On the universality of the inner-outer interaction model and its connection to the attached-eddy hypothesis across incompressible and compressible wall-bounded turbulence

The inner-outer interaction model (IOIM), first proposed by Marusic et al. (2010) and later refined by Baars et al. (2016), has proven to be a successful turbulence model. In this study, we compared the IOIM's parameters for a range of Re_τ and Ma_b. While the universal signal has high degrees of similarity, the amplitude modulation coefficients (Γ) and linear transfer kernels display Re_τ and Ma_b effects, where varying the reference location also causes changes. These variations correspond to the physical structures from the attached eddy hypothesis (AEH), where we find they represent the balance between the attached and detached eddies' effects at different locations. As the prediction signal nears the wall, the decreasing large-scale coherence between the reference and the prediction signal, due to the differing structures experienced at their respective locations, is compensated by Γ, representing the increased population of the attached eddies, while the near-wall viscous eddies are captured by the universal signal. With this perspective, we found transformations to collapse Γ for incompressible flows and differing reference locations.