# Las ecuaciones de Reynolds y la relación de clausura

## Fecha

2009-02-27 00:00:00

## Tipo

artículo original

## Autores

Mercado Escalante, José Roberto

## Resumen

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; theone is interpret by us as a jump in the index of occupation of the space. Our mainresult consists of which the Reynolds stress is expressed like the fractional derived onefrom the average velocity.Being the order of the derived one index of space occupation; what the Reynoldsequations transform into differential integral equations. We formulate a model of fractionalPrandtl where the squared root of the Reynolds stress depends of the fractionalderived one from the average velocity and the model of Prandtl is recovered when thefractional derived one tends to the whole of value. A regularizated transition appearsbetween velocity of the inertial sub-layer and the viscous and the constant of Nikuradseis obtained like the hydraulic equivalent of the Euler’s constant, who measuresthe reason of the two scales. We analyze the Reynolds equations for a flow betweentwo planes parallels, through an equation of stationary Fokker-Planck. The velocityprofile 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, asa jump of discontinuity of the Reynolds stress in as much parameter of order, withrupture of the symmetry; and at micro level, as a jump in the index of occupation ofthe space.Keywords: Reynolds equations and stress, boundary layer, viscous layer, Prandtl’smodel, fractional derivatives, inverse problem, Camassa-Holm equation, second-order transition,order parameter.