Abstract
The temporal evolution of nonlinear, incompressible ensembles is examined first for the one-dimensional Burgers' equation and then for the incompressible, unsteady Navier-Stokes equations. It is shown that local closure of the averaged problem can be obtained for finite ensembles of Burgers' equation in the limit as the number of moments tends to infinity. This limit behaviour is verified via direct numerical computations for the onedimensional inviscid and viscous Burgers' equation. Closure is found to occur at reasonably low order. It is shown that this technique can be extended to obtain a local closure of the convective terms of the Navier-Stokes Reynoldsaveraged equations.
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