  Based on the characteristics of the multi-scale and similarity at different
scales in turbulent flow, we propose a scale decomposition for solving the
turbulence problem of incompressible Newtonian fluid. The solution domain is
decomposed into two-level scales, the large scale component represents mean
flow and large scale eddies, and the small scale one represents the turbulent
fluctuations. The problem is solved in large scale by the equations of motion
and the effect of the turbulent fluctuations on the mean flow is evaluated
approximately by using equivalent eddy. Furthermore, the effect of equivalent
eddy is decomposed into two parts including convective effect and diffusion
effect, which is expressed as a function of mean quantities in large scale. The
modified Naiver-Stokes equations are established, there ensures the closure of
the equations in large scale. Finally, the modified Naiver-Stokes equations is
verified by the numerical simulation. Flow around cylinder is numerically
investigated and able to obtain flow behavior from low to high Reynolds
numbers. A general-purpose turbulence model is established in this study, which
is worthy of engineering application.
