The　article　mainly　concerns　modeling　the　stochastic　input　and　its　propagation　in　incompressible　Navier-Stokes(N-S)　flow　simulations.　The　stochastic　input　is　represented　spectrally　by　employing　orthogonal　polynomial　functionals　from　the　Askey　scheme　as　trial　basis　to　represent　the　random　space.　A　standard　Galerkin　projection　is　applied　M　the　random　dimension　to　derive　the　equations　in　the　weak　form.　The　resulting　set　of　deterministic　equations　is　then　solved　with　standard　methods　to　obtain　the　mean　solution　and　variance　of　the　stochastic　velocity.　In　this　article,　the　main　method　employs　the　Hermite　polynomial　as　the　basis　in　random　space.　Cavity　problems　arc　given　to　demonstrate　the　process　of　numerical　simulation.　Furthermore.　Monte-Carlo　simulation　method　is　applied　to　illustrate　the　accurate　numerical　results.　2009　Wiley　Periodicals.　Inc.　Numer　Methods　Partial　Differential　Eq　26:　662-674,　2010