On the steady streaming induced by vibrating walls

SIAM Journal on Applied Mathematics

Volumn 72, Issue 5, 2012, Pages 1406-1427

  Ilin, Konstantin ^a   Morgulis, Andrey ^b,c  

^a UNIVERSITY OF YORK   (United Kingdom)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

^c SOUTHERN MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Asymptotic methods; Oscillating boundary layers; Steady streaming

Indexed keywords

ASYMPTOTIC EXPANSION; ASYMPTOTIC METHOD; BODY FORCES; DRIFT VELOCITIES; FLOW BOUNDARIES; GENERAL THEORY; HIGH REYNOLDS NUMBER; INCOMPRESSIBLE VISCOUS FLOWS; LAGRANGIAN VELOCITY; LANGMUIR CIRCULATIONS; LEADING ORDERS; OSCILLATING BOUNDARIES; PERISTALTIC PUMPING; PLANE WAVE; SOLID WALL; STEADY STREAMING; STOKES LAYER; TRANSVERSE VIBRATIONS;

ASYMPTOTIC ANALYSIS; BOUNDARY LAYERS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; VISCOUS FLOW;

OSCILLATING FLOW;

EID: 84868247330     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/110859634     Document Type: Article

References (30)

1. A. Bertelsen, A. Svardal, and S. Tjøtta, Nonlinear streaming effects associated with oscillating cylinders, J. Fluid Mech., 59 (1973), pp. 493-511.
2. F. Carlsson, M. Sen, and H. A. Löfdahl, Fluid mixing induced by vibrating walls, Eur. J. Mech. B Fluids, 24 (2005), pp. 366-378.
3. L. A. Chudov, Some shortcomings of classical boundary-layer theory, in Numerical Methods in Gas Dynamics. A Collection of Papers of the Computational Center of the Moscow State University, G. S. Roslyakov and L. A. Chudov, eds., Izdalel'stvo Moskovskogo Universiteta, 1963 (in Russian).
4. A. D. D. Craik and S. Leibovich, A rational model for Langmuir circulations, J. Fluid Mech., 73 (1976), pp. 401-426.
5. P. W. Duck and F. T. Smith, Steady streaming induced between oscillating cylinders, J. Fluid Mech., 91 (1979), pp. 93-110.
6. Y. C. Fung and C. S. Yih, Peristaltic transport, J. Appl. Mech., 35 (1968), pp. 669-675.
7. E. W. Haddon and N. Riley, The steady streaming induced between oscillating circular cylinders, Quart. J. Mech. Appl. Math., 32 (1979), pp. 801-812.
8. J. Hoepffner and K. Fukagata, Pumping or drag reduction?, J. Fluid Mech., 635 (2009), pp. 171-187.
9. K. Ilin, Viscous boundary layers in flows through a domain with permeable boundary, Eur. J. Mech. B Fluids, 27 (2008), pp. 514-538.
10. K. Ilin and A. Morgulis, Steady streaming between two vibrating planes at high Reynolds numbers, preprint, arXiv:1108.2710v1 [physics.flu-dyn] (2011).
11. K. Ilin and M. A. Sadiq, Steady viscous flows in an annulus between two cylinders produced by vibrations of the inner cylinder, preprint, arXiv:1008.4704v2 [physics.flu-dyn] (2010).
12. M. Y. Jaffrin and A. H. Shapiro, Peristaltic pumping, Ann. Rev. Fluid Mech., 3 (1971), pp. 13-37.
13. V. B. Levenshtam, Asymptotic expansion of the solution of a problem of vibrational convection, Zh. Vychisl. Mat. Mat. Fiz., 40 (2000), pp. 1416-1424 (in Russian);
14. English translation in Comput. Math. Math. Phys., 40 (2000), pp. 1357-1365.
15. J. Lighthill, Acoustic streaming, J. Sound and Vibration, 61 (1978), pp. 391-418.
16. M. S. Longuet-Higgins, Mass transport in water waves, Philos. Trans. Roy. Soc. London Ser. A, 245 (1953), pp. 535-581.
17. M. S. Longuet-Higgins, Peristaltic pumping in water waves, J. Fluid Mech., 137 (1983), pp. 393-407.
18. A. H. Nayfeh, Perturbation Methods, John Wiley & Sons, New York, London, Sydney, 1973.
19. N. Riley, Oscillating viscous flows, Mathematika, 12 (1965), pp. 161-175.
20. N. Riley, Oscillatory viscous flows. Review and extension, J. Inst. Math. Appl., 3 (1967), pp. 419-434.
21. N. Riley, The steady streaming induced by a vibrating cylinder, J. Fluid Mech., 68 (1975), pp. 801-812.
22. N. Riley, Steady streaming, Ann. Rev. Fluid Mech., 33 (2001), pp. 43-65.
23. K. P. Selverov and H. A. Stone, Peristaltically driven channel flows with applications towards micromixing, Phys. Fluids, 13 (2001), pp. 1838-1859.
24. J. T. Stuart, Double boundary layers in oscillatory viscous flow, J. Fluid Mech., 42 (1966), pp. 673-687.
25. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics, Dover, New York, 1990.
26. V. A. Trenogin, The development and applications of the Lyusternik-Vishik asymptotic method, Uspekhi Mat. Nauk, 25 (1970), pp. 123-156.
27. V. A. Vladimirov, Viscous flows in a half space caused by tangential vibrations on its boundary, Stud. Appl. Math., 121 (2008), pp. 337-367.
28. Ch.-Y. Wang, On high-frequency oscillatory viscous flows, J. Fluid Mech., 32 (1968), pp. 55-68.
29. D. E. Wilson and R. L. Panton, Peristaltic transport due to finite amplitude bending and contraction waves, J. Fluid Mech., 90 (1979), pp. 145-159.
30. M. Yi, H. H. Bau, and H. Hu, Peristaltically induced motion in a closed cavity with two vibrating walls, Phys. Fluids, 14 (2002), pp. 184-197.