El-Naschie’s E-infinity theory is applied to turbulence. The Hausdorff-fractal dimension for turbulent flow is defined, the critical values for laminar flow (D
=3.98) and turbulent flow (D
=4.23) are obtained, and the fractal dimension for fully developed turbulent flow is D
>6.8. It is also shown that the Navier–Stokes equations are invalid for an exact model of turbulent flow and that two-dimensional planar turbulence does not exist in nature.
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