Abstract
PRANDTL'S hypothesis1,2 about turbulent motion in a simple shear layer proposes that the typical values of the fluctuating velocity components in the x and y directions, u and v, are each proportional to lδU/δy where l is the mixing length (Mischungsweg). Prandtl2,3 says that l “may be considered as the diameter of the masses of fluid moving as a whole in each individual case; or again, as the distance traversed by a mass of this type before it becomes blended in with neighbouring masses….”; and also that l is “somewhat similar, as regards effect, to the mean free path in the kinetic theory of gases”. It follows that the Reynolds shear stress −ρuv is proportional to ρl2(δU/δy)2 and l is defined so that the constant of proportionality is unity. Prandtl, however, described this expression as “only a rough approximation”.
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References
Prandtl, L., Z. angew. Math. Mech., 5, 136–139 (1925).
Tollmien, W., Schlichting, H., and Görtler, H., Ludwig Prandtl Gesammelte Abhandlungen (edited by Springer, Berlin, 1961).
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Prandtl, L., and Tietjens, O., Applied Hydro-and Aero-mechanics (McGraw-Hill, New York, 1934).
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BRADSHAW, P. Possible origin of Prandt's mixing-length theory. Nature 249, 135–136 (1974). https://doi.org/10.1038/249135b0
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DOI: https://doi.org/10.1038/249135b0
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