Turbulence: An Old Challenge and New Perspectives

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Turbulence at very large Reynolds numbers (often called developed turbulence) is widely considered to be one of the happier provinces of the turbulence realm, as it is widely thought that two of its basic results are well-established, and have a chance to enter, basically untouched, into a future complete theory of turbulence. These results are the von Kármán–Prandtl universal logarithmic law in the wall-region of wall-bounded turbulent shear flow, and the Kolmogorov–Obukhov scaling laws for the local structure of developed turbulent flow.However, doubts have been expressed over the years about the fluid mechanical assumptions that underlie these laws.

After a concise review of the problem of turbulence as a whole we will show in the present paper that the von Kármán–Prandtl universal logarithmic law is based on an assumption which,though plausible, in fact is not quite correct. We will come to the conclusion, based on theoretical considerations and on processing of experimental data, that the universal logarithmic law does not describe the real features of developed turbulent wall-bounded flow of viscous fluid; it should be jettisoned and replaced by a different law, a scaling law.

Experimental evidence for the local structure of turbulent flows is now not sufficiently well-established to allow a similarly definite conclusion. However, the application of the new approach presented here makes it very plausible that the classical, non-modified version of Kolmogorov–Obukhov ‘K–41’ laws gives an adequate description of the local features of developedturbulent flows.

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