A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations

Marsden, Olivier; Bogey, Christophe; Bailly, Christophe

doi:10.1121/1.4864793

Cited by 34 publications

(24 citation statements)

References 45 publications

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“…The description of the solver is detailed in Ref. 25 and summarized hereafter. Explicit finite differences based on 11-point stencils are used to compute the spatial derivatives involved in the Navier-Stokes equations.…”

Section: Methodsmentioning

confidence: 99%

Irregular reflection of weak acoustic shock pulses on rigid boundaries

Desjouy

Ollivier

Marsden³

et al. 2016

Journal of the Acoustical Society of America

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The reflection of weak shockwaves on rigid boundaries at grazing angles was studied in different geometrical configurations. It was shown that even in the case of weak shocks, irregular reflection of N-waves can lead to the formation of a three shocks pattern with a Mach stem, a triple point above the rigid surface and an angle reflection which differs from the incident one. Experiments were done using spark generated spherical shock waves with peak pressure lower than 10 kPa. Reflection patterns of shocks were obtained using a Schlieren visualization setup. Both regular and irregular regimes of reflection were observed. Numerical simulations of the nonlinear propagation were also performed. They were based on the high-order finite difference solution of the two dimensional Navier-Stokes equations. Optical measurements were compared with the results of simulations. Both experimental and numerical results showed the growth of the Mach stem with the distance of propagation. In the case of a randomly or periodically rough surface, the Mach stem is shorter, and nonlinear interactions between reflected waves occurs. [This work was supported by the Labex Centre Lyonnais d’Acoustique of Université de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ANR-11-IDEX-0007).]

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Section: Methodsmentioning

confidence: 99%

Irregular reflection of weak acoustic shock pulses on rigid boundaries

Desjouy

Ollivier

Marsden³

et al. 2016

Journal of the Acoustical Society of America

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“…The fluid flow is described by the conservative variables

boldU = {false[ρ, ρ u_{1}, ρ u_{2}, ρ false(e + u_{1}^{2} false/ 2 + u_{2}^{2} false/ 2 false) false]}^{T}

, where u i is the component of the velocity vector in the direction x i , for i = 1,2, and e indicates the specific internal energy. The evolution of the conservative variables is finally governed by the 2‐D Navier‐Stokes equations, as formulated by Marsden et al () and Sabatini et al ().…”

Section: Problem Definition and Case Studiesmentioning

confidence: 99%

“…In the last three decades, numerous studies on the propagation and breaking of GWs generated by different sources have been conducted by performing 2‐D and 3‐D simulations of the Navier‐Stokes equations (e.g., Fritts & Alexander, ; Snively & Pasko, , and references therein). The use of the full set of the fluid dynamic equations to investigate the 2‐D and 3‐D propagation of IAWs is a relatively recent subject of research, made feasible by advances of computational capabilities (de Groot‐Hedlin, , , ; Marsden et al, ; Sabatini et al, , ; Zettergren & Snively, , ). In this work, the propagation of an IAW through the small‐scale inhomogeneities induced by the breaking of a MW is analyzed by direct numerical simulations of the 2‐D Navier‐Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Modeling of the Propagation of Infrasonic Acoustic Waves Through the Turbulent Field Generated by the Breaking of Mountain Gravity Waves

Sabatini

Snively

Bailly

et al. 2019

Geophysical Research Letters

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The nonlinear propagation of low‐frequency acoustic waves through the turbulent fluctuations induced by breaking mountain gravity waves is investigated via 2‐D numerical simulations of the Navier‐Stokes equations, to understand the effects of atmospheric dynamics on ground‐based infrasound measurements. Emphasis is placed on acoustic signals of frequency around 0.1 Hz, traveling through tens‐of‐kilometers‐scale gravity waves and subkilometer‐scale turbulence. The sensitivity of the infrasonic phases to small‐scale fluctuations is found to depend on the altitudes through which they are refracted toward the Earth. For the considered cases, the dynamics in the stratosphere impact the refracting acoustic waves to a greater extent than those in the thermosphere. This work clearly demonstrates the need for accurate descriptions of the effects of atmospheric dynamics on acoustic propagation, such as here captured by the full set of fluid dynamic equations, as well as of the subsequent effects on measured signals.

