DERIVATION OF THE UNIVERSAL PHYSICAL EQUATION OF TURBULENCE AND ITS CANONICAL FORM

The fully- detailed derivation of the universal physical equation ofturbulence has been given. Instead of the conventional Reynolds average, a new method, named off-center ensemble average, is used to obtain the equation. Through some mathematical approximations and without introducing any empirical coefficients, the equation may provide a secondary order of accuracy, which satisfies the needs of engineering study of turbulence. In one-dimensional case, the momentum equation of turbulence is simplified as the mixed Burgers-Korteveg de Vries equation-the canonical equation of turbulence. The analysis of the Burgers-Kerteweg-de Vries equation gives the criterion of transition. The physical meaning of the equations is briefly discussed. It shows that dissipation and dispersion coexist as two basic physical principles of turbulence. The development of dissipation is monotonic, describing the conversion of the kinetic turbulence energy into heat due to viscosity. Dispersion can be either positive or negative. It represents the energy transformation between the mean flow and the large and micro-eddies before the energy is finally dissipated into molecular heat. Positive dispersion corresponds to cascading down process and negative dispersion means collection of energy. The mechanison of intermittency and anisotropy, and the effects of noise and developing history on turbulence are also discussed.