On the stability of two-dimensional parallel flows. I. General theory
Author:
C. C. Lin
Journal:
Quart. Appl. Math. 3 (1945), 117-142
MSC:
Primary 76.1X
DOI:
https://doi.org/10.1090/qam/13983
MathSciNet review:
13983
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A. B. Bassett, Proc. Roy. Soc. London (A) 52, 273–276 (1893).
H. Bateman, Bull. Nat. Research Council, Washington, no. 84, 372–384 (1932).
O. Blumenthal, Sitz. Akad. Wiss., München, 563–595 (1913).
H. Faxen, Arkiv Mat. Ast. Fysik 21A, no. 26, 11 p. (1928). (Curved.)
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S. Goldstein, Modern developments in fluid dynamics, The Clarendon Press, Oxford, 1938, pp. 135–136, 157, 194–200, 564.
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O. Haupt, Sitz. Akad. Wiss., München, 289 (1912).
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H. Jeffreys, Proc. London Math. Soc. (2) 23, 428–436 (1924).
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C. L. Pekeris, Jour. Aero. Sci. 5, 237–240 (1938).
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Lord Rayleigh, Scientific papers, Cambridge University Press, Cambridge, vol. 6, p. 266 (1914); vol. 6, p. 341 (1915).
Lord Rayleigh, Scientific papers, Cambridge University Press, Cambridge, vol. 6, p. 447 (1916). (Curved.)
O. Reynolds, Scientific papers, Cambridge University Press, Cambridge, vol. 2, pp. 535–577 (1895).
P. Savic, Phil. Mag. (7) 32, 245–252 (1941).
P. Savic and J. W. Murphy, Phil. Mag. (7) 34, 139–144 (1943).
H. Schlichting, Ann. d. Phys. (5) 14, 905–936 (1932).
H. Schlichting, Nachr. Ges. Wiss. Göttingen, 160–198 (1932). (Rotating cylinders.)
H. Schlichting, Zeit. angew. Math. Mech. 13, 171–174 (1933).
H. Schlichting, Nachr. Ges. Wiss. Göttingen, 181–208 (1933).
H. Schlichting, Naturwissenschaften 22, 376–381 (1934).
H. Schlichting, Nachr. Ges. Wiss. Göttingen 1, 47–78 (1935).
Th. Sexl, Ann. Phys. 83, 835–848 (1927); 84, 807–822 (1927). (Circular tube.)
F. R. Sharpe, Trans. Amer. Math. Soc. 6, 496–503 (1905).
H. Solberg, Proc. 1st Int. Congress Appl. Mech., Delft, 1924, pp. 387–394.
A. Sommerfeld, Proc. 4th Int. Congress Math., Rome, 1908, pp. 116–124.
R. V. Southwell and L. Chitty, Trans. Roy. Soc. London (A) 229, 205–253 (1930); Aeronautical Research Committee R. and M. no. 1200, (1930).
H. B. Squire, Proc. Roy. Soc. London (A) 142, 621–628 (1933).
J. L. Synge, Trans. Roy. Soc. Canada 27, 1–18 (1933).
J. L. Synge, J. Math. Physics 15, 205–210 (1936).
J. L. Synge, Semicentennial publications of the Amer. Math. Soc., 1938, vol. 2, pp. 227–269.
J. L. Synge, Proc. 5th Int. Congress Appl. Mech., Cambridge, Mass., U.S.A., 1938, Wiley and Sons, New York, 1939, pp. 326–332.
J. L. Synge, Proc. Roy. Soc. London (A) 167, 250–256 (1938). (Curved.)
K. Tamaki and W. J. Harrison, Trans. Cambridge Phil. Soc. 22, 425–438 (1920). (Curved.)
G. I. Taylor, Phil. Trans. Roy. Soc. London (A) 223, 289–343 (1923); also, Proc. 1st Int. Congress Appl. Mech. Delft, 1924, p. 89. (Curved.)
G. I. Taylor, Proc. Roy. Soc. London (A) 156, 307–317 (1936).
G. I. Taylor, Proc. Roy. Soc. London (A) 157, 546–564 (1936).
G. I. Taylor, Proc. 5th Int. Congress Appl. Mech., Cambridge, Mass., U.S.A., 1938, Wiley and Sons, New York, 1939, pp. 304–310.
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O. Teitjens, Zeit. angew. Math. Mech. 5, 200–217 (1925).
W. Tollmien, Nachr. Ges. Wiss. Göttingen, 21–44 (1929); Proc. 3rd Int. Congress Appl. Mech., Stockholm, 1930, vol. 1, pp. 105–108; Vorträge aus dem Gebeite der Aerodynamik und verwandte Gebeite, Aachen, 1929, Julius Springer, Berlin, 1930, pp. 18–21.
