On a wellposed turbulence model doi:10.3934/dcdsb.2006.6.111 Abstract Full Text (247.9K) Related Articles
W. Layton  University of Pittsburgh, Department of Mathematics, Pittsburgh, PA 15260, United States (email) Abstract: 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 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 nonphysical 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.
Keywords: turbulence, large eddy simulation.
Received: August 2004; Revised: August 2005; Published: October 2005. 
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