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.


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