Spatio-temporal Proper Orthogonal Decomposition of turbulent channel flow

TL;DR

This paper extends Proper Orthogonal Decomposition to analyze turbulent channel flow by incorporating both spatial and temporal eigenfunctions, revealing self-similar structures and energy transfer mechanisms in wall turbulence.

Contribution

It introduces a spatio-temporal POD framework for turbulent flow, linking eigenfunctions to flow symmetries and providing insights into energy transfer and convection velocities.

Findings

Dominant eigenfunctions exhibit self-similarity and wall-attached structures.

Identifies a fundamental time scale of 200-300 viscous wall units.

Provides a mode-specific energy budget and nonlinear effects expression.

Abstract

An extension of Proper Orthogonal Decomposition is applied to the wall layer of a turbulent channel flow (Re {\tau} = 590), so that empirical eigenfunctions are defined in both space and time. Due to the statistical symmetries of the flow, the igenfunctions are associated with individual wavenumbers and frequencies. Self-similarity of the dominant eigenfunctions, consistent with wall-attached structures transferring energy into the core region, is established. The most energetic modes are characterized by a fundamental time scale in the range 200-300 viscous wall units. The full spatio-temporal decomposition provides a natural measure of the convection velocity of structures, with a characteristic value of 12 u {\tau} in the wall layer. Finally, we show that the energy budget can be split into specific contributions for each mode, which provides a closed-form expression for nonlinear effects.