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.
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