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

Published online by Cambridge University Press:  23 November 2018

R. Sabatini Open the ORCID record for R. Sabatini [Opens in a new window] ,
O. Marsden ,
C. Bailly  and
O. Gainville
R. Sabatini*
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, Unité mixte de recherche CNRS 5509, École Centrale de Lyon, 69134 Écully CEDEX, France CEA, DAM, DIF, F-91297 Arpajon, France Department of Physical Sciences, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USA
O. Marsden
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, Unité mixte de recherche CNRS 5509, École Centrale de Lyon, 69134 Écully CEDEX, France
C. Bailly
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, Unité mixte de recherche CNRS 5509, École Centrale de Lyon, 69134 Écully CEDEX, France
O. Gainville
Affiliation:
CEA, DAM, DIF, F-91297 Arpajon, France
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Acoustics: Acoustics Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 754 - 789
Copyright
© 2018 Cambridge University Press 

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References

Assink, J., Waxler, R. & Velea, D. 2017 A wide-angle high Mach number modal expansion for infrasound propagation. J. Acoust. Soc. Am. 141 (3), 1781–1792.Google Scholar
Assink, J. D., Le Pichon, A., Blanc, E., Kallel, M. & Khemiri, L. 2014 Evaluation of wind and temperature profiles from ECMWF analysis on two hemispheres using volcanic infrasound. J. Geophys. Res. Atmos. 119, 8659–8683.Google Scholar
Assink, J. D., Waxler, R., Frazier, W. G. & Lonzaga, J. 2013 The estimation of upper atmospheric wind model updates from infrasound data. J. Geophys. Res. Atmos. 118, 10707–10724.Google Scholar
Batchelor, G. K. 2012 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bergmann, P. G. 1946 The wave equation in a medium with a variable index of refraction. J. Acoust. Soc. Am. 17 (4), 329–333.Google Scholar
Berland, J., Bogey, C. & Bailly, C. 2007 High-order, low dispersive and low dissipative explicit schemes for multi-scale and boundary problems. J. Comput. Phys. 224 (2), 637–662.Google Scholar
Berry, A. & Daigle, G. A. 1988 Controlled experiments of the diffraction of sound by a curved surface. J. Acoust. Soc. Am. 83 (6), 2047–2058.Google Scholar
Bertin, M., Millet, C. & Bouche, D. 2014 A low-order reduced model for the long-range propagation of infrasounds in the atmosphere. J. Acoust. Soc. Am. 136, 37–52.Google Scholar
Blanc-Benon, P., Dallois, L. & Juvé, D. 2001 Long-range sound propagation in a turbulent atmosphere within the parabolic approximation. Acta Acust. 87, 659–669.Google Scholar
Bogey, C. & Bailly, C. 2002 Three-dimensional non-reflective boundary conditions for acoustic simulations: far-field formulation and validation test cases. Acta Acust. Unit. Ac. 88, 463–471.Google Scholar
Bogey, C. & Bailly, C. 2004 A family of low dispersive and low dissipative explicit schemes for noise computations. J. Comput. Phys. 194 (1), 194–214.Google Scholar
Bogey, C., Cacqueray, N. D. & Bailly, C. 2009 A shock-capturing methodology based on adaptive spatial filtering for high-order nonlinear computations. J. Comput. Phys. 228, 1447–1465.Google Scholar
Brachet, N., Brown, D., Bras, R. Le, Cansi, Y., Mialle, P. & Coyne, J. 2010 Monitoring the Earth’s atmosphere with the global IMS infrasound network. In Infrasound Monitoring for Atmospheric Studies (ed. Le Pichon, A., Blanc, E. & Hauchecorne, A.), pp. 77–118. Springer.Google Scholar
Candel, S. M. 1977 Numerical solution of conservation equations arising in linear wave theory: application to aeroacoustics. J. Fluid Mech. 83 (3), 465–493.Google Scholar
Chunchuzov, I. P., Kulichkov, S. N. & Firstov, P. P. 2013 On acoustic n-wave reflections from atmospheric layered inhomogeneities. Izv. Atmos. Ocean. Phys. 49 (3), 258–270.Google Scholar
Chunchuzov, I. P., Kulichkov, S. N., Popov, O. E. & Hedlin, M. 2014 Modeling propagation of infrasound signals observed by a dense seismic network. J. Acoust. Soc. Am. 135 (1), 38–48.Google Scholar
