ISAC-CNR and INFN Sez. Lecce, 73100 Lecce, Italy.
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy.
Phys Rev Lett. 2015 Dec 31;115(26):264502. doi: 10.1103/PhysRevLett.115.264502. Epub 2015 Dec 29.
A novel investigation of the nature of intermittency in incompressible, homogeneous, and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension D from the original three dimensional case to a strongly decimated system with D=2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set E(k)∼k(-5/3+3-D) explains the results. At small scales, the intermittency of the vorticity field is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D∼2.98. These effects must be connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism.
对不可压缩、均匀各向同性湍流的间歇性本质进行了新的研究，方法是在分形傅里叶集上对纳维-斯托克斯方程进行数值研究。通过将分形维数 D 从原来的三维情况改变为具有 D=2.5 的强烈简化系统，其中只有大约 3%的傅里叶模式相互作用，从而测试了能量传递和涡拉伸机制的稳健性。这是一种独特的方法，可以探测湍流能量级联的统计特性，而不会破坏方程的任何原始对称性。虽然直接能量级联仍然存在，但在动能谱中观察到偏离了 Kolmogorov 标度。一个基于修正的模型，其中修正项与分形集的余维数呈线性关系，即 E(k)∼k(-5/3+3-D)，解释了这些结果。在小尺度上，涡度场的间歇性被观察为分形模式减少的函数，几乎是拟正态分布，已经在 D∼2.98 时出现。这些效应必须与三体到三体非线性能量传递机制的真正改变联系起来。
