Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows

TL;DR

This study investigates the nonlinear mechanisms behind the self-sustaining process in wall-bounded turbulence, identifying key flow structures and interactions that sustain turbulence in the buffer and logarithmic layers.

Contribution

It introduces a resolvent analysis approach to pinpoint and remove the principal forcing mode, revealing its critical role in turbulence sustenance in minimal channel simulations.

Findings

Removing the principal forcing mode inhibits turbulence, especially in the buffer layer.

Flow structures like spanwise rolls and oblique streaks drive nonlinear interactions.

The self-sustaining process involves limited wavenumber interactions, validating similarities across layers.

Abstract

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 which 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 that 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 toward 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.