Vorticities in a LES Model for 3D Periodic Turbulent Flows

This paper is devoted to the study of a LES model to simulate turbulent 3D periodic flow. We focus our attention on the vorticity equation derived from this LES model for small values of the numerical grid size δ. We obtain entropy inequalities for the sequence of corresponding vorticities and corresponding pressures independent of δ, provided the initial velocity u0 is in Lx2 while the initial vorticity ω0  =  ∇  ×  u0 is in Lx1. When δ tends to zero, we show convergence, in a distributional sense, of the corresponding equations for the vorticities to the classical 3D equation for the vorticity.