Uncovering the parameter variations of the inner–outer interaction model across incompressible and compressible wall-bounded turbulence

The inner–outer interaction model (IOIM), first proposed by Marusic et al. ( Science , 2010, vol. 329, pp. 193–196), has proven to be an effective turbulence model for canonical and non-canonical wall-bounded flows, where a reference velocity signal from the logarithmic region acts as the input for predicting near-wall velocity fluctuations. Its most recent iteration by Baars et al. ( Phys. Rev. Fluids , 2016, vol. 1, p. 054406) further proposes a user-independent scale separation point, refining model parameters. In this study, we compared the long-perceived universal IOIM’s parameters, including the linear transfer kernel, amplitude modulation coefficients and the universal signal for a range of Reynolds and Mach numbers, where mathematical relationships between the parameters are proposed. We observed that while the universal signals exhibit a high degree of similarity, particularly near the wall, the amplitude modulation coefficients and linear transfer kernels display Reynolds and Mach number effects, where varying the reference location also causes them to exhibit significant changes. We have found transformations to collapse amplitude modulation coefficients for incompressible flows and differing reference locations, improving modelling via the IOIM across flow parameters. Despite this, compressibility effects cannot be suitably accounted for currently and remain a future challenge for the IOIM framework.