Criticality and the fractal structure of -5/3 turbulent cascades

Inducing intermittency in the inverse cascade of two dimensional turbulence by a fractal forcing

We demonstrate that like in the forward cascade of three dimensional turbulence that displays intermittency (lack of self-similarity) due to the concentration of energy dissipation in a small set of fractal dimension less than three, the inverse cascade of two-dimensional turbulence can also display lack of self-similarity and intermittency if the energy injection is constrained in a fractal set of dimension less than two. A series of numerical simulations of two dimensional turbulence are examined, using different forcing functions of the same forcing length-scale but different fractal dimens…

Intermittency in the Enstrophy Cascade of Two-dimensional Fully-developed Turbulence: Universal Features

Intermittency (externally induced) in the two-dimensional (2D) enstrophy cascade is shown to be able to maintain a finite enstrophy along with a vorticity conservation anomaly. Intermittency mechanisms of three-dimensional (3D) energy cascade and 2D enstrophy cascade in fully-developed turbulence (FDT) seem to have some universal features. The parabolic-profile approximation (PPA) for the singularity spectrum f(a) in multi-fractal model is used and extended to the appropriate microscale regimes to exhibit these features. The PPA is also shown to afford, unlike the generic multi-fractal model, …

充分发展湍流的耗散多重分形级联模型的广义分形维数

Generalized Fractal Dimension for a Dissipative Multi-fractal Cascade Model for Fully Developed Turbulence

针对Meneveau-Sreenivasan多重分形级联模型在惯性区微小耗散下$D_q$奇异性问题，本文提出含耗散参数的广义分形维数拟设，并推广到双参数对称耗散情形。

三角形腔内流动中莫法特涡旋的分形标度

Fractal Scaling of Moffatt Vortices in Triangular Cavity Flow

研究三角形腔内流动角涡的形成、量化及分形特征，用数值求解纳维-斯托克斯方程并结合莫法特理论分析涡旋级联，通过面积-周长法研究分形性质，提出经验关系，发现角涡分形维数与涡旋大小强度相关，不同形状腔内角涡级联有稳健分形行为。

Spiral chains in wavenumber space of two dimensional turbulence

Abstract Self-similar, fractal nature of turbulence is discussed in the context of two dimensional turbulence, by considering the fractal structure of the wave-number domain using spirals. In loose analogy with phyllotaxis in plants, each step of the cascade can be represented by a rotation and a scaling of the interacting triad. Using a constant divergence angle and a constant scaling factor, one obtains a family of such fractals depending on the distance of interactions. Scaling factors in such sequences are given by the square roots of known ratios such as the plastic ratio, the supergolden…

Spectrum of turbulent Kelvin-waves cascade in superfluid helium

To explain the observed decay of superfluid turbulence at very low temperature, it has been proposed that a cascade of Kelvin waves (analogous to the classical Kolmogorov cascade) transfers kinetic energy to length scales which are small enough that sound can be radiated away. We report results of numerical simulations of the interaction of quantized vortex filaments. We observe the development of the Kelvin-waves cascade, and compute the statistics of the curvature, the amplitude spectrum (which we compare with competing theories) and the fractal dimension.