W. Tollmien, Nachr. Ges. Wiss. Göttingen (Neue Folge) 1, 70–114 (1935).
W. Tollmien, Zeit. angew. Math. Mech. 15, 96–100 (1935).
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
A. B. Bassett, Proc. Roy. Soc. London (A) 52, 273–276 (1893).
H. Bateman, Bull. Nat. Research Council, Washington, no. 84, 372–384 (1932).
O. Blumenthal, Sitz. Akad. Wiss., München, 563–595 (1913).
H. Faxen, Arkiv Mat. Ast. Fysik 21A, no. 26, 11 p. (1928). (Curved.)
K. O. Friedrichs, Fluid dynamics (mimeographed lecture notes, Brown University, 1942), ch. 4, pp. 200–209.
S. Goldstein, Proc. Camb. Phil. Soc. 32, 40–54 (1936).
S. Goldstein, Modern developments in fluid dynamics, The Clarendon Press, Oxford, 1938, pp. 135–136, 157, 194–200, 564.
H. Görtler, Zeit. angew. Math. Mech. 20, 138–147 (1940). (Curved.)
H. Görtler, Nachr. Ges. Wiss. Göttingen 2, 1–26 (1940). (Curved.)
G. Hamel, Nachr. Ges. Wiss. Göttingen, 261–270 (1911).
W. H. Harrison, Proc. Camb. Phil. Soc. 20, 455–459 (1920–1921).
O. Haupt, Sitz. Akad. Wiss., München, 289 (1912).
T. H. Havelock, Proc. Roy. Soc. London (A) 98, 428–437 (1921).
W. Heisenberg, Ann. d. Phys. 74, 577–627 (1924).
S. H. Hollingdale, Phil. Mag. (7) 29, 209–257 (1940).
L. Hopf, Ann. d. Phys. 4, 1–60 (1914).
H. Jeffreys, Proc. London Math. Soc. (2) 23, 428–436 (1924).
Th. von Kármán, Proc. 1st Int. Congress Appl. Mech., Delft, 1924, p. 97; Abh. Aerodynam. Inst. Tech. Hochschule, Aachen, 4, (1925).
Th. von Kármán, Proc. 4th Int. Congress Appl. Mech., Cambridge, England, 1934, Cambridge University Press, Cambridge, 1935, pp. 54–60, 77.
Lord Kelvin, Mathematical and physical papers, Cambridge University Press, vol. 4, pp. 186– 187 (1880).
Lord Kelvin, Mathematical and physical papers, Cambridge University Press, vol. 4, pp. 321– 330, 330–337 (1887).
L. V. King, Phil. Mag. (6) 31, 332–338 (1916).
H. A. Kramers, Zeit. f. Phys. 39, 828–836 (1926).
R. E. Langer, Trans. Amer. Math. Soc. 33, 23–64 (1931); 34, 447–480 (1932).
R. E. Langer, Bull. Amer. Math. Soc. 46, 257–263 (1940).
L. Lichtenstein, Hydromechanik, Julius Springer, Berlin, 1929, pp. 409–414.
C. C. Lin, Proc. Nat. Acad. Sci. U.S.A. 30, 316–324 (1944).
J. W. Lewis, Proc. Roy. Soc. London (A) 117, 388–407 (1928). (Curved.)
L. A. Lorentz, Abh. theoret. Phys. (Leipzig) 1, 43–71 (1907).
W. T. MacCreadie, Proc. Nat. Acad. Sci. U.S.A. 17, 381–388 (1931).
R. von Mises, Deut. Math. Ver. 21, 241–248 (1912).
R. von Mises, Festschrift Heinrich Weber, Teubner, Leipzig and Berlin, 1912, pp. 252–282.
F. Noether, Sitz. Akad. Wiss., München, 309–329 (1913).
F. Noether, Deut. Math. Ver. 23, 138–144 (1914).
F. Noether, Zeit. angew. Math. Mech. 1, 125–138, 218–219 (1921).
F. Noether, Zeit. angew. Math. Mech. 6, 232–243, 339–340, 428, 497–498 (1926).
W. M. F. Orr, Proc. Roy. Irish Acad. 27, 9–26, 69–138 (1906–1907).
C. W. Oseen, Arkiv. Mat. Ast. Fysik 7, no. 15, 20 p. (1911).
C. L. Pekeris, Proc. Cambridge Phil. Soc. 32, 55–66 (1936).
C. L. Pekeris, Jour. Aero. Sci. 5, 237–240 (1938).
L. Prandtl, Zeit. angew. Math. Mech. 1, 431–436 (1921); 11, 407 (1931); Phys. Zeit. 23, 19–23 (1922); Vorträge aus dem Gebeite der Aerodynamik und Verwandter Gebeite, Aachen, 1929, Julius Springer, Berlin, 1930, pp. 1–7.
