论文标题
二维逆向能量抗湍流中粒子对的两次拉格朗日速度相关函数
Two-time Lagrangian velocity correlation function for particle pairs in two-dimensional inverse energy-cascade turbulence
论文作者
论文摘要
我们在数值上研究了二维能量逆cascade湍流中粒子对的两次拉格朗日速度相关函数（TTLVCF）。我们通过不完整的相似性来考虑相关函数的自我相似性。在此框架中，我们提出了一种相关函数的自相似形式，其比例指数不能仅通过基于Kolmogorov的现象学使用维度分析来确定。结果，相关函数的缩放定律可以取决于初始分离。这种初始分离依赖性经常在实验室实验和对相关函数直接相关的相对色散的直接数值模拟中观察到。我们通过直接数值模拟二维逆cascade湍流来验证自相似形式。所涉及的缩放指数和对有限雷诺数效应的依赖性依据是经验确定的。然后，我们考虑相关函数的比例定律对相对分散的含义，即Richardson-Obukhov $ t^3 $ Law。我们的结果表明，在Infinite Reynolds编号中，有可能不收回Richardson-Obukhov $ T^3 $法律。
We numerically investigate a two-time Lagrangian velocity correlation function (TTLVCF) for particle pairs in two-dimensional energy inverse-cascade turbulence. We consider self similarity of the correlation function by means of incomplete similarity. In this framework, we propose a self-similar form of the correlation function, whose scaling exponents cannot be determined by only using the dimensional analysis based on the Kolmogorov's phenomenology. As a result, the scaling laws of the correlation function can depend on the initial separation. This initial-separation dependency is frequently observed in laboratory experiments and direct numerical simulations of the relative dispersion, which is directly related to the correlation function, at moderate Reynolds numbers. We numerically verify the self-similar form by direct numerical simulations of two-dimensional energy inverse-cascade turbulence. The involved scaling exponents and the dependencies on finite Reynolds number effects are determined empirically. Then, we consider implication of the scaling laws of the correlation function on the relative dispersion, i.e. the Richardson-Obukhov $t^3$ law. Our results suggest a possibility not to recover the Richardson-Obukhov $t^3$ law at infinite Reynolds number.
