The stochastic modeling of random wake past a circular cylinder

We study the random laminar wake past a circular cylinder corresponding to a random Reynolds number. The random flow is computed using two different stochastic methods, i.e. the generalized polynomial chaos and the multi-element generalized polynomial chaos method. Rigorous convergence to the correct statistics of the velocity field is established. The random flow is subsequently decomposed into random modes according to a new type of orthogonal decomposition developed in this paper. This orthogonal decomposition which is substantially built upon the proper orthogonal decomposition framework defines an optimal set of random projectors for the stochastic Navier-Stokes equations which, after a suitable averaging operation, leads to a deterministic temporal evolution, i.e. a system of ordinary deterministic differential equations. This allow to construct a reduced order Galerkin model of the random flow as superimposition of deterministic temporal evolution of random spatial structures. Numerical applications are presented and discussed.