How does filtering change the perspective on the scale-energetics of the near-wall cycle?

Abstract

We investigate the flux of kinetic energy across length scales in a turbulent pipe flow. We apply explicit spatial filtering of DNS data and assess the effect of different filter kernels (Fourier, Gauss, box) on the local structure of the inter-scale energy flux ($\Pi$) and its statistics. Qualitatively, the mean energy flux at each wall-normal distance is robust with respect to the filter kernel, whereas there are significant differences in the estimated intensity and distribution of localised $\Pi$ events. We find conflicting correlations between typical flow structures in the buffer layer (streaks, vortices and different $Q$ events) and regions of forward/backward transfer in the instantaneous $\Pi$ field. In particular, cross-correlations are highly upstream-downstream symmetric for the Fourier kernel, but asymmetric for the Gauss and box kernel. We show that for the Gauss and box kernel, $\Pi$ events preferably sit on the inclined meander at the borders of streaks where strong shear layers occur, whereas they appear centred on top of the streaks for the Fourier kernel. Moreover, using the Fourier kernel we reveal a direct coincidence of backward scatter and fluid transport away from the wall ($Q_{1}$), which is absent for the Gauss and the box kernel. However, all kernels equally predict backward scatter directly downstream of $Q_{1}$ events. Our findings expand the common understanding of the wall cycle and might impact modelling and control strategies. Altogether, our results suggest that interpretations of the inter-scale energy flux relying on Fourier filters should be taken with caution, because Fourier filters act globally in physical space, whereas $\Pi$ events are strongly spatially localised. Our Python post-processing tool eFlux for scale separation and flux computations in pipe flows is freely available and can be easily adapted to other flow geometries.