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“…However, their accurate resolution is still a challenging task and requires well-suited numerical techniques. To the best of the authors' knowledge, numerical simulations of such equations have generally been performed in two dimensions, on Cartesian grids (de Groot-Hedlin, Hedlin & Walker 2011; Marsden, Bailly & Bogey 2014;Sabatini et al , 2016a or in cylindrical coordinates under the hypothesis of axial symmetry (de Groot-Hedlin 2012, 2016). A three-dimensional computation, based on simplified equations, was carried out by Del Pino et al (2009), however without including nonlinear, viscous and thermal conduction effects.…”

Section: Numerical Modelling Of Infrasound Propagationmentioning

confidence: 99%

“…where p = p −p is the pressure perturbation, ρ = ρ −ρ is the density perturbation, τ ij is the viscous stress tensor, q i is the heat flux, Λ ρ and Λ ρe t are two source-forcing terms and δ ij is the Kronecker symbol. Note that, in keeping with Marsden et al (2014), the hydrostatic equilibrium condition dp/dx 3 = −ρg is here subtracted from the Navier-Stokes equations in order to bypass its high-precision computation at each time step. Moreover, because of the non-vanishing terms ∂τ 12 /∂x 1 and ∂q 2 /∂x 2 , the initial undisturbed atmosphere, determined from experimental data, is not fully consistent with the Navier-Stokes equations and thus would tend to evolve in time.…”

Section: Governing Equations Sound Propagation Is Governed By the Thrmentioning

confidence: 99%

Three-dimensional direct numerical simulation of infrasound propagation in the Earth’s atmosphere

et al. 2018

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A direct numerical simulation of the three-dimensional unsteady compressible Navier–Stokes equations is performed to investigate the infrasonic field generated in a realistic atmosphere by an explosive source placed at ground level. To this end, a high-order finite-difference method originally developed for aeroacoustic applications is employed. The maximum overpressure and the main frequency of the signal recorded at 4 km distance from the source location are about 4000 Pa and 0.2 Hz, respectively. The atmosphere is parametrized as a vertically stratified medium, constructed by specifying vertical profiles of the temperature and the horizontal wind which reproduce measurements. The computation is carried out up to 140 km altitude and 450 km range. The goal of the present paper is twofold. On the one hand, the feasibility of using a direct numerical simulation of the three-dimensional fluid dynamic equations for the detailed description of long-range propagation in the atmosphere is proven. On the other hand, a physical analysis of the infrasonic field is realized. In particular, great attention is directed towards some important phenomena which are not taken into account or not well predicted by classical propagation models. To begin with, the present study clearly demonstrates that the weakly nonlinear ray theory may lead to an incorrect evaluation of the waveform distortion of high-amplitude waves propagating towards the lower thermosphere. In addition, signals recorded in the shadow zones are investigated. In this regard, the influence on the acoustic field of temperature and wind inhomogeneities of length scale comparable with the acoustic wavelength is analysed. The role of diffraction at the thermospheric caustic is finally examined and it is pointed out that the amplitude of the source may have a strong impact on the length of the shadow zone.

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A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations

Cited by 34 publications

References 45 publications

Irregular reflection of weak acoustic shock pulses on rigid boundaries

Irregular reflection of weak acoustic shock pulses on rigid boundaries

Numerical Modeling of the Propagation of Infrasonic Acoustic Waves Through the Turbulent Field Generated by the Breaking of Mountain Gravity Waves

Three-dimensional direct numerical simulation of infrasound propagation in the Earth’s atmosphere

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