Print Email Facebook Twitter A steady solution for Prandtl’s self-similar vortex sheet spirals Title A steady solution for Prandtl’s self-similar vortex sheet spirals Author Van Kuik, G.A.M. Faculty Aerospace Engineering Department Aerospace Design, Integration and Operations Date 2008-05-07 Abstract Prandtl's [L. Prandtl, Über die Entstehung von Wirbeln in der idealen Flüssigkeit, mit Anwendung auf die Tragflügeltheorie und andere Aufgaben, in: von Kármán, Levi-Cevita (Eds.), Vorträge aus dem Gebiete der Hydro- und Aerodynamik, Springer, Berlin, 1922] self-similar, semi-infinite, free vortex sheets are characterized by a two-dimensional unsteady flow around an invariable exponential spiral. A similar but steady spiral flow has been published by Schmidt and Sparenberg [G.H. Schmidt, J.A. Sparenberg, On the edge singularity of an actuator disk with large constant normal load, J. Ship Research 21 (1977) 125]. This flow is shown to be, kinematically, the steady solution in Prandtl's class of spirals but with a different dynamic boundary condition since it is not a free vortex sheet but carries a constant load. Due to the kinematic similarity, the analysis of Prandtl's spirals by van Kuik [G.A.M. van Kuik, The flow induced by Prandtl's self-similar vortex sheet spirals at infinite distances from the spiral kernel, Eur. J. Mech. B/Fluids 23 (4) (2004) 607–616] is also valid for the spiral with steady flow. As for Prandtl's spirals, the steady spiral flow requires a description on a multi-branched Riemann surface, by which an interpretation in the single-branched two-dimensional surface is impossible. Subject SpiralVortex sheetsPrandtl To reference this document use: http://resolver.tudelft.nl/uuid:791fce8a-e31b-448b-ab1d-495c018d9561 DOI https://doi.org/10.1016/j.euromechflu.2008.05.007 Publisher Elsevier ISSN 0997-7546 Source European Journal of Mechanics B/Fluids, 28 (2), 2009 Part of collection Institutional Repository Document type journal article Rights (c) 2008 2008 Elsevier Masson SAS Files PDF kuik224701.pdf 256.67 KB Close viewer /islandora/object/uuid:791fce8a-e31b-448b-ab1d-495c018d9561/datastream/OBJ/view