By Davidson P., et al. (eds.)
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If these are clearly established a great point would be secured, but its reasoning is somewhat obscure, and needs much amplification. The conception of ‘mean-mean-motion’ is a very delicate one and it is not made evident in what sense u, v, w are continuous functions, or on what conditions the derivatives, etc. are supposed to be formed. The whole argument turns on questions of this kind, and it is just here that explanations are wanting. A margin instruction pencilled on the review in Rayleigh’s hand, indicated that the report was to be copied (meaning that a clerk was to transcribe the review) presumably for onward transmission to Osborne Reynolds.
20. G¨ottingen, Lesezimmer des Mathematischen Instituts. html. Klein’s seminar protocol book, no. 27. G¨ottingen, Lesezimmer des Mathematischen Instituts. html. , 1904). However, the eﬀorts in the seminar to determine the (unknown) eddy viscosity of Boussinesq’s approach proved futile. 4 In spite of the emphasis on the riddles of turbulence in these seminars, it is commonly reported that Prandtl ignored turbulence as a research theme until many years later. For example, the editors of his Collected Papers dated his first publication in the category Turbulence and Vortex Formation to the year 1921 (see below).
46 Bodenschatz & Eckert and his collaborators were able to reproduce Eiﬀel’s discovery: at a critical air speed the drag coeﬃcient suddenly dropped to a much lower value. Prandtl also oﬀered an explanation of the new phenomenon. He assumed that the initially laminar boundary layer around the sphere becomes turbulent beyond a critical air speed. On the assumption that the transition from laminar to turbulent flow in the boundary layer is analogous to Reynolds’ case of pipe flow, Prandtl displayed the sphere drag coeﬃcient as a function of the Reynolds number, UD/ν (flow velocity U, sphere diameter D, kinematic viscosity ν), rather than, as did Eiﬀel, of the velocity; thus he demonstrated that the eﬀect occurred at roughly the same Reynolds number even if the individual quantities diﬀered widely (the diameters of the spheres ranged from 7 to 28cm; the speed in the wind tunnel was varied between 5 and 23m/s).
A journey through turbulence by Davidson P., et al. (eds.)