Abstract

MERCADO, José Roberto; GUIDO, Pedro; SANCHEZ-SESMA, Jorge  and  INIGUEZ, Mauro. Formulas for Drag Coefficient and the Navier-Stokes Fractional Equation. Tecnol. cienc. agua [online]. 2014, vol.5, n.2, pp.149-160. ISSN 2007-2422.

The aim of this paper is to find the relationship between the Navier-Stokes fractional equation and formulas for the drag coefficient, such as the Kármán-Schoenherr, Prandtl-Kármán, and Nikuradse. Scale changes produce a renormalization of boundary layer equations, which contains the key hypothesis about the thinness of this layer and leads to a multifractal description. A generalization is obtained from the Blasius experimental result for friction. By adjusting the relation of the number of features of the multifractal, the formulas that are the objective of this study can be inferred and represented as a bi-multifractal. This allows for an analysis with the critical Reynolds number and indicates that the Kármán-Schoenherr is the most suitable formula for the right boundary of the viscous sublayer. The adjustments resulted in refining the relation between Euler and Reynolds numbers, or obtaining the decays related to the drag coefficient. The results are applied to the description of the turbulent boundary layer and the interactions between flows and bottoms (for rivers, deserts and hurricanes).

Keywords : Navier-Stokes fractional equation; drag coefficient; multifractal; boundary layer.