A numerical study on fully developed turbulent flows is conducted by solving the integral Navier-Stokes (N-S) equation with Gaussian wavelet transformation.Gaussian wavelet is used to obtain the N-S equation with flexion as a fundamental quantity in an infinite domain.The (N-S) equation with flexion as a fundamental quantity in a finite domain is shown.The integral N-S equation is regarded as a special diffusion equation and the pressure term,convective term are regarded as source terms.The general solution of the integral equation is obtained with the characteristic method.The results are used to the analysis of channel turbulent flows in asymmetric and symmetric channels.A comparison of the calculated mean statistical quantity with the experimental result is made.