Attached eddies in turbulent channel flow: pressure fluctuations and scale interactions

Abstract

The multi-scale behavior of eddies in wall-bounded turbulent flows has hindered understanding of their nature. However, in the present study, statistical and dynamical features of wall-bounded turbulent flows are explored with a modern view of coherent structures in wall turbulence, incorporating Townsend's attached eddy hypothesis. Through this analysis, the ultimate goal is to elucidate the mechanism for the maintenance of wall turbulence.

In Part I, numerical experiments isolating an attached eddy only at a prescribed spanwise length scale are performed to examine characteristics of pressure fluctuations of self-sustaining attached eddies. The pressure field of each attached eddy is statistically and dynamically self-similar with respect to the corresponding spanwise size, implying that structures of pressure fluctuations indeed emerge in the form of Townsend's attached eddies. Also, time sequences obtained from minimal unit simulations show that both rapid (linear) and slow (nonlinear) pressure fluctuations are amplified together with the streamwise meandering streaks in the self-sustaining cycle.

In Part II, large eddy simulation of turbulent channel flow is conducted to clarify the scale-by-scale interactions. From energy spectra of each constituent of the turbulent kinetic energy equation in wavenumber space along with analyses of scale interactions, a comprehensive view of the energy transfer mechanism is described. Turbulent kinetic energy produced by the lift-up effect in the self-sustaining process of attached eddies is absorbed by the negative turbulent transport energy originating from nonlinear interactions between larger attached eddies. Then, the absorbed energy is transported to the region where the turbulent transport spectra have a positive value via the energy cascade and dissipated there. The energy redistribution mechanism through the pressure-strain term has also been shown to the self-sustaining process of attached eddies. Therefore, the dominant mechanism for the maintenance of wall turbulence is revealed as the self-sustaining process of attached eddies at each length scale.