Hairpin vortices in turbulent boundary layers

Abstract

The present work presents a number of parallel and spatially developing simulations of boundary layers to address the question of whether hairpin vortices are a dominant feature of near-wall turbulence, and which role they play during transition. In the first part, the parent–offspring regeneration mechanism is investigated in parallel (temporal) simulations of a single hairpin vortex introduced in a mean shear flow corresponding to either turbulent channels or boundary layers (Reτ ≲ 590). The effect of a turbulent background superimposed on the mean flow is considered by using an eddy viscosity computed from resolved simulations. Tracking the vortical structure downstream, it is found that secondary hairpins are only created shortly after initialization, with all rotational structures decaying for later times. For hairpins in a clean (laminar) environment, the decay is relatively slow, while hairpins in weak turbulent environments (10% of νt) dissipate after a couple of eddy turnover times. In the second part, the role of hairpin vortices in laminar–turbulent transition is studied using simulations of spatial boundary layers tripped by hairpin vortices. These vortices are generated by means of specific volumetric forces representing an ejection event, creating a synthetic turbulent boundary layer initially dominated by hairpin-like vortices. These hairpins are advected towards the wake region of the boundary layer, while a sinusoidal instability of the streaks near the wall results in rapid development of a turbulent boundary layer. For Reθ > 400, the boundary layer is fully developed, with no evidence of hairpin vortices reaching into the wall region. The results from both the parallel and spatial simulations strongly suggest that the regeneration process is rather short-lived and may not sustain once a turbulent background is developed. From the transitional flow simulations, it is conjectured that the forest of hairpins reported in former direct numerical simulation studies is reminiscent of the transitional boundary layer and may not be connected to some aspects of the dynamics of the fully developed wall-bounded turbulence.

Amplitude and wall-normal distance variation of small scales in turbulent boundary layers

“…Small-scale vortices have been observed in shear layers along the backs of low-speed streamwise velocity regions [5,9]. These vortices may have a hairpin vortex structure: thin and long, arching over large scales in the flow [5,8], though the persistence of hairpin vortices at high Reynolds number is a topic of continued debate [4,14,15]. The vortices may also have a more disorganized or chaotic structure at higher Reynolds number [4].…”

Self-sustaining processes at all scales in wall-bounded turbulent shear flows

“…The relevance of this 'bottom-up' scenario based on Λ-vortices, especially in the high Reynolds number regime, is, however, not universally accepted. Some recent studies have challenged the idea that hairpin vortices are a prominent feature of high Reynolds number turbulence and that the parent-offspring mechanism is active in turbulent environments with counter-evidence [21,22]. Even more importantly, and independent of the question of the existence or not of prominent Λ-vortices, a growing number of recent results suggest that buffer-layer motions are not ultimately necessary to sustain large-scale and very-large-scale motions.…”

A física estatística da turbulência

“…A Fig. 6, fruto de simulações numéricas [57], exibe a profusão de vórtices-grampo nas CLTs, também observada em experimentos, após laboriosos tratamentos estatísticos [58].…”