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The „NEW“ Mechanics of Fluids of Ludwig Prandtl

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Ludwig Prandtl, ein Führer in der Strömungslehre

Abstract

The title of this short note comes from a survey lecture delivered at an AGARE) Conference on Flow Separation by Schlichting 1975 in Göttingen, organized for the hundredth anniversary of Prandtl’s birth. Among a number of reasons he alluded for accepting to prepare the lecture on an „account of the scientific life of Ludwig Prandtl“ the most motivating one is as follows: „I was myself personaly close to Prandtl, because, since my student days, that is for almost fifty years, I have worked almost exclusively in the field of the new mechanics of fluids, whose foundation was erected by him“.

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References

  • BOIS P.A., DERIAT E., GATIGNOL R., RIGOLOT A. 1994. „Asymptotic modelling in fluid mechanics“, Springer, Lecture Notes in Physics.

    Google Scholar 

  • BROWN S.N., STEWARTSON K. 1969. „Laminar separation“, Annual Review of Fluid Mechanics, 1, 45–72.

    Article  Google Scholar 

  • CHENG H.K. 1978. „Liftingline theory of oblique wings“, AIAA Journal, 16, 1211–1213.

    Article  MATH  Google Scholar 

  • CHENG H.K. and MURILLO L.E. 1984. „Lunate-tail swimming propulsion as a problem of curved lifting-line in unsteady flow“, J. Fluid Mech., 143, 327–350.

    Article  MATH  Google Scholar 

  • DEGANI A.T., WALKER J.D., SMITH. 1998. „Unsteady separation past moving surface“, J. Fluid Mech., 375, 1–38.

    Article  MathSciNet  MATH  Google Scholar 

  • ECKHAUS W. 1973. „Mached asymptotic expansions and singular perturbations“. North-Holland.

    Google Scholar 

  • ECKHAUS W. 1979.“Asymptotic analysis of singular perturbations“. Studies in Math. Appl., 9, North-Holland.

    MATH  Google Scholar 

  • GERMAIN P. 1973. „Méthodes asymptotiques en mécanique des fluides“in Mécanique des Fluides. Eds. Balian & Peube, Gordon and Breach, p. 7–147.

    Google Scholar 

  • GOLDSTEIN S. 1930. „Concerning some solutions of the boundary layer equations in hydrodynamics“, Proc. Lamb Phil. Soc, 26, 1–30.

    Article  MATH  Google Scholar 

  • GOLDSTEIN S. 1969. „Fluid mechanics in the first half of this century“, Annual Review of Fluid mechanics, 1, 1–28.

    Article  Google Scholar 

  • GUERMOND H.K. 1990. „A generalized lifting-line theory for curved and swept wings“, J. Fluid Mech., 211, 497–513.

    Article  MathSciNet  MATH  Google Scholar 

  • GUERMOND H.K. AND SELLIER A. 1991. „A unified unsteady lifting-line theory“, J. Fluid Mech., 229, 427–451.

    Article  MathSciNet  MATH  Google Scholar 

  • GUIRAUD J.P. AND SLAMA G. 1981. „Sur la théorie asymptotique de la ligne portante en régime incompressible oscillatoire“, La Recherche Aérospatiale, 1, 1–6.

    Google Scholar 

  • GUIRAUD J.P. 1994. „Going on with with asymptotics“in Asymptotic Modelling in Fluid Mechanics, eds. Bois P.A. and al, Springer, 257–307.

    Google Scholar 

  • JAMES E.C. 1975. „Lifting-line theory for an unsteady wing as a singular perturbation problem“, Journal of Fluid Mechanics, 70, 753–771.

    Article  MATH  Google Scholar 

  • KAPLUN S. 1954. „The role of coordinate systems in boundary layer theory“, Z. angew. Math. Phys., 5, 111–135.

    Article  MathSciNet  MATH  Google Scholar 

  • KITA T. AND MIYAI Y. 1978. „An alternative treatment of lifting-line theory as a perturbation problem“, Z. angew. Math. Phys., 29, 596–607.

    Google Scholar 

  • LAGERSTROM P.A. 1964. „Laminar flow theory“in High Speed Aerodynamics and Jet Propulsion, vol. 4, Princeton Univ. Press., 20–282.

    Google Scholar 

  • LAGERSTROM P.A. 1988. „Matched asymptotic expansions. Ideas and techniques“, Applied Mathematics Sciences, 76, Springer.

    MATH  Google Scholar 

  • LAGRéE P.Y. 1994. „Upstream influence in mixed convection at small Richardson number on triple, double and single deck scales“in Asymptotic Modelling in Fluid Mechanics, eds Bois P.A. and al, Springer, 229–238.

    Google Scholar 

  • LIGHTHILL M.J. 1953. „On boundary layers and upstream influence“, Proc. roy. Soc. London A, 217, 478–507.

