Scaling and interaction of self-similar modes in models of high Reynolds number wall turbulence
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.
© 2017 The Author(s). Published by the Royal Society. Accepted September 13, 2016. This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. The support of AFOSR grant no. FA9550-12-1-0469 and AFOSR/EOARD grant no. FA9550-14-1-0042 is gratefully acknowledged. Authors' contributions: R.M. carried out the original analysis. All authors contributed to the manuscript and have approved it. The authors declare that they have no competing interests.
Accepted Version - 1609.06890.pdf