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On the relation between adjacent inviscid cell type solutions to the rotating-disk equations

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Summary

Over a large range of the axial coordinate a typical higher-branch solution of the rotating-disk equations consists of a chain of inviscid cells separated from each other by viscous interlayers. In this paper the leading-order relation between two adjacent cells will be established by matched asymptotic expansions for general values of the parameter appearing in the equations. It is found that the relation between the solutions in the two cells crucially depends on the behaviour of the tangential velocity in the viscous interlayer. The results of the theory are compared with accurate numerical solutions and good agreement is obtained.

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References

  1. AbramowitzM. and StegunI. A.,Handbook of mathematical functions. Nat. Bur. Standards, Washington, 1966.

    Google Scholar 

  2. BodonyiR. J., On rotationally symmetric flow above an infinite rotation disk,J. Fluid Mech. 67 (1975) 657–666.

    Google Scholar 

  3. BulirschR. and StoerS., Numerical treatment of ordinary differential equations by extrapolation methods,Num. Math. 8 (1966) 1–13, 93–104.

    Google Scholar 

  4. DijkstraD. and ZandbergenP. J., Some further investigations on non-unique solutions of the Navier-Stokes equations for the Karman swirling flow,Archives of Mechanics 30 (1978) 411–419 (Warszwawa).

    Google Scholar 

  5. Dijkstra, D., On the relation between adjacent inviscid cell type solutions to the rotating disk equations,Memorandum THT, Department TW (1979).

  6. KuikenH. K., The effect of normal blowing on the flow near a rotating disk of infinite extent,J. Fluid Mech. 47 (1971) 789–798.

    Google Scholar 

  7. Modern Computing Methods, N.P.L. notes on applied science 16; H.M. Stationery Office London (1961).

  8. OckendonH., An asymptotic solution for steady flow above an infinite rotating disk with suction,Quart. J. Mech. Appl. Math. 25 (1972) 291–301.

    Google Scholar 

  9. ZandbergenP. J. and DijkstraD., Non-unique solutions of the Navier-Stokes equations for the Karman swirling flow,J. Engg. Math. 11 (1977) 167–188.

    Google Scholar 

  10. Zandbergen, P. J., New solutions of the Karman problem for rotating flows,Proc. IUTAM symposium on approximation methods for Navier-Stokes Problems, Paderborn, West-Germany (september 1979).

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Authors and Affiliations

  1. Department of Applied Mathematics, Twente University of Technology, Enschede, The Netherlands

    D. Dijkstra

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  1. D. Dijkstra
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Dijkstra, D. On the relation between adjacent inviscid cell type solutions to the rotating-disk equations. J Eng Math 14, 133–154 (1980). https://doi.org/10.1007/BF00037623

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  • DOI: https://doi.org/10.1007/BF00037623

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