Un análisis sobre la turbulencia bidimensional

Abstract

The objective of this theoretical work was to show the properties or characteristics of a turbulent flow when a two-dimensional nature of two types is required over the flow: confined in a plane and, when this is three-dimensional but does not show variations along one of the axes. Therefore, the reynolds equations, the equations of the vorticity mean field and the energy of the three-dimensional turbulent flow were obtained. These equations were subjected to a transformation of dimensional order reduction given by the conditions, which in the first case, assumed all derivatives along the vertical axis x₃ equal to zero, as well as the component of the velocity mean field <u₃> and the velocity disturbance field component u₃ 'equal to zero too. On the second case, an invariance along the x₃ axis was the only condition. Finding that in both cases, the dimensional reduction prohibits the phenomenon of stretching and tilting of the vortexes, present in the three-dimensional turbulence. In the first case the absence of this phenomenon is complete, while in the second this phenomenon does not happen only in the vortexes with direction along x₃. It was demostrated that this distinction in the behavior of the vortexes causes a quase-conservative state of the energy of the flow, so that the life time of it is larger compared to the time of life of the three-dimensional turbulent flow, which dissipates the energy with a dissipation rate proportional to U³ / L.