Separating large-scale superposition and modulation in turbulent channels

Abstract

The presence of very-large-scale motions in wall-bounded turbulent flows is commonly associated with their footprint in the form of the superposition of the large scales at the wall and the additional amplitude modulation of small-scale near-wall turbulence. These two phenomena are currently understood to be interlinked, with the superposed large-scale velocity gradient causing the modulation of small-scale activity in the proximity of the wall. To challenge this idea, we devise a numerical strategy that selectively suppresses either superposition or amplitude modulation, in an effort to isolate and study the remaining phenomenon. Results from our direct numerical simulations indicate that a positive correlation between the amplitude of the small scales in the near-wall region and the large-scale signal in the outer flow persists even when near-wall large-scale motions are suppressed – i.e. in absence of superposition. Clearly, this kind of correlation cannot be caused by the near-wall large-scale velocity or its gradients, as both are absent. Conversely, when modulation is blocked, the near-wall footprints of the large scales seem to disappear. This study has been carried out on channel flows at friction Reynolds number $Re_\tau =1000$ in both standard simulation domains and minimal streamwise units (MSUs), where the streamwise fluctuation energy is enhanced. The consistency of the results obtained by the two approaches suggests that MSUs can capture correctly this kind of scale interaction at a much reduced cost.

Universal relative scaling of longitudinal structure functions in shear-dominated turbulence

“…The influence of large scales on small scales has also been demonstrated in shear-driven flows (e.g. Mathis, Hutchins & Marusic 2009;Ganapathisubramani et al 2012;Baars, Hutchins & Marusic 2016;Jacobi et al 2021;Andreolli et al 2023).…”

The Chimera Revisited: Wall- and Magnetically-Bounded Turbulent Flows

“…There is an ongoing discussion on the interaction between structures-whether large structures in the outer layer are superimposed onto inner layer structures or if the mechanism involves amplitude modulation [45,46]. There is also a discussion about whether the large structures are "active" or "passive", i.e., whether they contribute to the turbulent shear RS or not [47].…”