The interaction of a shockwave with a turbulent upstream flow results in a rapid compression and amplification of the turbulence, and the behavior of this phenomenon is relevant to a range of problems involving shock driven mixing, such as inertial confinement fusion. The canonical shock-turbulence interaction problem of a normal shock passing through a field of homogenous isotropic turbulence is investigated in Large Eddy Simulation (LES), which allows for consideration of flow regimes that would be impractical in contemporary direct numerical simulations. The LES uses a modified version of the stretched-vortex model (Kosovic et al. 2002) to approximate the behavior of small scale eddies in the flow, and the effect of shockwaves on subgrid-scale modeling is considered. Results from the LES are presented over a range of upstream flow parameters and shock strengths, with particular focus on the spectral behavior of the turbulence. The stretched-vortex model includes Reynolds number effects, but for Taylor Reynolds numbers larger than 100 these effects are found to be small in the LES. The inertial range scales of the turbulence appear to relax to isotropy very quickly downstream of the shock, while the large scales of the turbulence remain anisotropic, and this results in a net transfer of energy into streamwise velocity fluctuations. This scale dependent relaxation to isotropy is used to explain discrepancies that have been observed between fluid simulations and linear analytical models of shock-turbulence interactions, and has implications for effective Reynolds Averaged Navier-Stokes (RANS) modeling of the subject problem.