Spectral analysis of inner-outer layer nonlinear interactions using minimal channel turbulence*

In the streamwise velocity spectra of high Reynolds number turbulent boundary layers, it is well known that in addition to the inner spectral peak originating from the inner-layer streaks, the outer peak originating from the large-scale motions in the outer layer appears, where the inner-outer layer interactions occur.

In this study, we conduct the large-eddy simulation of the minimal channel turbulence to clarify the inner-outer layer interactions. In this minimal channel, we design the spanwise extent such that the large-scale motions are removed from the computational domain, while inner-layer streaks are well resolved and thus may investigate the changes in turbulence phenomena due to the inner-outer layer interactions.

Our results show that little change occurs in the inner-layer turbulence despite the absence of large-scale motions, although the low-wavenumber components of the turbulent kinetic energy (TKE) in the outer layer increase. To explain these results, we compute the budgets of the spectral TKE transport and elucidate the inter-scale transport effects. The analysis indicates that the low-wavenumber turbulence in the outer layer mainly transports the energy to the high-wavenumber turbulence in the outer layer and not to the inner-layer turbulence, leading to little change in the inner layer. Furthermore, we discuss the nonlinear interactions between the large and small scales in the inner layer by investigating the triadic interactions of the wavenumbers.