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Unsteady viscous flow over irregular boundaries

Published online by Cambridge University Press:  26 April 2006

C. Pozrikidis
C. Pozrikidis
Affiliation:
Department of Applied Mechanics and Engineering Science, University of California at San Diego, La Jolla, CA 92093-0411, USA
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Abstract

Unsteady viscous flow over irregular and fractal walls is discussed, and the flow generated by the longitudinal and transverse vibrations of an infinite periodic two-dimensional wall with cylindrical grooves is considered in detail. The behaviour of the Stokes layer and the functional dependence between the drag force and the frequency are illustrated in a broad band of frequencies for walls with sinusoidal corrugations and a family of walls with triangular asperities leading to fractal shapes. It is shown that, in the case of longitudinal oscillations, the drag force on a fractal wall with self-similar structure exhibits a power-law dependence on the frequency with an exponent that is related to the fractal dimension of the microstructure expressing the gain in surface area with increasing spatial resolution. Numerical evidence suggests that, in the case of transverse oscillations, the dissipative component of the drag force may show a power-law dependence on the frequency, but the exponent is not directly related to the geometry of the microstructure. The significance of these results on the behaviour of the drag force on walls with three-dimensional irregularities is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 11 - 34
Copyright
© 1993 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Avnir, D., Farin, D. & Pfeifer, P. 1984 Molecular fractal surfaces. Nature. 308, 261–263.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Brady, M. A. & Pozrikidis, C. 1993 Diffusive transport across irregular and fractal walls. Proc. R. Soc. Lond.. A 442, 571–583.Google Scholar
Chandler, G. A. & Graham, I. G. 1988 Product integration-collocation methods for noncompact integral operator equations. Math. Comput. 50, 125–138.Google Scholar
Charlaix, E., Kushnick, A. P. & Stokes, J. P. 1988 Experimental study of dynamic permeability in porous media. Phys. Rev. Lett. 61, 1595–1598.Google Scholar
Davis, R. T. 1979 Numerical methods for coordinate generation based on Schwartz–Christoffel transformations. Proc. 4th Am. Inst. Aero. Astro. CFD Conf., Williamsburgh, VA
Feder, J. 1988 Fractals. Plenum.
Gist, G. A. 1989 Ultrasonic attenuation and fractal surfaces in porous media. Phys. Rev. B. 39, 7295–7297.Google Scholar
Johnson, D. L., Koplik, J. & Dashen, R. 1987 Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mech. 176, 379–402.Google Scholar
Kaneko, A. & Honji, H. 1979 Double structure of steady streaming in the oscillatory viscous flow over a wavy wall. J. Fluid Mech. 93, 727–736.Google Scholar
Katz, A. J. & Thompson, A. H. 1985 Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett. 54, 1325–1328.Google Scholar
Koch, D. L. 1987 Attenuation of a compressional sound wave in the presence of a fractal boundary. Phys. Fluids. 30, 2922–2927.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, 2nd edn. Pergamon.
Lyne, W. H. 1971 Unsteady viscous flow over a wavy wall. J. Fluid Mech. 50, 33–48.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Ralph, M. E. 1986 Oscillatory flows in wavy-walled tubes. J. Fluid Mech. 168, 515–540.Google Scholar
Sobey, I. J. 1980 On flow through furrowed channels. Part 1. Calculated flow patterns. J. Fluid Mech. 96, 1–26.Google Scholar
Warner, K. L. & Beamish, J. R. 1987 Ultrasonic attenuation and pore microstructure in a liquid-4He-filled ceramic. Phys. Rev. B 36, 5698–5701.Google Scholar
Warner, K. L. & Beamish, J. R. 1989 Reply to comment ‘Ultrasonic attenuation and fractal surfaces in porous media’. Phys. Rev. B 39, 7298–7299.Google Scholar