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.
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.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2014年第7期202-205,共4页
Acta Physica Sinica
基金
国家自然科学基金(批准号:40975027)资助的课题~~
关键词
间歇湍流
分数阶
维数
扩散
intermittent turbulence, fractional derivatives, dimension, diffusion
