In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers (criteria) based on turbulent kinetic and dissipation rates associated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged Navier- Stokes equations (RANS). The RNG k-ε models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 10² to 10⁷ is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥3×10⁶. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.