Scaling and interaction of self-similar modes in models of high-Reynolds number wall turbulence

TL;DR

This paper explores how self-similar resolvent modes in high-Reynolds number wall turbulence influence nonlinear interactions, revealing that turbulence scaling can be understood from a single reference plane, impacting turbulence modeling.

Contribution

It demonstrates that the self-similarity of resolvent modes governs nonlinear interactions, simplifying the understanding of turbulence scaling in wall flows.

Findings

Turbulence scaling behavior can be derived from a single reference plane.

Self-similar modes influence nonlinear interactions across scales.

Implications for turbulence modeling and self-sustaining mechanisms.

Abstract

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.