Tensor geometry in the turbulent cascade
Tensor geometry in the turbulent cascade
复制标题
湍流级联中的张量几何
DOI：
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复制
发表时间：
2017
影响因子：
3.7
通讯作者：
N. Ouellette
中科院分区：
文献类型：
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作者：
Joseph G. Ballouz;N. Ouellette
高度湍流的定义特征是能量从注入尺度到耗散尺度的净定向传输。这种叶栅通常在傅立叶空间中描述，模糊了它与流动力学的联系。在这里，我们用机械术语重新描述能量级联，注意到对于一些尺度来说，为了将能量传递给其他尺度，它们必须对它们做机械功。这个功可以表示为湍流应力和应变率的内积。但是，和所有内积一样，这两个张量的相对排列很重要，并决定了能量转移的强度。我们表明，这种张量排列在二维和三维的行为非常不同，特别是，张量特征值影响的内积在非常不同的方式。通过比较观察到的能量通量的最大可能，如果张量是在完美的对齐，我们定义的能量级联的效率。使用数据从直接数值模拟的各向同性湍流，我们表明，这种效率可能是令人惊讶的低，在惯性范围内的平均值约为25%，虽然它是空间异质性。我们的研究结果有影响的应力和应变率的大小如何影响尺度之间的能量通量，并可能有助于解释为什么在二维和三维的能量级联是不同的。
The defining characteristic of highly turbulent flows is the net directed transport of energy from the injection scales to the dissipation scales. This cascade is typically described in Fourier space, obscuring its connection to the mechanics of the flow. Here, we recast the energy cascade in mechanical terms, noting that for some scales to transfer energy to others, they must do mechanical work on them. This work can be expressed as the inner product of a turbulent stress and a rate of strain. But, as with all inner products, the relative alignment of these two tensors matters, and determines how strong the energy transfer will be. We show that this tensor alignment behaves very differently in two and three dimensions; in particular, the tensor eigenvalues affect the inner product in very different ways. By comparing the observed energy flux to the maximum possible if the tensors were in perfect alignment, we define an efficiency for the energy cascade. Using data from a direct numerical simulation of isotropic turbulence, we show that this efficiency is perhaps surprisingly low, with an average value of approximately 25 % in the inertial range, although it is spatially heterogeneous. Our results have implications for how the stress and strain-rate magnitudes influence the flux of energy between scales, and may help to explain why the energy cascades in two and three dimensions are different.