ASYMPTOTIC REYNOLDS-AVERAGED CLOSURE OF NONLINEAR ENSEMBLES

The authors show that the Reynolds-averaged representation of finite-d imensional dynamical systems with quadratic nonlinearity can be closed in the limit of infinite moment. The closure is posed for problems wi th algebraic moment hierarchies, and tested on regular ensembles of th e viscous Burgers equation and ensembles whose individual members are chaotic solutions of the Lorenz equations. The solvability of the aver aged system of equations and the equivalence of direct simulation and Reynolds-averaged computation, using a simple one-dimensional model pr oblem, are demonstrated.