Sea currents could produce as much energy as wind currents because the average density of the oceans is about 850 times greater than that of air. Being able to accurately predict current power data is of critical importance in extracting the renewable energy potential of a specific ocean region. However, the classical power prediction formulas do not take into account the fluctuations around the mean, or turbulence. Because ocean currents are turbulent, a greater understanding of the existence of turbulence is a key factor in current power estimations. This paper principally investigates the use of the generalized gamma distribution in developing a new current power prediction formula that takes into account deviations from the mean. In addition, mean power and energy fluxes are calculated with the developed formula for the upper layers of the ocean (between 0 and 20 m) at the southern outlet of the Dardanelles as a case study. To estimate mean power and energy fluxes, 3-year hourly time series data with an average current speed of 0.381 m/s are used. Finally, the mean power and the energy fluxes are estimated to be 46.45 W/m2 and 407.23 kWh/m2/year, respectively.