Turbulence is one of the most common nature phenomena in everyday experience, but that is not adequately understood yet. This article reviews the history and present state of development of the turbulence theory and indicates the necessity to probe into the turbulent features and mechanism with the different methods at different levels. Therefore this article proves a theorem of turbulent transportation and a theorem of turbulent intensity by using the theory of the nonequilibrium thermodynamics,turbulent intensity and the turbulent transportation. The macroscopic cause of the development of fluid turbulence is a result from shearing effect of the velocity together with the temperature, which is also the macroscopic cause of the stretch and fold of trajectory in the phase space of turbulent field. And it is proved by the observed data of atmosphere that the phenomenological coefficient of turbulent intensity is not only a function of the velocity shear but also a function of temperature shear, viz the stability of temperature stratification, in the atmosphere. Accordingly, authenticity of the theorem, which is proved by the theory of nonequilibrium thermodynamics, of turbulent intensity is testified by the facts of observational experiment.