Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-19T22:35:15.252Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscosity, surface tension and gravity effects on acoustic reflection and refraction

Published online by Cambridge University Press:  14 December 2018

R. Krechetnikov Open the ORCID record for R. Krechetnikov [Opens in a new window]
R. Krechetnikov*
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, AB, T6G 2G1, Canada
*
†Email address for correspondence: krechet@ualberta.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

The idea of the present work is to study from a unifying viewpoint the effects of viscosity, surface tension and gravity on acoustic reflection and refraction at a fluid interface, with the focus on modifications of Snell’s (Snell–Descartes’) law. While all these effects can be treated individually due to separation of the associated time scales, the contributions of surface tension to the gravity and viscosity cases are considered as well. The analysis reveals a number of phenomena among which are dispersive refraction laws, surface tension enhancing reflection, acoustic field generating vorticity at the interface, and viscosity enhancing/suppressing reflection as well as giving rise to extra reflected and transmitted waves.

JFM classification

Acoustics: Acoustics Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 822 - 836
Copyright
© 2018 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

Abdolali, A. & Kirby, J. T. 2017 Role of compressibility on tsunami propagation. J. Geophys. Res. Oceans 122, 9780–9794.Google Scholar
Abdolali, A., Kirby, J. T. & Bellotti, G. 2015 Depth-integrated equation for hydro-acoustic waves with bottom damping. J. Fluid Mech. 766, R1.Google Scholar
Bondi, H. 1947 Waves on the surface of a compressible liquid. Proc. Camb. Phil. Soc. 43, 75–95.Google Scholar
Brekhovskikh, L. M. 1960 Waves in Layered Media. Academic Press.Google Scholar
Dahl, P. H. 2007 High-frequency underwater sound. In Wiley Encyclopedia of Electrical and Electronics Engineering, pp. 1–19. John Wiley.Google Scholar
Dalrymple, R. A. & Rogers, B. D. 2007 A note on wave celerities on a compressible fluid. In Proceedings of the 30th International Conference on Coastal Engineering (ICCE) 2006, San Diego, CA (ed. Smith, J. M.), pp. 3–13. World Scientific.Google Scholar
Dombey, N. & Calogeracos, A. 1999 Seventy years of the Klein paradox. Phys. Rep. 315, 41–58.Google Scholar
Drinkwater, B. W. 2016 Dynamic-field devices for the ultrasonic manipulation of microparticles. Lab on a Chip 16, 2360–2375.Google Scholar
Fermi, E. 1951 Elementary Particles. Yale University Press.Google Scholar
Fletcher, N. H. 1974 Adiabatic assumption for wave propagation. Am. J. Phys. 42, 487–489.Google Scholar
Godin, O. A. 2006 Anomalous transparency of water–air interface for low-frequency sound. Phys. Rev. Lett. 97, 164301.Google Scholar
Godin, O. A. & Fuks, I. M. 2012 Transmission of acoustic-gravity waves through gas–liquid interfaces. J. Fluid Mech. 709, 313–340.Google Scholar
Kadri, U. & Stiassnie, M. 2012 Acoustic-gravity waves interacting with the shelf break. J. Geophys. Res. 117, C03035.Google Scholar
Kadri, U. & Stiassnie, M. 2013 Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction. J. Fluid Mech. 735, R6.Google Scholar
Kinsler, L. E., Frey, A. R., Coppens, A. B. & Sanders, J. V. 1999 Fundamentals of Acoustics. Wiley.Google Scholar
Klein, O. 1929 Die Reflexion von Elektronen an einem Potentialsprung nach der Relativistischen Dynamik von Dirac. Z. Phys. 53, 157–165.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon Press.Google Scholar
Munk, W. H., Spindel, R. C., Baggeroer, A. & Birdsall, T. G. 1994 The Heard Island feasibility test. J. Acoust. Soc. Am. 96, 2330–2342.Google Scholar
Papadakis, E. P. 1999 Ultrasonic Instruments and Devices. Academic Press.Google Scholar
Pierce, A. D. 1989 Acoustics: An Introduction to its Physical Principles and Applications. Acoustical Society of America.Google Scholar
Tolstoy, I. 1963 The theory of waves in stratified fluids including the effects of gravity and rotation. Rev. Mod. Phys. 35, 207–230.Google Scholar
Tolstoy, I. 1965 Effect of density stratification on sound waves. J. Geophys. Res. 70, 6009–6015.Google Scholar
Watson, T. & Young, S. R. 2008 Therapeutic ultrasound. In Electrotherapy: Evidence-based Practice, pp. 179–200. Churchill Livingstone.Google Scholar
Whitaker, R. W. & Norris, D. E. 2008 Infrasound propagation. In Handbook of Signal Processing in Acoustics, pp. 1497–1519. Springer.Google Scholar
Zhang, L. & Swinney, H. L. 2017 Sound propagation in a continuously stratified laboratory ocean model. J. Acoust. Soc. Am. 141, 3186–3189.Google Scholar