Quasisteady streaming with rarefaction effect induced by asymmetric sawtooth-like plane waves

Physics of Fluids

Volumn 8, Issue 9, 1996, Pages 2537-2551

  Yano, Takeru ^a   Inoue, Yoshinori ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; STREAMLINES(FLOW); WAVES;

EID: 0030480218     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869036     Document Type: Article

References (29)

1. Y. Inoue and T. Yano, "Propagation of strongly nonlinear plane waves," J. Acoust. Soc. Am. 94, 1632 (1993); "Propagation of acoustic shock waves of large amplitude," in Frontiers of Nonlinear Acoustics, edited by M. F. Hamilton and D. T. Blackstock (Elsevier, London, 1990), pp. 141-146.
2. Y. Inoue and T. Yano, "Propagation of strongly nonlinear plane waves," J. Acoust. Soc. Am. 94, 1632 (1993); "Propagation of acoustic shock waves of large amplitude," in Frontiers of Nonlinear Acoustics, edited by M. F. Hamilton and D. T. Blackstock (Elsevier, London, 1990), pp. 141-146.
3. ρ is the specific heat for the ideal gas at constant pressure. See, M. J. Lighthill, "Viscosity effects in sound wave of finite amplitude," in Surveys in Mechanics, edited by G. K. Batchelor and R. M. Davies (Cambridge University Press, Cambridge, 1956), pp. 250-351.
4. Strictly speaking, condition Re≫1 signifies the limit as Re→∞, mathematically.
5. S. Osher and S. R. Chakravarthy, "Very high order accurate TVD schemes," in Oscillation Theory, Computation, and Methods of Compensated Compactness, edited by C. Dafemos, J. Ericksen, D. Kinderlehrer, and M. Slemrod (Springer, New York, 1986), pp. 229-274.
6. S. Osher and F. Solomon, "Upwind difference schemes for hyperbolic systems of conservation laws," Math. Comput. 38, 339 (1982).
7. S. I. Soluyan and R. V. Khokhlov, "Propagation of acoustic waves of finite amplitude in a dissipative medium," Vestn. Moskov. Univ. Fiz. Astron. 3, 52 (1961).
8. D. T. Blackstock, "Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude," J. Acoust. Soc. Am. 39, 1019 (1966).
9. O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Consultants Bureau, New York, 1977).
10. D. G. Crighton, "Basic theoretical nonlinear acoustics," in Frontiers in Physical Acoustics, edited by D. Sette (North-Holland, Amsterdam, 1986), pp. 1-52.
11. T. Yano and Y. Inoue, "Numerical study of strongly nonlinear acoustic waves, shock waves, and streaming caused by a harmonically pulsating sphere," Phys. Fluids 6, 2831 (1994).
12. T. Yano and Y. Inoue, "Strongly nonlinear waves radiated by a circular piston," in Advances in Nonlinear Acoustics, edited by H. Hobek (World Scientific, Singapore, 1993), pp. 583-588; "Strongly nonlinear waves and streaming in the near field of a circular piston," J. Acoust. Soc. Am. (in press).
13. T. Yano and Y. Inoue, "Strongly nonlinear waves radiated by a circular piston," in Advances in Nonlinear Acoustics, edited by H. Hobek (World Scientific, Singapore, 1993), pp. 583-588; "Strongly nonlinear waves and streaming in the near field of a circular piston," J. Acoust. Soc. Am. (in press).
14. M. J. Lighthill, "The energy distribution behind decaying shocks. - 1. Plane waves," Philos. Mag. 41, 1101 (1950).
15. J. E. Phythian, "The energy distribution behind a decaying two-dimensional shock," Q. J. Mech. Appl. Math. 5, 318 (1952).
16. C. L. Morfey and V. W. Sparrow, "Plane compression front steepening in nonlinear media forms both a shock and a reflected wave," J. Acoust. Soc. Am. 93, 3085 (1993).
17. That is, we shall seek a weak solution of the system (4)-(6) See, J. Smoller, Shock Waves and Reaction-Diffusion Equations (Springer, New York, 1983), Chap. 15.
18. R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves (Springer, New York, 1948), Sec. 40.
19. S. Earnshaw, " On the mathematical theory of sound," Trans. R. Soc. London. 150, 133 (1860).
20. D. T. Blackstock, "Propagation of plane sound waves of finite amplitude in nondissiputive, fluids," J. Acoust. Soc. Am. 34, 9 (1962).
21. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), Sec. 2.8.
22. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergarnon, Oxford, 1987), Sec. 102, problem 1, p. 390.
23. 2.
24. Y. Inoue and T. Yano, "Propagation of strongly nonlinear plane N waves," J. Fluid Mech. (submitted).
25. See Ref. 19, Sec. 6.10.
26. If X″ (t) has some minima in the period 2 π, then the shocks of the same number may be formed in each wave cycle; see, for example, Y. Inoue and Y. Gotoh, "Formation of weak shock waves caused by a sphere pulsating at large amplitude and low frequency," J. Sound Vib. 146, 269 (1991). It is easy to extend Eq. (32) to such a situation.
27. See Ref. 20, Sec. 101, problem 4, pp. 384-385. See also, T. Yano, "The mean pressure and density in a strongly nonlinear plane acoustic wave," J. Acoust. Soc. Am. 100 (in press).
28. I. I. Glass L. E. Heuckroth, and S. Molder, "One-dimensional overtaking of a shock wave by a rarefaction wave," ARS J.31, 1453 (1961).
29. A. H. Nayfeh and A. Kluwick, "A comarison of three perturbation methods for nonliner hyperbolic waves," J. Sound Vib. 48, 293 (1976).