水动力turbulence中能量级联的局部性，I.光滑粗粒化
Localness of energy cascade in hydrodynamic turbulence, I. Smooth coarse-graining
摘要：
我们介绍了一种新的方法尺度分解的流体动能（或其他二次积分）带通贡献从一系列的长度尺度。我们的分解是基于平滑，分级过滤器内核的“Germano身份”的多尺度推广。我们采用这种方法推导出一个预算方程，描述了传输的湍流动能在空间和尺度。结果表明，尺度间的能量传递是由当地的三元相互作用，假设只有在湍流惯性范围内预期的标度特性。我们推导出严格的上界的非本地三和弦的贡献，扩展Eyink（2005）的低通滤波的工作。我们还对我们严格的上界和Kraichnan（1966，1971）的标度预测提出了不同指数的物理解释。Kraichnan预测的更快的衰变被认为是在空间上平均后，从非本地三和弦转移的有符号贡献中的额外取消的结果。这幅图得到了带有相移去混叠的Navier-Stokes湍流的$512^3$伪谱模拟数据的支持。
英文摘要：
We introduce a novel approach to scale-decomposition of the fluid kinetic energy (or other quadratic integrals) into band-pass contributions from a series of length-scales. Our decomposition is based on a multiscale generalization of the ``Germano identity'' for smooth, graded filter kernels. We employ this method to derive a budget equation that describes the transfers of turbulent kinetic energy both in space and in scale. It is shown that the inter-scale energy transfer is dominated by local triadic interactions, assuming only the scaling properties expected in a turbulent inertial-range. We derive rigorous upper bounds on the contributions of non-local triads, extending the work of Eyink (2005) for low-pass filtering. We also propose a physical explanation of the differing exponents for our rigorous upper bounds and for the scaling predictions of Kraichnan (1966,1971). The faster decay predicted by Kraichnan is argued to be the consequence of additional cancellations in the signed contributions to transfer from non-local triads, after averaging over space. This picture is supported by data from a $512^3$ pseudospectral simulation of Navier-Stokes turbulence with phase-shift dealiasing.
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