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Phys. Fluids 30, 2922 (1987); doi:10.1063/1.866069 (6 pages)
Attenuation of a compressional sound wave in the presence of a fractal boundary
(Received 20 March 1987; accepted 16 June 1987)
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Add to FacebookThe attenuation of a compressional sound wave propagating through a fluid bounded by a solid surface of fractal dimension 2≤df<3 is studied. At high sound wave frequency ω, the attenuation is caused primarily by the viscous dissipation within a boundary layer near the solid surface of thickness δ=(μ/ρω)1/2, where μ is the viscosity and ρ the density of the fluid. Because the surface area ‘‘seen’’ by the boundary layer increases with decreasing δ, one might expect the attenuation γ to scale in a self‐similar manner with δ, i.e., γ∼δ2‐da, where 2≤da<3. A multiple scales analysis based on a wide separation in the length scales of successively smaller levels of surface structure is used to determine the dependence of the attenuation on the boundary layer thickness. While the possibility of a self‐similar scaling of the attenuation is confirmed, the attenuation exponent da is generally quite different from the fractal dimension df. In fact the presence of a fractal surface area df≠2 is neither a necessary nor sufficient criterion for a self‐similar scaling of the attenuation da≠2.
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0031-9171 (print)
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A. J. Katz and A. H. Thompson, Phys. Rev. Lett. 54, 1325 (1985).
S. H. Liu, Phys. Rev. Lett. 55, 529 (1985).
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