Abstract
In the early 1920s the turbulence problem was perceived as the quest for a theory concerning the onset of turbulence. Its solution was expected along the Orr-Sommerfeld approach. It reached centre stage as a research subject for applied mechanics and mathematics. By the mid 1920s, however, Prandtl regarded fully developed turbulence as the greater turbulence problem for which he suggested the “mixing length” concept. A test case was the turbulent friction along a wall. Empirical data suggested at first that the mean velocity profile with growing distance from the wall obeys a power law; by 1929 it became clear that for high Reynolds numbers it was rather a logarithmic law. The derivation of the “wall law” became subject of a fierce rivalry between Prandtl and Kármán.
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Notes
- 1.
Noether (1921, p. 126). Translation ME.
- 2.
Schiller (1921, p. 436). Translation ME.
- 3.
Personal File L. Schiller, PA 0254, University Archive Leipzig.
- 4.
Schiller (1921, p. 443) . Translation ME.
- 5.
Prandtl (1921, p. 434) . Translation ME.
- 6.
ZAMM 1, 1921, pp. 419–420. Translation ME.
- 7.
ZAMM 2, 1922, p. 322.
- 8.
Kármán to Levi-Civita, 12 April 1922. TKC 18.8. Translation ME.
- 9.
Burgers to Kármán, 15 May 1923. TKC 4.21.
- 10.
ZAMM 3, 1924, pp. 272–276. For more details about the birth of the international mechanics congresses see Battimelli (1988) and Eckert (2006, Sect. 4.3).
- 11.
Heisenberg (1922, p. 139) . Translation ME.
- 12.
Heisenberg (1924, p. 577) . Translation ME.
- 13.
Schiller (1925, pp. 566–567) . Translation ME.
- 14.
Prandtl (1925, p. 137) . Translation ME.
- 15.
Prandtl (1927, p. 62) . Translation ME.
- 16.
The theory of jet broadening was published in ZAMM (Tollmien 1926) . For more details on the genesis of the mixing length approach see Eckert (2006, Sect. 5.3) and Bodenschatz and Eckert (2011, pp. 54–56).
- 17.
Prandtl (1927, p. 62) . Translation ME.
- 18.
Tollmien (1929, p. 42) . Translation ME.
- 19.
Tollmien (1929, p. 43) . Translation ME.
- 20.
Kármán to Prandtl, 12 February 1921. GOAR 3684. Translation ME.
- 21.
Prandtl to Birnbaum, 7 June 1923. MPGA, Abt. III, Rep. 61, Nr. 137. Translation ME.
- 22.
Prandtl (1930, p. 9) . Translation ME.
- 23.
Kármán to Burgers, 12 December 1929. TKC 4.22. Translation ME.
- 24.
Prandtl (1932, p. 21). Translation ME.
- 25.
Kármán to Prandtl, 26 September 1932. AMPG, Abt. III, Rep. 61, Nr. 793. Translation ME. For more detail on this rivalry see Eckert (2017, Sect. 6.8).
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Eckert, M. (2019). The Turbulence Problem in the 1920s. In: The Turbulence Problem. SpringerBriefs in History of Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-31863-5_2
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