Computing turbulent flow is very difficult but forms the basis for computational experiments in Meteorology and Oceanography. To overcome the difficulty and complexity in turbulence computation, a spectrally hyperviscous version of Navier-Stokes equations(SHNSE) has been suggested.The theoretical results that we obtained are the convergence of Galerkin solutions and the continuous dependence on data for the SHNSE, the estimates for the number of determining nodes and determining modes, and the inviscid limit in the case of unforced turbulence. In the computational analysis, Numerical experiments are conducted to validate some of the theoretical properties of the SHNSE and to investigate optimal parameter choices. Numerical results indicate that the SHNSE model has strong potential to be a highly robust platform for studying turbulence which can retain spectral accuracy while significantly reducing the number of degrees of freedom needed for accurate simulation.