Chunchuzov, I. P., Kulichkov, S. N., Popov, O. E., Perepelkin, V. G., Vasilev, A. P., Glushkov, A. I. & Firstov, P. P. 2015 Characteristics of a fine vertical wind-field structure in the stratosphere and lower thermosphere according to infrasonic signals in the zone of acoustic shadow. Izv. Atmos. Ocean. Phys. 51 (1), 57–74.Google Scholar
Chunchuzov, I. P., Kulichkov, S. N., Popov, O. E., Waxler, R. & Assink, J. 2011 Infrasound scattering from atmospheric anisotropic inhomogeneities. Izv. Atmos. Ocean. Phys. 47 (5), 540–557.Google Scholar
Del Pino, S., Després, B., Havé, P., Jourdren, H. & Piserchia, P. F. 2009 3D finite volume simulation of acoustic waves in the earth atmosphere. Comput. Fluids 38, 765–777.Google Scholar
Drob, D. P., Picone, J. M. & Garcés, M. 2003 Global morphology of infrasound propagation. J. Geophys. Res. Atmos. 108 (D21), 4680.Google Scholar
Evers, L. G. & Haak, H. W. 2010 The characteristics of infrasound, its propagation and some early history. In Infrasound Monitoring for Atmospheric Studies (ed. Le Pichon, A., Blanc, E. & Hauchecorne, A.), pp. 3–27. Springer.Google Scholar
Frisk, G. V. 1994 Ocean and Seabed Acoustics. A Theory of Wave Propagation. PTR Prentice Hall.Google Scholar
Gainville, O., Blanc-Benon, P., Blanc, E., Roche, R., Millet, C., Le Piver, F., Despres, B. & Piserchia, P. F. 2010 Misty picture: a unique experiment for the interpretation of the infrasound propagation from large explosive sources. In Infrasound Monitoring for Atmospheric Studies (ed. Le Pichon, A., Blanc, E. & Hauchecorne, A.), pp. 575–598. Springer.Google Scholar
Gallin, L.-J., Rénier, M., Gaudard, E., Farges, T., Marchiano, R. & Coulouvrat, F. 2014 One-way approximation for the simulation of weak shock wave propagation in atmospheric flows. J. Acoust. Soc. Am. 135, 2559–2570.Google Scholar
Godin, O. A. 2002 An effective quiescent medium for sound propagating through an inhomogeneous, moving fluid. J. Acoust. Soc. Am. 112 (4), 1269–1275.Google Scholar
de Groot-Hedlin, C. 2012 Nonlinear synthesis of infrasound propagation through an inhomogeneous, absorbing atmosphere. J. Acoust. Soc. Am. 132, 646–656.Google Scholar
de Groot-Hedlin, C. 2016 Long-range propagation of nonlinear infrasound waves through an absorbing atmosphere. J. Acoust. Soc. Am. 139, 1565–1577.Google Scholar
de Groot-Hedlin, C. 2017 Infrasound propagation in tropospheric ducts and acoustic shadow zones. J. Acoust. Soc. Am. 142 (4), 1816–1827.Google Scholar
de Groot-Hedlin, C., Hedlin, M. A. H. & Walker, K. 2011 Finite difference synthesis of infrasound propagation through a windy, viscous atmosphere: application to a bolide explosion detected by seismic networks. Geophys. J. Intl 185, 305–320.Google Scholar
Inoue, Y. & Yano, T. 1997 Propagation of strongly nonlinear plane N-waves. J. Fluid Mech. 341, 59–76.Google Scholar
Jacobsen, D. A. & Senocak, I. 2013 Multi-level parallelism for incompressible flow computations on GPU clusters. Parallel Comput. 39 (1), 1–20.Google Scholar
Jensen, F. B., Kuperman, W. A., Porter, M. B. & Schmidt, H. 2011 Computational Ocean Acoustics. Springer.Google Scholar
Kulichkov, S. N. 2004 Long-range propagation and scattering of low-frequency sound pulses in the middle atmosphere. Meteorol. Atmos. Phys. 85, 47–60.Google Scholar
Lacanna, G. & Ripepe, M. 2013 Influence of near-source volcano topography on the acoustic wavefield and implication for source modeling. J. Volcanol. Geotherm. Res. 250, 9–18.Google Scholar
Lalande, J.-M., Sèbe, O., Landès, M., Blanc-Benon, P., Matoza, R. S., Le Pichon, A. & Blanc, E. 2012 Infrasound data inversion for atmospheric sounding. Geophys. J. Intl 190, 687–701.Google Scholar
Le Pichon, A., Blanc, E., Drob, D., Lambotte, S., Dessa, X., Lardy, M., Bani, P. & Vergniolle, S. 2006 Infrasound monitoring of volcanoes to probe high-altitude winds. J. Geophys. Res. 110 (D13), 1–12.Google Scholar
Le Pichon, A., Blanc, E. & Hauchecorne, A.(Eds) 2010 Infrasound Monitoring for Atmospheric Studies. Springer Science + Business Media.Google Scholar
