Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-10T05:55:19.476Z Has data issue: false hasContentIssue false
  • English
  • Français

New model for acoustic waves propagating through a vortical flow

Published online by Cambridge University Press:  23 June 2017

Jim Thomas Open the ORCID record for Jim Thomas [Opens in a new window]
Jim Thomas*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A new amplitude equation is derived for high-frequency acoustic waves propagating through an incompressible vortical flow using multi-time-scale asymptotic analysis. The reduced model is derived without an explicit spatial-scale separation ansatz between the wave and vortical fields. As a consequence, the model is seen to capture very well the features of the wave field in the regime where the spatial scales of the wave and vortical fields are comparable, a regime for which an optimal reduced model does not seem to be available.

JFM classification

Acoustics: Acoustics Compressible Flows: Compressible Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 658 - 674
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ablowitz, M. J. 2011 Nonlinear Dispersive Waves – Asymptotic Analysis and Solitons. Cambridge University Press.Google Scholar
Auregan, Y., Maurel, A., Pagneux, V. & Pinton, J. F. 2002 Sound–Flow Interactions, Springer.Google Scholar
Baudet, C., Ciliberto, S. & Pinton, J. F. 1991 Spectral analysis of the von Karman flow using ultrasound scattering. Phys. Rev. Lett. 67, 193–195.Google Scholar
Berthet, R. & Coste, C. 2003 Using a partial-wave method for sound–mean-flow scattering problems. Phys. Rev. E 67, 036604.Google Scholar
Berthet, R., Fauve, S. & Labbe, R. 2003 Study of the sound vortex interaction: direct numerical simulations and experimental results. Eur. Phys. J. B 32, 237–242.Google Scholar
Brambley, E. J. 2016 Correction to ‘On the acoustics of an impedance liner with shear and cross flow’, by Campos, Legendre and Sambuc. Proc. R. Soc. Lond. A 472, 20160153.Google Scholar
Brillant, G., Chilla, F. & Pinton, J. F. 2004 Spectral analysis of the von Karman flow using ultrasound scattering. Eur. Phys. J. B 37, 229–239.Google Scholar
Broadbent, E. G. 1977 Acoustic ray theory applied to vortex refraction. J. Inst. Maths Applics. 19, 1–27.Google Scholar
Bühler, O. 2014 Waves and Mean Flows. Cambridge University Press.Google Scholar
Campos, L. M. B. C., Legendre, C. & Sambuc, C. 2014 On the acoustics of an impedance liner with shear and cross flow. Proc. R. Soc. Lond. A 470, 20130732.Google Scholar
Colonius, T., Lele, S. K. & Moin, P. 1994 The scattering of sound waves by a vortex: numerical simulations and analytical solutions. J. Fluid Mech. 260, 271–298.Google Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.Google Scholar
Fabrikant, A. L. 1983 Sound scattering by vortex flows. Sov. Phys. Acoust. 29, 152–155.Google Scholar
Fabrikant, A. L., Stepanyants, Y. A. & Stepaniants, I. A. 1998 Propagation of Waves in Shear Flows, World Scientific Series on Nonlinear Science Series A, vol. 18. World Scientific.Google Scholar
Faou, E., Germain, P. & Hani, Z. 2016 The weakly nonlinear large-box limit of the 2D cubic nonlinear Schrödinger equation. J. Am. Math. Soc. 29, 915–982.CrossRefGoogle Scholar
Ford, R. & Llewellyn Smith, S. G. 1999 Scattering of acoustic waves by a vortex. J. Fluid Mech. 386, 305–328.Google Scholar
Georges, T. M. 1972 Acoustic ray paths through a model vortex with a viscous core. J. Acoust. Soc. Am. 51, 206–209.Google Scholar
Hattori, Y. & Llewellyn Smith, S. G. 2002 Axisymmetric acoustic scattering by vortices. J. Fluid Mech. 473, 275–294.Google Scholar
Howe, M. S. 2002 Theory of Vortex Sound. Cambridge University Press.Google Scholar
Kambe, T. & Mya Oo, U. 1981 Scattering of sound by a vortex ring. J. Phys. Soc. Japan 50, 3507–3516.CrossRefGoogle Scholar
Kraichnan, R. H. 1953 The scattering of sound in a turbulent medium. J. Acoust. Soc. Am. 25, 1096–1104.CrossRefGoogle Scholar
Labbe, R. & Pinton, J. F. 1998 Propagation of sound through a turbulent vortex. Phys. Rev. Lett. 81, 1413–1416.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Lesieur, M. 2008 Turbulence in Fluids, 4th edn. Fluid Mechanics and Its Applications, vol. 84. Springer.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically, I. General theory. Proc. R. Soc. Lond. 211, 564–587.Google Scholar
Lighthill, M. J. 1953 On the energy scattered from the interaction of turbulence with sound or shock waves. Proc. Camb. Phil. Soc. 49, 531–551.Google Scholar
Llewellyn Smith, S. G. & Ford, R. 2001 Three-dimensional acoustic scattering by vortical flows. 1. General theory. Phys. Fluids 13, 2876–2889.Google Scholar
Lund, F. & Rojas, C. 1989 Ultrasound as a probe of turbulence. Physica D 37, 508–514.Google Scholar
Manneville, S., Robres, J. H., Maurel, A., Petitjeans, P. & Fink, M. 1999 Vortex dynamics investigation using an acoustic technique. Phys. Fluids 11, 3380–3389.Google Scholar
Manneville, S., Roux, P., Tanter, M., Maurel, A., Fink, M., Bottausci, F. & Petitjeans, P. 2001 Scattering of sound by a vorticity filament: an experimental and numerical investigation. Phys. Rev. E 63, 036607.Google Scholar
Oljaca, M., Gu, X., Glezer, A., Baffico, M. & Lund, F. 1998 Ultrasound scattering by a swirling jet. Phys. Fluids 10, 886–898.CrossRefGoogle Scholar
Ostashev, V. E. & Wilson, D. K. 2015 Acoustics in Moving Inhomogeneous Media, 2nd edn. CRC.Google Scholar
Rayleigh, J. W. S. & Lindsay, R. B. 1945 The Theory of Sound. vol. 2. Dover.Google Scholar
Roberts, A. J. 1985 An introduction to the technique of reconstitution. SIAM J. Math. Anal. 16, 1243–1257.CrossRefGoogle Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Seifer, S. & Steinberg, V. 2004 Flow induced ultrasound scattering: experimental studies. Phys. Fluids 16, 1587–1602.Google Scholar
Seifer, S. & Steinberg, V. 2005 Spatial and temporal turbulent velocity and vorticity power spectra from sound scattering. Phys. Rev. E 71, 045601(R).Google Scholar
Thomas, J. 2016 Resonant fast–slow interactions and breakdown of quasi-geostrophy in rotating shallow water. J. Fluid Mech. 788, 492–520.CrossRefGoogle Scholar
Thomas, J., Smith, K. S. & Bühler, O. 2017 Near-inertial wave dispersion by geostrophic flows. J. Fluid Mech. 817, 406–438.CrossRefGoogle Scholar
Wagner, G. L. & Young, W. R. 2016 A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic. J. Fluid Mech. 802, 806–837.CrossRefGoogle Scholar