Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session ZC41: Turbulence: Mixing
12:50 PM–3:00 PM,
Tuesday, November 21, 2023
Room: 206
Chair: Alais Hewes, McGill University
Abstract: ZC41.00008 : On the Taylor-Prandtl controversy
2:21 PM–2:34 PM
Presenter:
Emmanuel Villermaux
(Aix-Marseille University)
Authors:
Emmanuel Villermaux
(Aix-Marseille University)
Lucas Rotily
(Aix-Marseille University)
We reexamine critically this problem on hand of several experiments with plane (2D) and round (3D) turbulent jets seeded with high and low diffusing scalars, and conclude that the microscopic equations for u and c have no reasons to be different in general, but that the difference between the u and c-fields is a genuine mixing problem. Denoting Sc=ν/D the Schmidt number of the scalar, we find that u=c1+1/√Sc is quantitatively consistent with all the observations we have on hand to date. Earlier measurements dating back two the 1930’s-40’s were all made for heat transport in air with Sc≈1, leading indeed to u=c2, an agreement with Taylor’s vision which is only coincidental. The relation above is grounded in a coupling, by molecular diffusion, between the eddies (lamellae, sheets) and the bath in which they move. This observation is also strictly at odd with Reynolds' analogy, although essentially an adaptation of it to eddies transporting momentum and mass, but liable to exchange mass with a smooth reservoir as they move along their brownian path.
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