Origin of turbulence-producing eddies in a channel flow

Abstract

A principal theoretical problem in understanding wall turbulence is the determination of how turbulence is created and sustained, i.e., the explanation of how energy is transferred from the mean flow to the turbulence. Flow-oriented vortical eddies have been associated with large Reynolds stresses and with the production of turbulence in the viscous region close to the wall. Their creation and evolution are investigated in a high-resolution direct numerical simulation of turbulent flow in a channel. An important finding is that they regenerate themselves by a process that appears to be weakly dependent on the outer flow. This involves the enhancement of streamwise vorticity at the wall, of opposite sign, at a location where a stress-producing eddy lifts from the wall.

Coherent structure generation in near-wall turbulence

“…Note that in linear evolution, the −(∂w/∂x)(∂u/∂y) term corresponds to the Ω∂u s /∂x generation term, responsible for creation of a ω x sheet (and x-circulation generation) in the streak trough region (figure 13b; see § 4.2). In the nonlinear regime of STG, the −(∂w/∂x)(∂u/∂y) term is largest in magnitude over all other terms, consistent with fully developed turbulence (Brooke & Hanratty 1993). However, this term actually contributes to the thin tail (C in figure 27c) of the near-wall ω x layer, not to the main vortex (SP).…”

“…Prior studies (e.g. Sendstad & Moin 1992;Brooke & Hanratty 1993) have proposed that near-wall ω x sheets (like those generated by STG) 'roll-up' due to their self-advection, an effect represented by the ω x advection terms in (18). In purely two-dimensional flow, near-wall vorticity sheets can roll up via two distinct mechanisms, illustrated in figure 28: (i) on the left side of a +ω x layer above a free-slip wall, with dipole-like 'head-tail' formation due to the wall image vorticity (see Jimenez & Orlandi 1993), as illustrated in the sequence in figure 28(a), or (ii) on the right side of a +ω x layer attached to a no-slip wall, due to lifting of the wall-generated ω x by a parent vortex, as in vortex wall-rebound (see Orlandi 1990), as shown by the sequence in figure 28(b).…”

“…An alternative parent-offspring scenario is proposed by Brooke & Hanratty (1993), who studied the spatiotemporal velocity field from DNS data, but found no hairpintype vortices. They propose that an opposite-signed offspring vortex forms immediately underneath a parent vortex, whose downstream end has lifted from the wall.…”

Streak interactions and breakdown in boundary layer flows

“…35 These results are in agreement with previous findings in plane Couette and Poiseuille flows. Jimenez and Moin 40 and Brooke and Hanratty 41 found that the largest contribution to the generation of streamwise vorticity comes from the tilting term ͑−‫ץ‬u / ‫ץ‬y͒͑‫ץ‬w / ‫ץ‬x͒. The latter authors computed the contribution of the term ͑‫ץ‬u / ‫ץ‬z͒͑‫ץ‬v / ‫ץ‬x͒ to be less than 10% of total production.…”

Velocity–vorticity correlation structure in turbulent channel flow

“…This special VVCS structure at y s,0 is called the limiting VVCS structure, whose characteristics are believed to be important for turbulence modelling. Brooke & Hanratty (1993) in their DNS study of channel flow presented the evidence for quasi-streamwise vortices for y + < 40, while Christensen & Adrian (2001) suggested that hairpin packets cannot reach more than 100 wall units. We have not be thorough at the current moderate Re, but a qualitative feature is discernible.…”