增强的逆级联能量在平均欧拉方程中
Enhanced inverse-cascade of energy in the averaged Euler equations
AI总结：
本文证明特定平滑核下涡旋团方法对应平均欧拉方程，并发现其非线性项修改增强二维湍流逆级联，影响大于尺度$\a$的运动，类似聚合物减阻效应。
摘要：
对于平滑核的特定选择，我们证明了控制涡旋团方法的偏微分方程组对应于平均欧拉方程。这些后者方程最近通过将欧拉方程在长度尺度为$\a$的拉格朗日涨落上平均而导出，同一系统也在描述二级聚合（非牛顿）流体的无粘不可压缩流动中遇到。虽然先前对该系统的研究注意到小于$\a$的模态之间的非线性相互作用受到抑制，但我们表明非线性平流项的修改也增强了二维湍流中能量的逆级联，从而也影响大于$\a$的运动尺度。后一种效应类似于在湍流中添加稀聚合物时发生的减阻现象。
英文摘要：
For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale $\a$, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than $\a$, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than $\a$ as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added.
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