An approach for numerically representing turbulence effects in the simulation of ocean current turbines (OCT)s is described. Ambient turbulence intensity and mean flow velocity are utilized to develop analytic expressions for flow velocities at a grid of nodes that are a function of time. This approach is integrated into the numerical simulation of an OCT to evaluate effects of turbulence on performance. For a case study a moored OCT with a 20 m rotor diameter is used. Mean power in the presence of ambient turbulence intensities (TI)s of 5% and 20% are found to be 370 kW and 384 kW, with standard deviations of 17.2 kW and 74.6 kW respectively. Similarly, the axial loads on a single blade of the three-bladed rotor are found to be 139 kN and 140 kN, with standard deviations of 3 kN and 12 kN respectively for these TIs.