Lagrangian studies in convective turbulence.
Lagrangian studies in convective turbulence.
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对流湍流的拉格朗日研究。
DOI：
10.1103/physreve.79.056301
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Schumacher
中科院分区：
文献类型：
--
作者：
J. Schumacher
我们提出了湍流三维瑞利-贝纳德对流的高分辨率直接数值模拟，重点关注流动的拉格朗日特性。该体积是一个纵横比为四的笛卡尔板，由顶部和底部的自由滑移平面界定，并具有周期性侧壁。湍流相对于垂直方向是不均匀的。这体现在不同的横向和垂直双粒子色散以及短期和中间时间色散对初始示踪剂位置的依赖性。与均匀各向同性湍流类似，色散特性除了取决于初始对分离之外，还取决于接近柯尔莫哥洛夫耗散长度的初始分离，产生双粒子色散的短程理查森式缩放制度。理查森常数大约是均匀各向同性湍流值的一半。多粒子统计非常接近均匀各向同性的情况。四个拉格朗日示踪剂的簇显示出在长时间限制内形成平坦、几乎共面的物体的明显趋势，并且偏离高斯预测。为了正确解析高达四阶的加速度分量的统计数据，我们付出了巨大的努力。我们发现垂直加速度比横向加速度的间歇性要小。垂直加速度与局部对流和传导热通量的联合统计表明，上升和下降的热羽流与最大加速度大小无关。事实证明，在拉格朗日框架中计算的努塞尔数在时间上缓慢地收敛到标准欧拉数。
We present high-resolution direct numerical simulations of turbulent three-dimensional Rayleigh-Bénard convection with a focus on the Lagrangian properties of the flow. The volume is a Cartesian slab with an aspect ratio of four bounded by free-slip planes at the top and bottom and with periodic side walls. The turbulence is inhomogeneous with respect to the vertical direction. This manifests in different lateral and vertical two-particle dispersion and in a dependence of the dispersion on the initial tracer position for short and intermediate times. Similar to homogeneous isotropic turbulence, the dispersion properties depend in addition to the initial pair separation and yield a short-range Richardson-like scaling regime of two-particle dispersion for initial separations close to the Kolmogorov dissipation length. The Richardson constant is about half the value of homogeneous isotropic turbulence. The multiparticle statistics is very close to the homogeneous isotropic case. Clusters of four Lagrangian tracers show a clear trend to form flat, almost coplanar, objects in the long-time limit and deviate from the Gaussian prediction. Significant efforts have been taken to resolve the statistics of the acceleration components up to order four correctly. We find that the vertical acceleration is less intermittent than the lateral one. The joint statistics of the vertical acceleration with the local convective and conductive heat flux suggests that rising and falling thermal plumes are not associated with the largest acceleration magnitudes. It turns out also that the Nusselt number which is calculated in the Lagrangian frame converges slowly in time to the standard Eulerian one.