Self-similarity in single-point turbulent statistics across different quadrants in turbulent rotor wakes

This paper presents a quadrant analysis of turbulent rotor wakes, placing a particular emphasis on the self-similarity in single-point turbulent statistics. The self-similarity analysis reveals that within the wake self-similar region, the distribution of the Reynolds shear stress -u′v′¯ and the turbulent kinetic energy k in different quadrants can also attain a state of self-similarity. The length scaling is the same for -u′v′¯, k, and their different quadrant contributions. However, the velocity scaling of the ejection contribution differs from that of -u′v′¯ and k. Additionally, the analysis of hole filtering and spectrum filtering effects on the self-similarity and scaling of the ejection contribution to -u′v′¯ reveals a strong connection between ejection events and large-scale coherent structures, as well as deceleration extreme events. This finding is further confirmed through quadrant analysis of the time evolution of velocity fluctuations. The present study can be helpful in improving our understanding of the turbulent wake self-similarity.