Group of Nonlinear Physics, University of Santiago de Compostela, Spain.
Phys Rev Lett. 2011 Aug 12;107(7):074502. doi: 10.1103/PhysRevLett.107.074502.
We report the experimental observation of Richardson dispersion and a double cascade in a thin horizontal fluid flow induced by Faraday waves. The energy spectra and the mean spectral energy flux obtained from particle image velocimetry data suggest an inverse energy cascade with Kolmogorov type scaling E(k) ∝ k(γ), γ ≈ -5/3 and an E(k) ∝ k(γ), γ ≈ -3 enstrophy cascade. Particle transport is studied analyzing absolute and relative dispersion as well as the finite size Lyapunov exponent (FSLE) via the direct tracking of real particles and numerical advection of virtual particles. Richardson dispersion with <ΔR(2)(t)> ∝ t(3) is observed and is also reflected in the slopes of the FSLE (Λ ∝ ΔR(-2/3)) for virtual and real particles.
我们报告了在由法拉第波引起的薄水平流体流动中 Richardson 弥散和双级联的实验观察。从粒子图像测速数据得到的能量谱和平均谱能量通量表明存在逆能级联，具有 Kolmogorov 型标度 E(k)∝k(γ)，γ≈-5/3 和 E(k)∝k(γ)，γ≈-3 涡度级联。通过对真实粒子的直接跟踪和虚拟粒子的数值平流，分析绝对和相对弥散以及有限大小 Lyapunov 指数（FSLE）来研究粒子输运。观察到具有 <ΔR(2)(t)>∝t(3)的 Richardson 弥散，并且在虚拟和真实粒子的 FSLE（Λ∝ΔR(-2/3))斜率中也反映了这一点。