L. Prandtl, Aerodynamic theory, edited by W. F. Durand, Julius Springer, Berlin, 1935, vol. 3, pp. 178–190.
Lord Rayleigh, Scientific papers, Cambridge University Press, Cambridge, vol. 1, pp. 474–487 (1880); vol. 3, pp. 17–23 (1887); vol. 3, pp. 575–584 (1892); vol. 4, pp. 203–209 (1895); vol. 6, p. 917 (1913).
Lord Rayleigh, Scientific papers, Cambridge University Press, Cambridge, vol. 6, p. 266 (1914); vol. 6, p. 341 (1915).
Lord Rayleigh, Scientific papers, Cambridge University Press, Cambridge, vol. 6, p. 447 (1916). (Curved.)
O. Reynolds, Scientific papers, Cambridge University Press, Cambridge, vol. 2, pp. 535–577 (1895).
P. Savic, Phil. Mag. (7) 32, 245–252 (1941).
P. Savic and J. W. Murphy, Phil. Mag. (7) 34, 139–144 (1943).
H. Schlichting, Ann. d. Phys. (5) 14, 905–936 (1932).
H. Schlichting, Nachr. Ges. Wiss. Göttingen, 160–198 (1932). (Rotating cylinders.)
H. Schlichting, Zeit. angew. Math. Mech. 13, 171–174 (1933).
H. Schlichting, Nachr. Ges. Wiss. Göttingen, 181–208 (1933).
H. Schlichting, Naturwissenschaften 22, 376–381 (1934).
H. Schlichting, Nachr. Ges. Wiss. Göttingen 1, 47–78 (1935).
Th. Sexl, Ann. Phys. 83, 835–848 (1927); 84, 807–822 (1927). (Circular tube.)
F. R. Sharpe, Trans. Amer. Math. Soc. 6, 496–503 (1905).
H. Solberg, Proc. 1st Int. Congress Appl. Mech., Delft, 1924, pp. 387–394.
A. Sommerfeld, Proc. 4th Int. Congress Math., Rome, 1908, pp. 116–124.
R. V. Southwell and L. Chitty, Trans. Roy. Soc. London (A) 229, 205–253 (1930); Aeronautical Research Committee R. and M. no. 1200, (1930).
H. B. Squire, Proc. Roy. Soc. London (A) 142, 621–628 (1933).
J. L. Synge, Trans. Roy. Soc. Canada 27, 1–18 (1933).
J. L. Synge, J. Math. Physics 15, 205–210 (1936).
J. L. Synge, Semicentennial publications of the Amer. Math. Soc., 1938, vol. 2, pp. 227–269.
J. L. Synge, Proc. 5th Int. Congress Appl. Mech., Cambridge, Mass., U.S.A., 1938, Wiley and Sons, New York, 1939, pp. 326–332.
J. L. Synge, Proc. Roy. Soc. London (A) 167, 250–256 (1938). (Curved.)
K. Tamaki and W. J. Harrison, Trans. Cambridge Phil. Soc. 22, 425–438 (1920). (Curved.)
G. I. Taylor, Phil. Trans. Roy. Soc. London (A) 223, 289–343 (1923); also, Proc. 1st Int. Congress Appl. Mech. Delft, 1924, p. 89. (Curved.)
G. I. Taylor, Proc. Roy. Soc. London (A) 156, 307–317 (1936).
G. I. Taylor, Proc. Roy. Soc. London (A) 157, 546–564 (1936).
G. I. Taylor, Proc. 5th Int. Congress Appl. Mech., Cambridge, Mass., U.S.A., 1938, Wiley and Sons, New York, 1939, pp. 304–310.
T. Y. Thomas, Amer. J. Math. 64, 754–767 (1942); Proc. Nat. Acad. Sci. U.S.A. 29, 243–246 (1943).
O. Teitjens, Zeit. angew. Math. Mech. 5, 200–217 (1925).
W. Tollmien, Nachr. Ges. Wiss. Göttingen, 21–44 (1929); Proc. 3rd Int. Congress Appl. Mech., Stockholm, 1930, vol. 1, pp. 105–108; Vorträge aus dem Gebeite der Aerodynamik und verwandte Gebeite, Aachen, 1929, Julius Springer, Berlin, 1930, pp. 18–21.
W. Tollmien, Nachr. Ges. Wiss. Göttingen (Neue Folge) 1, 70–114 (1935).
W. Tollmien, Zeit. angew. Math. Mech. 15, 96–100 (1935).
G. N. Watson, Theory of Bessel functions, Cambridge University Press, Cambridge, ed. 1, 1922, or ed. 2, 1944, p. 198; for Stokes’ phenomenon, see p. 201.
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