Abstract: A unilateral statistical average scheme is used to derive a new set of closed equations of incompressible turbulent flows,which is capable of describing both of statistical mean flow and intermittent coherent flow without introducing any empirical treatments and coefficients.Besides the special average scheme,the concepts of symmetic drift flows,orthotropic trubulence and the chain of momentum transference are also used in the original derivation.More important,the obtained energy equation of series form suggests that the infinite terms in the equation are corresponding to infinite layers of structures of trubulence.If all the terms of the series are taken for determining the length scale,one obtains statistical mean results.On the other hand,if only parts of terms are taken,coherent flows would appear.To verify the adaptablity of the equations,three benchmark flows,i.e.free shear flow,boundary layer transition flow and separated flow,are numerically simulated on PC computers.Both of accurate results of statistical mean flows and vivid structures of coherent flows are obtained.