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Acoustic propagation in inhomogeneous fluids: regularization via the introduction of fine particles

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Języki publikacji
EN
Abstrakty
EN
It is shown, using analytical methodologies, that the velocity field blow-up suffered by vertically ascending acoustic waves in an isothermal atmosphere can be eliminated via the introduction of fine particles. Assuming the inhomogeneous generalization of the particle-laden flow model known as the (linearized) Marble–Thompson model-1, it is established that bounded, exponentially decreasing, shock amplitudes can be obtained provided the mass fraction of particles exceeds a critical value, for which an exact expression is derived. Lastly, supporting numerical results are presented, special cases are discussed, and possible follow-on studies are noted.
Rocznik
Strony
59--73
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Acoustics Division, U.S. Naval Research Laboratory, Stennis Space Center, MS 39529, USA
Bibliografia
  • 1. Lord Rayleigh, On the vibrations of an atmosphere, Philosophical Magazine (Ser. 5), 29, 173–180, 1890.
  • 2. H. Lamb, Hydrodynamics, 6th ed., Dover, New York, 1945. 5See, e.g., [25] and the references cited therein
  • 3. G.B. Whitham, Linear and Nonlinear Waves, Wiley, New York, 1974.
  • 4. H. Lamb, On the theory of waves propagated vertically in the atmosphere, Proceedings of the London Mathematical Society (Ser. 2), 7, 122–141, 1908.
  • 5. H.S. Carslaw, J.C. Jaeger, Operational Methods in Applied Mathematics, 2nd ed., Dover, New York, 1963.
  • 6. R.S. Keiffer, P.M. Jordan, I.C. Christov, Acoustic shock and acceleration waves in selected inhomogeneous fluids, Mechanics Resarch Communications, 93, 80–88, 2018.
  • 7. C. Truesdell, R.A. Toupin, The Classical Field Theories, [in:] S. Flügge (Ed.), Handbuch der Physik, vol. III/1, Springer, Berlin, 1960, pp. 491–529.
  • 8. P.M. Jordan, Finite-amplitude acoustics under the classical theory of particle-laden flows, Evolution Equations & Control Theory (EECT), 8, 101–116, 2019.
  • 9. A.D. Pierce, Acoustics: An Introduction to its Physical Principles and Applications, Acoustical Society of America, Chicago, 1989.
  • 10. P.A. Thompson, Compressible-Fluid Dynamics, McGraw–Hill, New York, 1972.
  • 11. R.A. Langel, W.J. Hinze, The Magnetic Field of the Earth’s Lithosphere: The Satellite Perspective, Cambridge University Press, Cambridge, 1998.
  • 12. H. Schlichting, Boundary-Layer Theory, 7th ed., McGraw–Hill, New York, 1979, pp. 90–91.
  • 13. D.G. Duffy, Transform Methods for Solving Partial Differential Equations, 2nd ed., Chapman & Hall/CRC, London, 2004.
  • 14. B.A. Boley, R.B. Hetnarski, Propagation of discontinuities in coupled thermoelastic problems, Journal of Applied Mechanics (ASME), 35, 489–494, 1968.
  • 15. A. Morro, Shock waves in thermo-viscous fluids with hidden variables, Archives of Mechanics, 32, 193–199, 1980.
  • 16. B. Straughan, Heat Waves, [in:] Applied Mathematical Sciences, vol. 177, Springer, Berlin, 2011, §4.1.
  • 17. D.R. Bland, Wave Theory and Applications, Oxford University Press, Oxford, 1988.
  • 18. G.I. Taylor, Waves and tides in the atmosphere, Proceedings of the Royal Society London A, 126, 169–183, 1929.
  • 19. C.L. Pekeris, The propagation of a pulse in the atmosphere. Part II, Physical Review, 73, 145–154, 1948.
  • 20. M. Ciarletta, B. Straughan, Poroacoustic acceleration waves, Proceedings of the Royal Society A, 462, 3493–3499, 2006.
  • 21. B. Straughan, Stability and Wave Motion in Porous Media, [in:] Applied Mathematical Sciences, vol. 165, Springer, Berlin, 2008.
  • 22. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002.
  • 23. P. Guidotti, J.V. Lambers, K. Solna, Analysis of wave propagation in 1D inhomogeneous media, Journal Numerical Functional Analysis and Optimization, 27, 25–55, 2006.
  • 24. D. Joyce, W.J. Parnell, R.C. Assier, I.D. Abrahams, An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems, Proceedings of the Royal Society A, 473, 20170080, 2017.
  • 25. W. E, Principles of Multiscale Modeling, Cambridge University Press, Cambridge, 2011.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
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Bibliografia
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