Abstract
The boundary-layer equations outside a rotating disk of radius a have been solved. It is shown that it is unnecessary to take special precautions for the sudden change in boundary conditions at the edge of the disk except if one is interested in the flow at distances which are smaller than about 10−3 a from the edge. The behaviour of the flow at large distances from the disk is investigated analytically with results which are confirmed by the numerical computations.
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References
Th. von Kerman, Laminare und turbulente Reibung, ZAMM 1 (1921) 233–252.
W.G. Cochran, The flow due to a rotating disk, Proc. Cambr. Phil. Soc. 30 (1934), 365–375.
F.T. Smith, A note on a wall jet negotiating a trailing edge, Q.J. Mech. Appl. Math. 31 (1978) 473–479.
S. Goldstein, Concerning some solutions of the boundary layer equations in hydrodynamics, Proc. Cambr. Phil. Soc. 26 (1930) 1–30.
H. Schlichting, Boundary layer theory, McGraw-Hill, New York (1968).
P.J. Zandbergen and D. Dijkstra, Non-unique solutions of the Navier-Stokes equations for the Karman swirling flow, J. Eng. Math. 11 (1977) 167–188.
M. Abramowitz and I.A. Stegun, Handbook of mathematical functions, Dover, New York (1965).
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Van de Vooren, A.I., Botta, E.F.F. Fluid flow induced by a rotating disk of finite radius. J Eng Math 24, 55–71 (1990). https://doi.org/10.1007/BF00128846
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DOI: https://doi.org/10.1007/BF00128846