Effect of filter kernel on scale-energetics of near-wall turbulent structures

TL;DR

This study examines how different filter kernels influence the calculation of inter-scale energy fluxes in turbulent pipe flow, revealing that kernel choice significantly affects local energy transfer interpretations.

Contribution

It provides a detailed comparison of filter kernels' effects on energy flux analysis and introduces a versatile Python tool for such analyses in turbulence research.

Findings

Mean energy flux profiles are robust across kernels.

Local energy transfer events vary significantly with kernel type.

Sharp spectral kernel shows symmetric upstream-downstream correlations, unlike Gaussian and box kernels.

Abstract

Inter-scale energy fluxes, $\Pi^\lambda$, are widely used as a diagnostic tool to analyse energy transfer across length scales, $\lambda$, in turbulence data. Here, we investigate how the choice of filter kernel (sharp spectral, Gaussian, box) affects the computed energy fluxes at constant filter width. We apply spatial filtering to a turbulent pipe flow simulation dataset and assess the effect on the local structure of $\Pi$. While the mean energy flux profile at each wall-normal distance is qualitatively robust across kernels, we observe significant differences in the intensity and spatial distribution of localised $\Pi$ events. Correlations between typical flow structures in the buffer layer (streaks, vortices, and Q-events) and regions of forward/backward transfer in the instantaneous $\Pi$ field differ markedly between kernel types. Cross-correlations appear strongly upstream--downstream symmetric when using the sharp spectral kernel, but asymmetric for the Gaussian and box kernels. For the Gaussian and box kernels $\Pi$ events tend to localise along the inclined meander of streaks, while they are centred on top of the streaks for the sharp spectral kernel. Moreover, using the sharp spectral kernel, we observe a coincidence of backward scatter and fluid transport away from the wall ($Q_1$), which does not appear with the Gaussian and box kernels. All kernels, however, predict backward scatter directly downstream of $Q_1$ events. The results suggest that interpretations of inter-scale energy flux based on sharp spectral scale separation should be treated with caution, since such kernels act non-local in physical space, whereas $\Pi$ events are inherently localised. Our python post-processing tool eFlux for scale separation and energy flux analysis in pipe flows is freely available and readily adaptable to other flow configurations and filter widths.