    Article  Google Scholar 

  • MAUSS J. 1994. „Asymptotic modelling for separating boundary layers“in Asymptotic Modelling in Fluid Mechanics, eds Bois P.A. and al, Springer, 239–254.

    Google Scholar 

  • NEILAND V.Ia. 1969. „On the theory of laminar separation in supersonic flow (in Russian), Izv. Ak. Naouk SSSR MJG, 4, 53–57.

    Google Scholar 

  • PRANDTL L. 1904. „Über Flüssigkeitsbewegung bei sehr kleiner Reibung“, Proceedings III Int. Math. Congress, Heidelberg, 484–491.

    Google Scholar 

  • PRANDTL L. 1918–1919. „Über Tragflügel Theorie I und II“, Mitteilung Nach, der Kgl. Ges. Wiss, Göttingen Math. Phys. Klasse, 451–477 und 107–137.

    Google Scholar 

  • ROSENHEAD L. 1963. „Laminar boundary layers“, Oxford at the Clarendon Press.

    MATH  Google Scholar 

  • SCHLICHTING H. 1960. „Boundary layer theory“, 4th ed., Mc Graw Hill.

    MATH  Google Scholar 

  • SCHLICHTING H. 1975. „An account of the scientific life of Ludwig Prandtl“, AG ARD Conference Proceedings on flow Separation CP 168, 1–30.

    Google Scholar 

  • SMITH F.T. 1977. „The laminar separation of an incompressible fluid streaming past a smooth surface“, Proc. Roy. Soc. London, 355, 443–463.

    Article  Google Scholar 

  • SMITH F.T. 1982. „On the high Reynolds number theory of laminar flows“, IMA Journal of Applied Mathematics, 28, 207–281.

    Article  MATH  Google Scholar 

  • STEWARTSON K., WILLIAMS P.G. 1969. „Self induced separation“, Proc. Roy. Soc. London A, 312, 181–206.

    Article  MATH  Google Scholar 

  • STEWARTSON K. 1974. „Multistructured boundary layers“, Adv. Appl. Mech., 14, 145–239

    Article  Google Scholar 

  • SYCHEV V.V. 1972. „On laminar separation“, (in Russian), Mekhnika Zhidkosti i Gaza, 47–59

    Google Scholar 

  • THURBER J.K. 1965. „An asymptotic method for determining the lift distribution of a swept-back wing of finite span“, Commun. Pure Apll. Maths., 18, 733–756

    Article  MathSciNet  MATH  Google Scholar 

  • THWAITES B. 1960. „Incompressible aerodynamics“, Clarendon Press, Oxford.

    MATH  Google Scholar 

  • VAN DYKE M.D. 1964 „Lifting-line theory as a singular perturbation problem“, Appl. Math. Mech., 28, 90–101

    Article  MathSciNet  MATH  Google Scholar 

  • VAN DYKE M.D. 1964. „ Perturbations methods in fluid mechanics“, Academic Press, New York; 1975, Parabolic Press.

    Google Scholar 

  • VAN DYKE M.D. 1962–1964. „Higher approximations in boundary layer theory. I: General Analysis“, J. Fluid Mech., 14, 161–177.

    Article  Google Scholar 

  • VAN DYKE M.D. 1962–1964. „Higher approximations in boundary layer theory. „II: Application to leading edge“, J. Fluid Mech., 14, 481–495.

    Article  Google Scholar 

  • VAN DYKE M.D. 1962–1964. „Higher approximations in boundary layer theory. „IV: Parabola in uniform stream“, J. Fluid Mech., 19, 145–159.

    Article  MathSciNet  MATH  Google Scholar 

  • VAN DYKE M.D. 1994. „Growing up with asymptotics“ in Asymptotic Modelling in Fluid Mechanics, eds. Bois P.A. and al, Springer, 3–10

    Google Scholar 

  • VAN DYKE M.D. 1994. „Nineteenth century roots of the boundary layer idea“, SIAM Rev., 36, 415–424

    Article  MathSciNet  MATH  Google Scholar 

  • VAN HOLTEN T. 1976. „ Some notes on unsteady lifting line theory“, J. Fluid Mech., 77, 561–574

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie/CNRS UMR, 7607, Paris, France

    Paul Germain

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  1. Paul Germain
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Gerd E. A. Meier

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© 2000 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

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Germain, P. (2000). The „NEW“ Mechanics of Fluids of Ludwig Prandtl. In: Meier, G.E.A. (eds) Ludwig Prandtl, ein Führer in der Strömungslehre. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-90498-0_3

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  • DOI: https://doi.org/10.1007/978-3-322-90498-0_3

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-90499-7

  • Online ISBN: 978-3-322-90498-0

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