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

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.

Accepted for publication in Philosophical Transactions of the Royal Society A. arXiv admin note: substantial text overlap with arXiv:1409.6047

References in corpus (2)

• A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator
• On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations

Cited by in corpus (4)

• Resolvent-based study of compressibility effects on supersonic turbulent boundary layers
• Self-similar mechanisms in wall turbulence studied using of resolvent analysis
• Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow
• Modal Analysis of Fluid Flows: An Overview