Based on the perturbation equation of the Navier-Stokes equation and the instability analysis of strongly nonlinear flow

a set of new control equations is presented featuring the interaction between dissipation and dispersion of turbulence. Three extra terms representing respectively the effects of extra strains

rotation and dispersion on the turbulent stresses introduced into the momentum equation. The defects of the original k-e modelart removed mainly by introducing new soerce terms. This modified k-i model has advantages of simplicity

self-consistency and clarity of physics It is able to handle complex flows and provides new perspectives for looking at a diversity cf turbulence probiems

such as intermuttency

coherent structvires

amsotropy

turbulent energy inversion and the cut-off of turbulence spectra.