達朗貝爾佯謬
笔记

↑  Jean le Rond d'Alembert (1752).
↑  Grimberg, Pauls & Frisch (2008).
↑  Falkovich (2011), p. 32.
↑  Reprinted in: Jean le Rond d'Alembert (1768).
↑  M.J. Lighthill, , Nature, 1956, 178 (4529): 343, Bibcode:1956Natur.178..343., doi:10.1038/178343a0
1 2  Landau & Lifshitz (1987), p. 15.
1 2  Batchelor (2000), pp. 264–265, 303, 337.
1 2 3  
Schlichting, Hermann; Gersten, Klaus,  8th revised and enlarged, Springer, 2000, ISBN 978-3-540-66270-9 , pp. XIX–XXIII.
1 2  
Veldman, A.E.P., , Journal of Engineering Mathematics, 2001, 39: 189–206, Bibcode:2001JEnMa..39..189V, doi:10.1023/A:1004846400131
1 2  Stewartson (1981).
↑  Feynman, R.P.; Leighton, R.B.; Sands, M., , Reading, Mass.: Addison-Wesley, 1963, ISBN 978-0-201-02116-5 , Vol. 2, §41–5: The limit of zero viscosity, pp. 41–9 – 41–10.
↑  Saint-Venant, A., , Comptes Rendus des Séances de l'Académie des Sciences, 1847, 24: 243–246  [2008-08-15], （原始内容存档于2011-08-06）
↑  Stokes, G.G., , Trans. Camb. Philos. Soc., 1851, 9: 8–106, Bibcode:1851TCaPS...9....8S . Reprinted in Stokes, G.G., , Mathematical and Physical Papers 2nd (Cambridge Univ. Press)
↑  The Stokes flow equations have a solution for the flow around a sphere, but not for the flow around a circular cylinder. This is due to the neglect of the convective acceleration in Stokes flow. Convective acceleration is dominating over viscous effects far from the cylinder (Batchelor, 2000, p. 245). A solution can be found when convective acceleration is taken into account, for instance using the Oseen equations (Batchelor, 2000, pp. 245–246).
1 2 3  Batchelor (2000), pp. 337–343 & plates.
↑  Batchelor (2000), p. 499, eq. (6.13.12).
↑  Kirchhoff, G., , Journal für die reine und angewandte Mathematik, 1869, 1869 (70): 289–298, doi:10.1515/crll.1869.70.289
1 2  Rayleigh, Lord, , Philosophical Magazine, 1876, 5 (2): 430–441 . Reprinted in: Scientific Papers 1:287–296.
↑  Helmholtz, H. L. F. von, , Monatsberichte der Königlichen Akademie der Wissenschaften zu Berlin, 1868, 23: 215–228 . Reprinted in: Philosophical Magazine (1868) 36:337–346.
↑  Batchelor (2000), pp. 338–339
1 2 3  Wu, T. Y., , Annual Review of Fluid Mechanics, 1972, 4: 243–284, Bibcode:1972AnRFM...4..243W, doi:10.1146/annurev.fl.04.010172.001331
1 2 3  Lamb, H.,  6th, Cambridge University Press: 679, 1994, ISBN 978-0-521-45868-9
↑  Levi-Civita, T., , Rendeconti del Circolo Matematico di Palermo, 1907, 23: 1–37, doi:10.1007/bf03013504
↑  
Lord Kelvin, , Nature, 1894, 50 (1300): 524–5, 549, 573–5, 597–8, Bibcode:1894Natur..50..524K, doi:10.1038/050524e0  Reprinted in: Mathematical and Physical Papers 4: 215–230.
↑  Batchelor (2000), p. 500.
↑  Batchelor (2000), pp. 493–494.
1 2  Prandtl (1904).
↑  Batchelor (2000) pp. 302–314 & 331–337.
↑  Garrett Birkhoff, Hydrodynamics: a study in logic, fact, and similitude, Princeton University Press, 1950
↑  Birkhoff (1950) p. 4.
↑  Birkhoff (1950) p. 21.
↑  James J. Stoker, , Bull. Amer. Math. Soc., 1951, 57 (6): 497–499  [2022-07-25], doi:10.1090/S0002-9904-1951-09552-X, （原始内容存档于2020-06-16）.
↑  Closest to the first quote comes, on page 5:
↑  For instance, the paradox of the constancy of the speed of light in all directions, was solved by the special theory of relativity.
↑  This article follows the derivation in Section 6.4 of Batchelor (2000).
稳定且分离的不可压缩势流在二维板周围流动， 並以恒压沿着两条与二维板边缘分离的自由流线流动。
圆柱体周围流动的压力分布。蓝色虚线是根据勢流理论的压力分布，导致了達朗貝爾佯謬。蓝色实线是在高雷诺数实验中发现的平均压力分布。压力是從圆柱表面徑向放射;正压在圆柱内，朝向中心，而负压繪於圆柱外。
圆柱體位於均匀洪流中，流线用于表示围绕在該柱旁的势流。