This study is an experimental investigation into the self-similarity behavior of first and second order statistical quantities derived from a jet flow based on a) the original data and b) its low-order representations derived from the Proper Orthogonal Decomposition (POD) and c) a comparison of both. The flow under investigation is an air-helium turbulent round jet with $\mathrm{Re}\approx 15400$ emerging from a tube into an ambient containing identical gas mass fraction and temperature as the jet at a constant pressure. Instantaneous two-dimensional velocity field measurements were obtained for downstream distances of $5.5d$ to $17.4d$ in the plane of the axis of the jet, via Particle Image Velocimetry. The snapshot POD algorithm was then applied to this data set to generate low-order representations with rank approximations 1, 5, 10 and 50. These then serve as the basis to derive the respective (rank truncated) statistical properties. All properties are non-dimensionalized with a self-similar framework as obtained from the original jet data. It is found that the statistical properties obtained from the low-order representations a) resemble in shape the asymptotic outline of the original jet and b) that the maximum values (for a given low-order representation) exhibit asymptotic states with increasing downstream distances. This is a strong indication that i) self-similar behavior is equally found in the low-order representations and that ii) this finding is mainly controlled by the large-scale vortices. The sole exception is the axial velocity root-mean-square values, where a distinct dip in the center line of the flow is found. This dip is successively filled up by smaller-scale turbulence for higher order truncations. Additionally, a new criterion – based on the maximum cross-correlation obtained through successive time traces of the temporal POD modes – is suggested to distinguish physically relevant modes from the POD basis in a more quantitative and explicit manner compared to traditional energy-based criteria.

这项研究是对基于a）原始数据和b）源自正确正交分解（POD）和c的低阶表示的一阶和二阶统计量自相似行为的实验研究。 ）两者的比较。所研究的气流是具有$\mathrm{回覆}\approx 15400$在恒定压力下从管子冒出的气体质量分数和温度与射流相同。瞬时二维速度场测量获得下游距离$5.5d$ 至 $17.4d$通过粒子图像测速技术在射流轴线的平面上。然后将快照POD算法应用于此数据集，以生成具有秩近似1、5、10和50的低阶表示形式。然后，这些低阶表示形式将用作导出各个（秩被截断的）统计属性的基础。所有属性均使用自原始射流数据获得的自相似框架进行无量纲化。发现从低阶表示中获得的统计特性在形状上类似于原始射流的渐近轮廓，并且b）最大值（对于给定的低阶表示）呈现出随着下游距离增加而渐近的状态。这有力地表明：i）在低阶表示中同样发现了自相似行为，并且ii）这一发现主要受大型涡旋控制。唯一的例外是轴向速度的均方根值，该值在流的中心线上有明显的下降。对于更高阶的截断，较小的湍流会逐渐填充该倾角。此外，建议采用新标准-基于通过时间POD模式的连续时间轨迹获得的最大互相关性-与传统的基于能量的标准相比，以更定量和明确的方式将物理相关模式与POD基础区分开。对于更高阶的截断，较小的湍流会逐渐填充该倾角。此外，建议采用新标准-基于通过时间POD模式的连续时间轨迹获得的最大互相关性-与传统的基于能量的标准相比，以更定量和明确的方式将物理相关模式与POD基础区分开。对于更高阶的截断，较小的湍流会逐渐填充该倾角。此外，建议采用新标准-基于通过时间POD模式的连续时间轨迹获得的最大互相关性-与传统的基于能量的标准相比，以更定量和明确的方式将物理相关模式与POD基础区分开。