Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence, modelling and simulation are outlined.
This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.
One contribution of 14 to a theme issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.
- Accepted September 13, 2016.
- © 2017 The Author(s)
Published by the Royal Society. All rights reserved.