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A global attractivity result for maps with invariant boxes
On a well-posed turbulence model
1. | University of Pittsburgh, Department of Mathematics, Pittsburgh, PA 15260, United States |
2. | Université Rennes 1, IRMAR, UMR CNRS 6625, F-35000 Rennes, France |
$\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.
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