Chen Wen
Department of Engineering Mechanics, Hohai University, No. 1 Xikang Road, Nanjing City, Jiangsu Province 210098, China.
Chaos. 2006 Jun;16(2):023126. doi: 10.1063/1.2208452.
This study makes the first attempt to use the 23-order fractional Laplacian modeling of Kolmogorov -53 scaling of fully developed turbulence and enhanced diffusing movements of random turbulent particles. Nonlinear inertial interactions and molecular Brownian diffusivity are considered to be the bifractal mechanism behind multifractal scaling of moderate Reynolds number turbulence. Accordingly, a stochastic equation is proposed to describe turbulence intermittency. The 23-order fractional Laplacian representation is also used to model nonlinear interactions of fluctuating velocity components, and then we conjecture a fractional Reynolds equation, underlying fractal spacetime structures of Levy 23 stable distribution and the Kolmogorov scaling at inertial scales. The new perspective of this study is that the fractional calculus is an effective approach to modeling the chaotic fractal phenomena induced by nonlinear interactions.
本研究首次尝试使用23阶分数阶拉普拉斯算子对充分发展湍流的柯尔莫哥洛夫-53标度以及随机湍流粒子的增强扩散运动进行建模。非线性惯性相互作用和分子布朗扩散率被认为是中等雷诺数湍流多重分形标度背后的双分形机制。据此，提出了一个随机方程来描述湍流间歇性。23阶分数阶拉普拉斯算子表示法还用于对脉动速度分量的非线性相互作用进行建模，然后我们推测了一个分数阶雷诺方程，其基础是列维23稳定分布的分形时空结构和惯性尺度下的柯尔莫哥洛夫标度。本研究的新观点是，分数阶微积分是对由非线性相互作用引起的混沌分形现象进行建模的有效方法。
