A new technique for devising new models of turbulent viscosity for unsteady quasi-periodic flows is proposed in the report. The turbulent flow simulation strategy is based on two different flowfield decompositions, the Reynolds averaging, and the phase averaging. Properties of the mean flow are recovered on the base of the time-averaging of quasi-periodic solution of the Reynolds averaged Navier-Stokes equations. This yields an upper bound for the turbulent viscosity of the Organised Eddy Simulation model. The methods under study are verified on a typical test case, the flow around a square cylinder.