Energy transfer and scale interactions in the formation and evolution of energy-eddies in turbulent boundary layers

The elementary structures of wall turbulence that carry most of the momentum and kinetic energy are typically referred to as energy-containing eddies (energy-eddies). While there is general agreement that energy-eddies can sustain themselves at all relevant length scales, the specific issues of how energy-eddies generate and evolve appears to be an open question. The aim of the present study is to investigate the spatial evolution and multi-scale interaction of energy-eddies in incompressible zero pressure gradient (ZPG) turbulent boundary layers (TBLs) by means of direct numerical simulation (DNS). To this end, energy-eddies are removed at the inflow of a ZPG-TBL DNS and turbulent kinetic energy (TKE) and Reynolds shear stress transport are examined using the spanwise spectral decomposition introduced by Kawata and Alfredson (PRL, 2018). The ZPG-TBL DNS setup consists of two concatenated domains, an auxiliary domain and the main domain, which run synchronously. The auxiliary domain is used to provide the inflow to the main domain in the following manner. A velocity cross-plane of the auxiliary domain is transferred at each time step to the inlet of the main domain with energy-eddies contained in this cross-plane removed. The wall-normal location and spanwise scale of the energy-eddies are identified by analyzing the spanwise spectra of turbulent transport as a function of the wall-normal distance. Analysis of the spanwise spectra of velocity and vorticity provide evidence suggesting that the formation of near-wall streaks is the primary process in the recovery of energy-eddies in ZPG-TBL. This result agrees with previous studies of channel flows by Kannadasan et al. (JFM, 2023). Our preliminary results reveal that a large number of DNS fields is required to conduct a statistically significant spectral analysis of the inter-scale transport. We will report results based on the extended DNS database