On a well-posed turbulence model.(English)Zbl 1089.76028

Summary: This report considers mathematical properties, important for practical computations, of a model for the simulation of motion of large eddies in a turbulent flow. In this model, closure is accomplished in the very simple way:
$\overline{uu}\sim \overline{\bar {\mathbf u}\bar {\mathbf u}},\text{ yielding the model }\nabla\cdot w = 0,\quad {\mathbf w}_t +\nabla (\overline{\mathbf{ww}})-\nu\Delta {\mathbf w}+\nabla q=\overline{\mathbf f}.$
In particular, we prove the existence and uniqueness of strong solutions, study the regularity of solutions of the model, and give a rigorous bound on the modelling error, $$\|{\mathbf u}- {\mathbf w}\|$$. Finally, we consider the question of non-physical vortices (false eddies), proving that the model correctly predicts that only a small amount of vorticity results when the total turning forces on the flow are small.

MSC:

 76F65 Direct numerical and large eddy simulation of turbulence 35Q35 PDEs in connection with fluid mechanics
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