Le Pichon, A., Ceranna, L. & Vergoz, J. 2012 Incorporating numerical modeling into estimates of the detection capabilities of the IMS infrasound network. J. Geophys. Res. 117 (D5).Google Scholar
Lekner, J. 1987 Theory of Reflection of Electromagnetic and Particle Waves. Springer Science + Business Media.Google Scholar
Lingevitch, J. F., Collins, M. D. & Siegmann, W. L. 1999 Parabolic equations for gravity and acousto-gravity waves. J. Acoust. Soc. Am. 105, 3049–3056.Google Scholar
Lonzaga, J. B., Waxler, R. M., Assink, J. D. & Talmadge, C. L. 2015 Modelling waveforms of infrasound arrivals from impulsive sources using weakly nonlinear ray theory. Geophys. J. Intl 200, 1347–1361.Google Scholar
Marchiano, R., Coulouvrat, F. & Grenon, R. 2003 Numerical simulation of shock wave focusing at fold caustics, with application to sonic boom. J. Acoust. Soc. Am. 114 (4), 1758–1770.Google Scholar
Marsden, O., Bailly, C. & Bogey, C. 2014 A study of infrasound propagation based on high-order finite difference solutions of the Navier–Stokes equations. J. Acoust. Soc. Am. 135, 1083–1095.Google Scholar
Ostashev, V. E., Salomons, E. M., Clifford, S. F., Lataitis, R. J., Wilson, D. K., Blanc-Benon, P. & Juvé, D. 2001 Sound propagation in a turbulent atmosphere near the ground: a parabolic equation approach. J. Acoust. Soc. Am. 109, 1894–1908.Google Scholar
Pierce, A. D. 1985 Acoustics: An Introduction to Its Physical Principles and Applications. Acoustical Society of America.Google Scholar
Pierce, A. D. 1990 Wave equation for sound in fluids with unsteady inhomogeneous flow. J. Acoust. Soc. Am. 87 (6), 2292–2299.Google Scholar
Rogers, P. H. & Gardner, J. H. 1980 Propagation of sonic booms in the thermosphere. J. Acoust. Soc. Am. 67 (1), 78–91.Google Scholar
Sabatini, R. & Bailly, C. 2015 Numerical algorithm for computing acoustic and vortical spatial instability waves. AIAA J. 53 (3), 692–702.Google Scholar
Sabatini, R., Marsden, O., Bailly, C. & Bogey, C. 2016a A numerical study of nonlinear infrasound propagation in a windy atmosphere. J. Acoust. Soc. Am. 140, 641–656.Google Scholar
Sabatini, R., Marsden, O., Bailly, C. & Gainville, O. 2015 Numerical simulation of infrasound propagation in the earth’s atmosphere: study of a stratospherical arrival pair. AIP Conf. Proc. 1685 (1), 090002.Google Scholar
Sabatini, R., Marsden, O., Bailly, C. & Gainville, O. 2016b Characterization of absorption and non-linear effects in infrasound propagation using an augmented Burgers’ equation. Geophys. J. Intl 207, 1432–1445.Google Scholar
Salomons, E. M. 1998 Caustic diffraction fields in a downward refracting atmosphere. J. Acoust. Soc. Am. 104 (6), 3259–3272.Google Scholar
Salomons, E. M., Blumrich, R. & Heimann, D. 2002 Eulerian time-domain model for sound propagation over a finite-impedance ground surface: comparison with frequency-domain models. Acta Acust. Unit. Ac. 88, 483–492.Google Scholar
Scott, J. F., Blanc-Benon, P. & Gainville, O. 2017 Weakly nonlinear propagation of small-wavelength, impulsive acoustic waves in a general atmosphere. Wave Motion 72, 41–61.Google Scholar
Sutherland, L. C. & Bass, H. E. 2004 Atmospheric absorption in the atmosphere up to 160 km. J. Acoust. Soc. Am. 115 (3), 1012–1032.Google Scholar
Sutherland, L. C. & Bass, H. E. 2006 Erratum: Atmospheric absorption in the atmosphere up to 160 km. J. Acoust. Soc. Am. 120 (5), 2985.Google Scholar
Waxler, R. 2002 A vertical eigenfunction expansion for the propagation of sound in a downward-refracting atmosphere over a complex impedance plane. J. Acoust. Soc. Am. 112, 2540–2552.Google Scholar
Waxler, R. 2004 Modal expansions for sound propagation in the nocturnal boundary layer. J. Acoust. Soc. Am. 115, 1437–1448.Google Scholar
Waxler, R., Assink, J. & Velea, D. 2017 Modal expansions for infrasound propagation and their implications for ground-to-ground propagation. J. Acoust. Soc. Am. 141 (2), 1290–1307.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley & Sons.Google Scholar