1997
DOI: 10.1017/s0022112096003758
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Asymptotic solutions for two-dimensional low Reynolds number flow around an impulsively started circular cylinder

Abstract: The unsteady flow field of an incompressible viscous fluid around an impulsively started cylinder with slow motion is studied in detail. Integral expressions are derived from the nonlinear vorticity equation, and are solved by the method of matched asymptotic expansions. To complete the matching process five regions are necessary and their regions are essentially governed by the following relations: (i) the initial flow is unsteady Stokes flow (I), (ii) the early transient flow near the cylinder is… Show more

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Cited by 8 publications
(13 citation statements)
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“…. The results obtained by Price & Tan [5], who only considered a special case in which the direction of   t Ω is fixed and parallel to that of 1 e all the time, can be recovered from the generalized fundamental solution (7) by simply putting…”
Section: Generalized Fundamental Solutionsmentioning
confidence: 99%
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“…. The results obtained by Price & Tan [5], who only considered a special case in which the direction of   t Ω is fixed and parallel to that of 1 e all the time, can be recovered from the generalized fundamental solution (7) by simply putting…”
Section: Generalized Fundamental Solutionsmentioning
confidence: 99%
“…Sano [6] obtained a long-time representation for the force on a sphere in response to an impulsively Jian-Jun Shu 2 started flow at a small but finite Reynolds number using the method of matched asymptotic expansions. Nakanishi et al [7] treated a two-dimensional version of the problem. Lovalenti & Brady [8,9] extended Sano's result to a step change in the free-stream velocity using a reciprocal theorem.…”
Section: Introductionmentioning
confidence: 99%
“…(ii) As obtained by Nakanishi et al (1997) for a simple circular cylinder, we expect (by virtue of (2.13)) that ζ (iii) Any non-integral term arising on the right-hand side of (3.20) or (3.21) is seen to obey ∇ 2 o F =0o r∇ 2 o F =c 2 F respectively if one sets ∇ 2 o = ∂ 2 /∂X 2 + ∂ 2 /∂Y 2 . Accordingly, the outer aproximations…”
Section: Assumptions and Notationmentioning
confidence: 97%
“…As explained in Nakanishi et al (1997) and Ueda et al (2001), one thus needs to distinguish five significant local domains, in the sense of Kida (1991) and Kida & Take (1995), in the (r, p)-plane, where r = |x|. These domains, depicted in figure 3 and labelled (I) to (V), are such that:…”
Section: Assumptions and Notationmentioning
confidence: 99%
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