The energy inversion phenomenon which widely exists in turbulent flows was analyzed. Its cause which was called dispersion effect in turbulent flows was revealed. On this basis

a modified Boussinesq hypothesis containing dispersion coefficient and a new kind of eddy viscosity model were presented. The dispersion coefficient had different forms when the modified Boussinesq hypothesis was coupled with different turbulence models. The condition and direction of energy transfer were also described. The credibility of the new model was verified in numerical simulation of wall boundary layer flow and back-facing step flow. The frictional resistance coefficient and the velocity profile for turbulent boundary layer were in good agreement with the experimental results; the reattachment length

the surface pressure coefficient on step-side wall and the turbulence intensity profile for backward-facing step flow were closer to the experimental results than the standard k-ε model. Results show that the introduction of dispersion term can improve the accuracy of the prediction significantly with very little expenses

so the model should be useful in engineering application.