Analysis of the Blasius’ Formula and the Navier–Stokes Fractional Equation

The objective of this paper is to find the relationship between the Blasius formula for friction factor and the Navier–Stokes Fractional equation. The renormalization that produces changes of scale of the boundary layer equations contains the essential hypothesis of the thinness of said layer, a characteristic which appears in all important outcomes, such as friction force and drag coefficient and gives rise to a multi-fractal description. A generalization of experimental results for the Blasius friction factor that is interpreted and generalized as a multi-fractal is obtained. Applying Hadamard functionals the friction factor is described as a fractional derivative whose order depends on the spatial occupancy index. Results are applied to the interactions between currents and boundaries (in rivers, deserts and hurricanes).