Application of E-infinity theory to turbulence

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.