Spectral analysis of the budget equation in turbulent channel flows at high Re

TL;DR

This paper uses spectral analysis of DNS data to explore how energy is transferred across scales and regions in high-Reynolds-number turbulent channel flows, revealing the role of large-scale structures and their influence on near-wall turbulence.

Contribution

It provides a detailed spectral decomposition of turbulence transport equations at high Reynolds numbers, highlighting the scale-dependent energy transfer mechanisms and the influence of very large-scale motions.

Findings

Outer-layer turbulence dominated by large-scale streamwise modes

Energy transfer from large scales to dissipation occurs more isotropically

Small-scale near-wall processes are Reynolds number independent

Abstract

The transport equations for velocity variances are investigated using data from DNS of incompressible channel flows at $Re_\tau$ up to 5200. Each term in the transport equation has been spectrally decomposed to expose the contribution of turbulence at different length scales to the processes governing the flow of energy in the wall-normal direction, in scale and among components. The outer-layer turbulence is dominated by very large-scale streamwise elongated modes. Away from the wall, production occurs primarily in these large-scale streamwise-elongated modes in the streamwise velocity, but dissipation occurs nearly isotropically in both velocity components and scale. For this to happen, the energy is transferred from the streamwise elongated modes to modes with a range of orientations through non-linear interactions, and then transferred to other velocity components. This allows energy to be transferred more-or-less isotropically from these large scales to the small scales at which dissipation occurs. The VLSMs also transfer energy to the wall-region resulting in a modulation of the autonomous near-wall dynamics. The near-wall energy flows are consistent with the well-known autonomous near-wall dynamics. Through the overlap region between outer and inner layer turbulence, there is a self-similar structure to the energy flows. The VLSM production occurs at spanwise scales that grow with $y$. There is transport of energy away from the wall over a range of scales that grows with $y$. And, there is transfer of energy to small dissipative scales which grow like $y^{1/4}$. Finally, the small-scale near-wall processes characterised by wavelengths less than 1000 wall units are largely Reynolds number independent, while the larger-scale outer layer process are strongly Reynolds number dependent. The interaction between them appears to be relatively simple.