Successes and surprises with computer-extended series

  • Milton van Dyke
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 141)


Shock Wave Piston Motion Dean Number Rotating Fluid Spherical Shock Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. BLASIUS, H. 1908 Grenzschichten in FlUssigkeiten mit kleiner Reibung. Z. Math. Phys. 56:1–37; English transl., NACA TM 1256Google Scholar
  2. DEAN, W. R. 1928 The stream-line motion of fluid in a curved pipe. Phil. Mag. (7) 5:673–695Google Scholar
  3. FUJIMOTO, Y. & MISHKIN, E. A. 1978 Analysis of spherically imploding shocks. Phys. Fluids 21:1933–1938CrossRefGoogle Scholar
  4. GUDERLEY, G. 1942 Starke kugelige und zylindrische Verdichtungsstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung 19:302–312Google Scholar
  5. REDDALL, W. F. 3rd 1972 The asymptotic trajectory of a strong planar shock wave arising from a non-self-similar piston motion. Ph.D. diss., Stanford Univ.Google Scholar
  6. SCHWARTZ, L. W. 1974 Computer extension and analytic continuation of Stokes' expansion for gravity waves. J. Fluid Mech. 62:553–578Google Scholar
  7. SMITH, A. M. O. & CLUTTER, D. W. 1963 Solution of the incompressible laminar boundary-layer equations; Solution of Prandtl's boundary-layer equations. Douglas Aircraft Corp. Engg. Papers 1525, 1530Google Scholar
  8. STOKES, G. G. 1880 Supplement to a paper on the theory of oscillatory waves. Mathematical and Physical papers, 1:314–326. CambridgeGoogle Scholar
  9. VAN DYKE, M. 1964 Higher approximations in boundary-layer theory. Part 3. Parabola in uniform stream. J. Fluid Mech. 19:145–159Google Scholar
  10. VAN DYKE, M. & GUTTMANN, A. J. 1978 Computer extension of the M2 expansion for a circle. Bull. Amer. Phys. Soc. 23:996, Abstract no. BD5Google Scholar
  11. WEIDMAN, P. D. & REDEKOPP, L. G. 1976 On the motion of a rotating fluid in the presence of an infinite rotating disk. Archives of Mechanics 28:1011–1024Google Scholar
  12. ZANDBERGEN, P. J. & DIJKSTRA, D. 1977 Non-unique solutions of the Navier-Stokes equations for the Karman swirling flow. J. Engg. Math. 11:167–188CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Milton van Dyke
    • 1
  1. 1.Stanford UniversityStanford

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