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A note on the far-asymptotics of Helmholtz–Kirchhoff flows

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Abstract

In this sequel to a rather recent paper on the classical problem of Helmholtz–Kirchhoff flows by Vic. V. Sychev (TsAGI Sci J 41(5):531–533, 2010), the representation of the flow far from the body and its specific implications discussed in that study are revisited. Here the concise derivation of these findings resorts to well-known Levi-Cività’s method and, alternatively, only fundamental properties of analytic functions and thin-airfoil theory. As particularly of interest when the well-known Kirchhoff parabola degenerates to an infinitely long cusp, integration constants debated controversially so far and important for the understanding and computation of those flows are specified by the integral conservation of momentum. Also, the parametric modification towards flows encompassing stagnant-fluid regions of finite extent and the previously unnoticed impact of higher-order terms on the associated high-Reynolds-number flows are addressed.

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Authors and Affiliations

  1. Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3/E322, 1040, Vienna, Austria

    B. Scheichl

  2. AC2T research GmbH (Austrian Center of Competence for Tribology), Viktor-Kaplan-Straße 2C, 2700, Wiener Neustadt, Lower Austria, Austria

    B. Scheichl

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  1. B. Scheichl
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Correspondence to B. Scheichl.

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Communicated by Tim Colonius.

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Scheichl, B. A note on the far-asymptotics of Helmholtz–Kirchhoff flows. Theor. Comput. Fluid Dyn. 28, 377–384 (2014). https://doi.org/10.1007/s00162-014-0322-9

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  • DOI: https://doi.org/10.1007/s00162-014-0322-9

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