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Steady Streaming Generated by Low-Amplitude Oscillations of a Cylinder

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Abstract

The problem of generation of steady streaming by an oscillating circular cylinder is considered. For the case of a finite oscillation frequency, the asymptotic expansion of the solution in terms of a small oscillation amplitude is constructed. In the leading steady term the two possible regimes of secondary streaming are analyzed. The fluid pumping effect of secondary streaming is studied. Energy efficient pumping regime is determined. The limits of applicability of high-frequency asymptotic solutions are established.

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REFERENCES

  1. G. G. Stokes, ‘‘On the effect of the internal friction of fluids on the motion of pendulums,’’ Trans. Cambridge Philos. Soc. 9, 8–106 (1851).

    Google Scholar 

  2. C. Zhang, X. Guo, L. Royon, and P. Brunet, ‘‘Unveiling of the mechanisms of acoustic streaming induced by sharp edges,’’ Phys. Rev. E 102, 043110 (2020).

    Article  Google Scholar 

  3. A. G. Yegorov and O. S. Zakharova, ‘‘The energy-optimal motion of a vibration-driven robot in a resistive medium,’’ J. Appl. Math. Mech. 74, 443–451 (2010).

    Article  MathSciNet  Google Scholar 

  4. D. Ahmed, M. Lu, A. Nourhani, et al., ‘‘Selectively manipulable acoustic-powered microswimmers,’’ Sci. Rep. 5, 9744 (2015).

    Article  Google Scholar 

  5. K. Chong, S. D. Kelly, S. T. Smith, and J. D. Eldredge, ‘‘Transport of inertial particles by viscous streaming in arrays of oscillating probes,’’ Phys. Rev. E 93, 013109 (2016).

    Article  Google Scholar 

  6. H. Zhu, P. Zhang, Z. Zhong, et al., ‘‘Acoustohydrodynamic tweezers via spatial arrangement of streaming vortices,’’ Sci. Adv. 7, eabc7885 (2021).

  7. H. Schlichting, ‘‘Berechnung ebener periodischer Grenzschichtströmungen,’’ Phys. Zeitschr. 33, 327–335 (1932).

    MATH  Google Scholar 

  8. J. Stuart, ‘‘Double boundary layers in oscillatory viscous flow,’’ J. Fluid Mech. 24, 673–687 (1966).

    Article  MathSciNet  Google Scholar 

  9. C. Y. Wang, ‘‘On high-frequency oscillating viscous flows,’’ J. Fluid Mech. 32, 55–68 (1968).

    Article  Google Scholar 

  10. N. Riley, ‘‘The steady streaming induced by a vibrating cylinder,’’ J. Fluid Mech. 68, 801–812 (1975).

    Article  Google Scholar 

  11. A. N. Nuriev and A. G. Egorov, ‘‘Asymptotic investigation of hydrodynamic forces acting on an oscillating cylinder at finite streaming Reynolds numbers,’’ Lobachevskii J. Math. 40 (6), 794–801 (2019).

    Article  MathSciNet  Google Scholar 

  12. A. Nuriev, A. Egorov, and A. Kamalutdinov, ‘‘Hydrodynamic forces acting on the elliptic cylinder performing high-frequency low-amplitude multi-harmonic oscillations in a viscous fluid,’’ J. Fluid Mech. 913, A40 (2021).

    Article  MathSciNet  Google Scholar 

  13. J. Holtsmark, I. Johnsen, T. Sikkeland, and S. Skavlem, ‘‘Boundary layer flow near a cylindrical obstacle in an oscillating incompressible fluid,’’ Acoust. Soc. Am. 26, 26–39 (1954).

    Article  MathSciNet  Google Scholar 

  14. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, Oxford, 1987).

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Correspondence to A. G. Egorov or A. N. Nuriev.

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(Submitted by D. A. Gubaidullin)

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Egorov, A.G., Nuriev, A.N. Steady Streaming Generated by Low-Amplitude Oscillations of a Cylinder. Lobachevskii J Math 42, 2102–2108 (2021). https://doi.org/10.1134/S1995080221090067

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  • DOI: https://doi.org/10.1134/S1995080221090067

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