Transport phenomena eddies

Equation 7.2.a-5 implicitly assumes perfectly ordered flow in that V (pyD Vx ) is specific for molecular diffusion. Deviations from perfectly ordered flow, as encountered with turbulent flow, lead to a flux that is also expressed as if it arose from a diffusion-like phenomenon, in order to avoid too complex mathematical equations. The proportionality factor between the flux and the concentration gradient is then called the turbulent or eddy diffusivity. Since this transport mechanism is considered to have the same driving force as molecular diffusion, the two mechanisms are summed and the resulting proportionality factor is called effective diffusivity, D,. In highly turbulent flow the contribution of... 

A closer analysis of this problem would reveal more complex situations, such as a fluid flowing around a solid body. In that case the streamlines may take off behind the body at the limit of zero viscosity of the fluid. However, all fluids exhibit some viscosity and no such phenomenon can be observed. Experiments show that vorticity is generally generated in a thin boundary layer, close to a solid surface. It is propagated from the wall by both viscous diffusion and convection. The vortices are transported with the fluid they are observable for some time after their appearance. If the experiment is made with a circular cylinder moving at a constant velocity, the eddies appear in the wake of the body and their regular distribution constitutes the famous, as well as beautiful, Karman vortex street . 

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