Mean velocity increment conditioned on gradient trajectories of various scalar variables in turbulence
Mean velocity increment conditioned on gradient trajectories of various scalar variables in turbulence
复制标题
以湍流中各种标量变量的梯度轨迹为条件的平均速度增量
作者：
Lipo Wang;N. Peters
本文着重讨论了几种标量形式的场变量的速度结构沿着梯度的一般性，如被动标量、速度矢量的笛卡尔投影、动能和能量耗散。这些标量变量的行为不同，这可以通过它们的控制方程中的源项不同的事实在数学上解释。因此，如果相应的源项瞬时很小，则可以合理地预期不同标量之间的一些共性。这种期望的有效性已经讨论了个别情况下，特别是在高雷诺数。结果表明，各标量沿沿着梯度的逐点平均应变率始终为负。通过分析标量梯度方向，可以看出，统计上具有大幅度的梯度向量彼此对齐，而具有小幅度的梯度向量往往是随机组织的。在两点速度增量方面，对于被动标量，最近已经推导出存在相对于梯度轨迹的弧长的速度差的近似线性缩放（Wang 2009 Phys.Rev.E79046325）。从理论上讲，这种标度也可以推广到其他标量与数值结果令人满意的协议。
This paper focuses on the generality of the velocity structure along the gradients of several field variables in scalar form, such as the passive scalar, the Cartesian projections of the velocity vector, kinetic energy and energy dissipation. These scalar variables behave differently, which can be explained mathematically by the fact that the source terms in their governing equations are different. Consequently, it is reasonable to expect some generalities among different scalars if the respective source terms are instantaneously small. The validity of this expectation has been discussed for individual cases, especially at high Reynolds numbers. It is found that the pointwise mean strain rates along gradients of various scalars are always negative. By analyzing the scalar gradient orientations, it is seen that statistically the gradient vectors with large magnitudes align with each other, whereas those with small magnitudes tend to be randomly organized. In terms of the two-point velocity increment, for the passive scalar it has recently been derived that there exists a nearly linear scaling of the velocity difference with respect to the arc length of gradient trajectories (Wang 2009 Phys. Rev. E 79 046325). Theoretically, this scaling can also be extended to other scalars with satisfactory agreement with numerical results.