  Approximation of the marginal distribution of the solution of the stochastic
Navier-Stokes equations on the two-dimensional torus by high order numerical
methods is considered. The corresponding rates of convergence are obtained for
a splitting scheme and the method of cubature on Wiener space applied to a
spectral Galerkin discretisation of degree $N$. While the estimates exhibit a
strong $N$ dependence, convergence is obtained for appropriately chosen time
step sizes. Results of numerical simulations are provided, and confirm the
applicability of the methods.
