论文标题
超级流体$ {^4} $的欧拉和拉格朗日二级统计
Eulerian and Lagrangian second-order statistics of superfluid ${^4}$He grid turbulence
论文作者
论文摘要
我们使用粒子跟踪速度法来研究超氟$^4 $ HE网格湍流的Eulerian和Lagrangian二阶统计。比量子涡流线之间的平均距离在尺度上大的尺度大距离，其尺寸大于量子涡流之间的平均距离，接近Kolmogorov-1941缩放，几乎是各向同性的。拉格朗日二阶结构函数和频率谱，以与干预距离相当的比例测量，表明了从几乎古典行为到由量子涡流线运动主导的政权的急剧过渡。使用流量的同质性，我们验证了一组连接各种二阶统计对象的关系，这些统计对象强调湍流行为的不同方面，从而允许进行多方面的分析。我们使用Eulerian能量光谱和二阶结构功能之间的双向桥梁关系来重建来自已知的二阶速度结构函数的能量光谱，反之亦然。使用Eulerian-Lagrangian桥从测得的Eulerian频谱重建的拉格朗日频谱与准经典范围内测得的Lagrangian Spectrum不同，这需要进一步研究。
We use particle tracking velocimetry to study Eulerian and Lagrangian second-order statistics of superfluid $^4$He grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov-1941 scaling and are almost isotropic. The Lagrangian second-order structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearly-classical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity of the flow, we verify a set of relations that connect various second-order statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the two-way bridge relations between Eulerian energy spectra and second-order structure functions to reconstruct the energy spectrum from the known second-order velocity structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the Eulerian-Lagrangian bridge differs from the measured Lagrangian spectrum in the quasi-classical range which calls for further investigation.
