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Asymptotics beyond all orders for a low Reynolds number flow

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Abstract

The solution for slow incompressible flow past a circular cylinder involves terms in powers of 1/log ε, ε times powers of 1/log ε, etc., where ε is the Reynolds number. Previously we showed how to determine the sum of all terms in powers of 1/log ε. Now we show how to go beyond all those terms to find the sum of all terms containing ε times a power of 1/log ε. The first sum gives the drag coefficient and represents a symmetric flow in the Stokes region near the cylinder. The second term reveals the asymmetry of the flow near the body. This problem is studied using a hybrid method which combines numerical computation and asymptotic analysis.

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Authors and Affiliations

  1. Dept. of Mathematics, Stanford University Stanford, 94305, Ca., USA

    Joseph B. Keller

  2. Dept. of Mechanical Engineering, Stanford University Stanford, 94305, Ca., USA

    Joseph B. Keller

  3. Dept. of Mathematics, Univ. of British Columbia, V6T 1Y4, Vancouver, British Columbia, Canada

    Michael J. Ward

Authors
  1. Joseph B. Keller
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  2. Michael J. Ward
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Keller, J.B., Ward, M.J. Asymptotics beyond all orders for a low Reynolds number flow. J Eng Math 30, 253–265 (1996). https://doi.org/10.1007/BF00118834

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  • DOI: https://doi.org/10.1007/BF00118834

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