Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows
The nonlinear mechanism in the self-sustaining process (SSP) of wall-bounded turbulence is investigated. Resolvent analysis is used to identify the principal forcing mode that produces the maximum amplification of the velocities in numerical simulations of the minimal channel for the buffer layer and a modified logarithmic (log) layer. The wavenumbers targeted in this study are those of the fundamental mode, which is infinitely long in the streamwise direction and once-periodic in the spanwise direction. The identified mode is then projected out from the nonlinear term of the Navier–Stokes equations at each time step from the simulation of the corresponding minimal channel. The results show that the removal of the principal forcing mode of the fundamental wavenumber can inhibit turbulence in both the buffer and log layer, with the effect being greater in the buffer layer. Removing other modes instead of the principal mode of the fundamental wavenumber only marginally affects the flow. Closer inspection of the dyadic interactions in the nonlinear term shows that contributions to the principal forcing mode come from a limited set of wavenumber interactions. Using conditional averaging, the flow structures that are responsible for generating the nonlinear interaction to self-sustain turbulence are identified as spanwise rolls interacting with oblique streaks. This method, based on the equations of motion, validates the similarities in the SSP of the buffer and log layer, and characterises the underlying quadratic interactions in the SSP of the minimal channel.
Additional Information© The Author(s), 2021. Published by Cambridge University Press. Received 14 April 2020; revised 26 September 2020; accepted 5 October 2020. Published online by Cambridge University Press: 05 March 2021. This work was funded in part by the Coturb programme of the European Research Council (ERC-2014.AdG-669505) during the 2017 Coturb Turbulence Summer Workshop at the Universidad Politécnica de Madrid. B.J.M. is grateful for the support of ONR under N00014-17-1-3022. A.L.-D. acknowledges the support of NASA under NNX15AU93A and of ONR under N00014-17-1-2310. The authors thank Professor J. Jiménez, Dr Y. Kwon and Dr A. Guseva for their insightful comments. The authors report no conflict of interest.
Submitted - 1911.07117.pdf