The flux of energy between scales in turbulence can be cast as the result of the interaction between a turbulent stress and a rate of strain. Efficient energy transfer requires that these two tensors be oriented properly relative to each other, but previous work has shown that the instantaneous alignment between them is poor. Here, we consider the temporal dynamics of this alignment in a direct numerical simulation of isotropic turbulence. We show that the orientation of the stress lags behind that of the strain rate, both at a single location and along trajectories. However, the timescale of the reorientation of the stress in these cases does not follow the expected dynamical scaling with length scale. To capture the proper dynamical scaling, we reformulate the energy flux between scales using the right Cauchy-Green strain tensor and the second Piola-Kirchhoff stress tensor. Our results highlight the key role played by the deformation of fluid elements in the physics of the energy cascade, and suggest that their irreversible deformation is a Lagrangian manifestation of the cascade's broken time-reversal symmetry.

中文翻译：

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湍流应力和应变率对齐的时间动态

由于湍流应力和应变率之间的相互作用，可以在湍流的尺度之间产生能量通量。有效的能量传递要求这两个张量相对于彼此正确定向，但是先前的工作表明，它们之间的瞬时对齐很差。在这里，我们在各向同性湍流的直接数值模拟中考虑了这种对准的时间动力学。我们表明，应力的方向在单个位置和沿轨迹都落后于应变率。但是，在这些情况下，应力重新定向的时间尺度不符合预期的长度尺度动态尺度。要获取适当的动态缩放比例，我们使用正确的柯西-格林应变张量和第二个Piola-Kirchhoff应力张量来重新设定尺度之间的能量通量。我们的结果突出了流体元素的变形在能量级联物理中所起的关键作用，并表明它们的不可逆形变是级联破碎的时间-逆向对称性的拉格朗日表现。