequency ground-based sound generator can increase the transparency of the ionosphere for the electromagnetic waves in HF (MHz) and VLF (kHz) ranges. The developed theoretical model can be used for interpreting an active experiment that includes the PSG impact on the atmosphere–ionosphere system, measurements of electromagnetic and acoustic fields, study of the variations in ionospheric transparency for the radio emissions from galactic radio sources, optical measurements, and the impact on atmospheric aerosols. The proposed approach can be useful for better understanding the mechanism of the acoustic channel of seismo-ionospheric coupling.

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Acoustic-gravity modons in the atmosphere

Annales Geophysicae ◽

10.1007/s00585-995-0973-3 ◽

1995 ◽

Vol 13 (9) ◽

pp. 973-975 ◽

Cited By ~ 20

Author(s):

L. Stenflo ◽

Y. A. Stepanyants

Keyword(s):

Internal Waves ◽

Gravity Waves ◽

Low Frequency ◽

Horizontal Direction ◽

Acoustic Gravity Waves ◽

Dipole Vortex ◽

Vortex Solutions

Abstract. It is shown that the equations governing low-frequency acoustic-gravity waves in a stable stratified atmosphere can have localized dipole-vortex solutions (modons). They propagate in the horizontal direction with a speed that is larger than that of all possible linear internal waves.

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Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere (part III: for arbitrary Prandtl number)

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171297000471 ◽

1997 ◽

Vol 20 (2) ◽

pp. 367-374 ◽

Cited By ~ 1

Author(s):

Hadi Yahya Alkahby

Keyword(s):

Prandtl Number ◽

Gravity Waves ◽

Acoustic Waves ◽

Thermal Conduction ◽

Thermal Condition ◽

Acoustic Gravity Waves ◽

Representative Model ◽

The Subject ◽

Thermally Conducting ◽

Isothermal Atmosphere

In this paper we will investigate the combined effect of Newtonian cooling, viscosity and thermal condition on upward propagating acoustic waves in an isothermal atmosphere. In part one of this series we considered the case of large Prandtl number, while in part two we investigated the case of small Prandtl number. In those parts we examined only the limiting cases, i.e. the cases of small and large Prandtl number, and it is more interesting to consider the case of arbitrary Prandtl number, which is the subject of this paper, because it is a better representative model. It is shown that if the Newtonian cooling coefficient is small compared to the frequency of the wave, the effect of the thermal conduction is dominated by that of the viscosity. Moreover, the solution can be written as a linear combination of an upward and a downward propagating wave with equal wavelengths and equal damping factors. On the other hand if Newtonian cooling is large compared to the frequency of the wave the effect of thermal conduction will be eliminated completely and the atmosphere will be transformed from the adiabatic form to an isothermal. In addition, all the linear relations among the perturbations quantities will be modified. It follows from the above conclusions and those of the first two parts, that when the effect of Newtonian cooling is negligible thermal conduction influences the propagation of the wave only in the case of small Prandtl number.

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