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On a well-posed turbulence model

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  • This report considers mathematical properties, important for practical computations, of a model for the simulation of the motion of large eddies in a turbulent flow. In this model, closure is accomplished in the very simple way:

    $\overline{u u} $˜ $\overline{\bar {u} \bar {u}}$, yielding the model
    $\nabla \cdot w= 0, \quad w_{t} + \nabla \cdot (\overline{w w}) - \nu \Delta w + \nabla q = \bar {f}$.

    In particular, we prove existence and uniqueness of strong solutions, develop the regularity of solutions of the model and give a rigorous bound on the modelling error, $||\bar {u} - w||$. 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.

    Mathematics Subject Classification: Primary: 76F65; Secondary: 35Q30.

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