On a well-posed turbulence model

This report considers mathematical proper-ties, 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: (uu) over bar similar to (uu) over bar, yielding the model del . w = 0, w(t) + del . ((ww) over bar) - v Delta w + del q = (f) over bar. 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, parallel to(u) over baru - w parallel to. 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.