We investigate the streamwise evolutions of energy and pressure spectra along the shear-layer region of very near-field grid-generated turbulence. The energy and pressure spectra evolve significantly in this near-field. The shear-layer and vortex-shedding frequencies appear immediately in different spectra but the shear-layer's spectral signature is very soon replaced by a broad power-law spectrum on both sides of that frequency. The spectra evolve further by filling the gap between the vortex shedding and the shear-layer frequencies eventually leading to near $-5/3$ power-law energy spectra at the point on the shear-layer region where the turbulence intensity reaches a maximum. The pressure spectrum reaches a $-7/3$ power-law shape significantly further downstream. These spectral scalings cover a range between the vortex-shedding frequency and frequencies larger than the shear-layer frequency. They are discussed in relation to turbulent coherent structures of various sizes, obtained by using Gaussian low-pass filtering of instantaneous turbulent flow fields. High enstrophy small-scale structures originate from the shear-layer instability whereas low enstrophy large-scale structures originate from the vortex shedding. The generation of near-field $-5/3$ energy and $-7/3$ pressure spectra involves cooperative interactions between these two different size structures.

中文翻译：

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网格产生湍流近场中谱和多尺度相干结构的幂律定标的形成

我们研究了非常近场网格产生的湍流沿剪切层区域的能量和压力谱的流向演化。能量和压力谱在此近场中显着变化。剪切层和涡流脱落频率立即出现在不同的频谱中，但是剪切层的频谱特征很快被该频率两侧的宽幂律谱所取代。通过填充涡旋脱落和剪切层频率之间的间隙，光谱进一步演化，最终导致接近$-5/3$在湍流强度达到最大值的剪切层区域上的点处的幂律能量谱。压力谱达到$-7/3$幂律形状在下游更明显。这些频谱缩放覆盖涡流脱落频率和大于剪切层频率的频率之间的范围。讨论了有关各种大小的湍流相干结构的问题，这些结构是通过使用瞬时湍流场的高斯低通滤波获得的。高涡旋小尺度结构起源于剪切层的不稳定性，而低涡旋小尺度结构起源于涡旋脱落。近场的产生$-5/3$ 能量和 $-7/3$ 压力谱涉及这两个不同大小结构之间的协同相互作用。