标题： 湍流相对分散的时间尺度 显示英文标题

标题： Timescales of Turbulent Relative Dispersion

摘要： 示踪剂在湍流流场中的分离遵循著名的理查森-奥布霍夫定律$t^{3/2}$，该定律通常通过尺度相关的有效扩散系数来解释。 在这里，借助最先进的数值模拟，我们重新审视了这一论点。发现速度差的拉格朗日相关时间增加得太快，无法验证这种方法，但加速度差在耗散时间尺度上失去相关性。 这导致速度差的渐近扩散$\propto t^{1/2}$，因此距离的长时间行为类似于布朗运动积分的结果。结果显示，收敛到此状态的时间与偏离巴切尔德初始球面运动状态的时间相同，该时间为尺度相关的能量耗散时间而非通常的周转时间。 最后，认为流体流动的间歇性不应影响相对运动的长时间行为。 显示英文摘要

摘要： Tracers in a turbulent flow separate according to the celebrated $t^{3/2}$ Richardson--Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences is found to increase too quickly for validating this approach, but acceleration differences decorrelate on dissipative timescales. This results in an asymptotic diffusion $\propto t^{1/2}$ of velocity differences, so that the long-time behavior of distances is that of the integral of Brownian motion. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally argued that the fluid flow intermittency should not affect this long-time behavior of relative