Auto-generation in wall turbulence by the interaction of weak eddies

Abstract

For channel flow, we explore how commonly found weak eddies can still auto-generate and produce new eddies. Before, only strong eddies (above a threshold strength) were considered to auto-generate. Such strong eddies are rarely observed in actual turbulent flows however. Here, the evolution of two weak conditional eddies with different initial strengths, initial sizes, and initial stream-wise spacing between them is studied. The numerical procedure followed is similar to Zhou et al. [“Mechanisms for generating coherent packets of hairpin vortices in channel flow,” J. Fluid Mech. 387, 353 (1999)]. The two eddies are found to merge into a single stronger eddy when the initial upstream eddy is taller than the downstream eddy, which further auto-generates when the initial stream-wise separation is small (<120 wall units). However, it is observed that non-merging cases with small initial stream-wise separation also auto-generated. In the initial condition, the two conditional eddies are placed near to each other so their velocity fields (low-speed streaks and ejection events) get superimposed and amplified as a function of stream-wise spacing. To examine this effect, a divergence free low-speed streak is superimposed on an eddy. It is found that these low-speed streak simulations do not auto-generate. On the other hand, a rapid lift-up of an eddy by ejection events plays a role in the onset of auto-generation, which also leads to a modified interpretation of auto-generation mechanism. It differed from the existing auto-generation mechanism at the later stages of auto-generation where blockage of mean flow and shear layer deformation is considered instead of vortex dynamics.