Spectral decomposition of wall-attached/detached eddies in compressible and incompressible turbulent channel flows

In the present study, we propose a spectral decomposition method to segregate the contributions of wall-attached/detached and self-similar/non-self-similar eddies by taking advantage of the proper orthogonal decomposition. It is applied to analyze the compressible and incompressible turbulent channel flows to verify the Reynolds number and compressibility effects on velocity fluctuations and investigate whether the temperature fluctuations share similar features. It is found that both the energetic wall-detached eddies and the small-scale wall-attached eddies (the so-called type C eddies) are self-similar, thereby supporting the methods of modeling them together. The medium-scale wall-attached eddies in the present study are equivalent to the original concept of attached eddies (type A eddies), whose features predicted by theories but not observed due to the interference of other types of eddies are fully revealed in the logarithmic region. Their growing hierarchy with the extension of the logarithmic region as the Reynolds number increases is reconfirmed to be responsible for the increment of inner peak of fluctuation variances. The large-scale wall-attached eddies representing the very-large-scale motions (type B eddies) manifest no inclination to have stronger superposition effects in the near-wall and logarithmic region, though intensified by the increasing Reynolds number. Compressibility, expectedly, only impacts the small-scale motions in the near-wall region. Regarding the temperature fluctuation, the large-scale type B eddies also show logarithmic decay in the logarithmic region. The type A eddies and the detached eddies are prominent, constituting a considerable portion of the spectra and variances.

Automated summary

This study proposes a spectral decomposition method to separate the contributions of wall-attached/detached and self-similar/non-self-similar eddies and analyzes their effects on velocity and temperature fluctuations in turbulent channel flows. The results show that different types of eddies have distinct features and impacts in different regions.