中文摘要：

间歇湍流意味着湍流涡旋并不充满空间，其维数介于2和3之间．湍流扩散为超扩散，且概率密度分布具有长尾特征．本文将流体力学的Navier．Stokes（NS）方程中的黏性项用分数阶的拉普拉斯算子表达．分析表明，分数阶拉普拉斯的阶数α和间歇湍流的维数D相联系．对于均匀各向同性的Kolmogorov湍流α=2，即用整数阶NS方程描述．而对于间歇性湍流，一定用分数阶的NS方程来描述．对于Kolmogorov湍流，扩散方差正比于t3，即Richardson扩散．而对于间歇性湍流，扩散方差要比Richardson扩散更强．

英文摘要：

Intermittent turbulence means that the turbulence eddies do not fill the space completely, so the dimension of an intermittent turbulence takes the values between 2 and 3. Turbulence diffusion is a super-diffusion, and the probability of density function is fat-tailed. In this paper, the viscosity term in the Navier-Stokes equation will be denoted as a fractional derivative of Laplatian operator. Dimensionless analysis shows that the order of the fractional derivative α is closely related to the dimension of intermittent turbulence D. For the homogeneous isotropic Kolmogorov turbulence, the order of the fractional derivatives α = 2, i.e. the turbulence can be modeled by the integer order of Navier-Stokes equation. However, the intermittent turbulence must be modeled by the fractional derivative of Navier-Stokes equation. For the Kolmogorov turbulence, diffusion displacement is proportional to t3, i.e. Richardson diffusion, but for the intermittent turbulence, diffusion displacement is stronger than Richardson diffusion.