Las ecuaciones de Reynolds y la relación de clausura

Abstract

We posed the problem to obtain the closure relation for the Reynolds equations. And like secondary target, to obtain analytical expressions for the Reynolds stress. Showing its jump of discontinuity like expression of the rupture of the symmetry; the one is interpret by us as a jump in the index of occupation of the space. Our main result consists of which the Reynolds stress is expressed like the fractional derived one from the average velocity. Being the order of the derived one index of space occupation; what the Reynolds equations transform into differential integral equations. We formulate a model of fractional Prandtl where the squared root of the Reynolds stress depends of the fractional derived one from the average velocity and the model of Prandtl is recovered when the fractional derived one tends to the whole of value. A regularizated transition appears between velocity of the inertial sub-layer and the viscous and the constant of Nikuradse is obtained like the hydraulic equivalent of the Euler’s constant, who measures the reason of the two scales. We analyze the Reynolds equations for a flow between two planes parallels, through an equation of stationary Fokker-Planck. The velocity profile for the viscous sub-layer is obtained as much; like for the inertial sub-layer. The fluid displays a transition of second order that is pronounced, at level macro, as a jump of discontinuity of the Reynolds stress in as much parameter of order, with rupture of the symmetry; and at micro level, as a jump in the index of occupation of the space. Keywords: Reynolds equations and stress, boundary layer, viscous layer, Prandtl’s model, fractional derivatives, inverse problem, Camassa-Holm equation, second-order transition, order parameter.