Turbulent vortices occur everywhere in flowing fluids and possess the properties of dissipation and dispersion. A set of new control equations is presented featuring the interaction between dissipation and dispersion of turbulence. By analysis of instability the rate of turbulent energy production is established. Two third-order derivative momentum equations are derived, one for weak and the other for strong vorticity. By this new theory various turbulent flow problems can be solved, such as: energy inversion in the vortex tail behind a bluff body, the coherent horseshoe vortices in a turbulent boundary layer, the delay in cascading down of turbulent energy through the spectrum, anisotropy of turbulence intensities, etc. Two computational examples are presented.

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