Hairpin vortices in turbulent boundary layers

Eitel-Amor, Georg; Flores, Oscar; Schlatter, Philipp

doi:10.1088/1742-6596/506/1/012008

Cited by 27 publications

(26 citation statements)

References 37 publications

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“…Furthermore, it is well established that hairpin vortices may appear as the consequence of the secondary instability and break-up of elongated streaks (Schmid & Henningson 2001). These and many other studies indicate that, unlike streaky structures, hairpin vortices are generated through nonlinear interactions (Eitel-Amor et al 2015). The fact that they naturally arise in many transitional and turbulent shear flows, as the consequence of the instability of streaks or induced by other causes (such as roughness elements or flow injection at wall), suggests the existence of a strong energy growth mechanism triggered by nonlinearity.…”

Section: Introductionmentioning

confidence: 68%

Hairpin-like optimal perturbations in plane Poiseuille flow

et al. 2015

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. In this work it is shown that hairpin vortex structures can be the outcome of a nonlinear optimal growth process, in a similar way as streaky structures can be the result of a linear optimal growth mechanism. With this purpose, nonlinear optimizations based on a Lagrange multiplier technique coupled with a direct-adjoint iterative procedure are performed in a plane Poiseuille flow at subcritical values of the Reynolds number, aiming at quickly triggering nonlinear effects. Choosing a suitable time scale for such an optimization process, it is found that the initial optimal perturbation is composed of sweeps and ejections resulting in a hairpin vortex structure at the target time. These alternating sweeps and ejections create an inflectional instability occurring in a localized region away from the wall, generating the head of the primary and secondary hairpin structures, quickly inducing transition to turbulent flow. This result could explain why transitional and turbulent shear flows are characterized by a high density of hairpin vortices.

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Section: Introductionmentioning

confidence: 68%

Hairpin-like optimal perturbations in plane Poiseuille flow

et al. 2015

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“…The energy decay seen in the impulse response needs further clarification, since the large-scale structures appear to have very little energy density, which was also noted by Eitel-Amor et al (2015). This hurdle could possibly disappear when, instead of response to isolated impulses, an appropriate sum of impulse responses is used; such forcing would represent the response to some spatio-temporally distributed forcing instead of a spatiotemporally localized forcing.…”

Section: Discussionmentioning

confidence: 94%

“…Codrignani (2014) extended the DNS-based study to different wall-normal locations for the impulse at a slightly lower Reynolds number of Re τ = 150. More recently, Eitel-Amor et al (2015) looked at the evolution of hairpin vortices at a higher Reynolds number of Re τ = 590, using the eLNSE as well as DNS to include a fully turbulent background. They found that the evolution of a single hairpin vortex observed in the turbulent DNS is well represented by the eddy-viscosity-enhanced LNSE; however, the linear model failed to capture regeneration, consistent with the earlier observations of Kim & Lim (2000).…”

Section: Introductionmentioning

confidence: 99%

Coherent structures in the linearized impulse response of turbulent channel flow

et al. 2019

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We study the evolution of velocity fluctuations due to an isolated spatio-temporal impulse using the linearized Navier-Stokes equations. The impulse is introduced as an external body force in incompressible channel flow at Re τ = 10000. Velocity fluctuations are defined about the turbulent mean velocity profile. A turbulent eddy viscosity is added to the equations to fix the mean velocity as an exact solution, which also serves to model the dissipative effects of the background turbulence on large-scale fluctuations. An impulsive body force produces flowfields that evolve into coherent structures containing long streamwise velocity streaks that are flanked by quasi-streamwise vortices; some of these impulses produce hairpin vortices. As these vortex-streak structures evolve, they grow in size to be nominally self-similar geometrically with an aspect ratio (streamwise to wallnormal) of approximately 10, while their kinetic energy density decays monotonically. The topology of the vortex-streak structures is not sensitive to the location of the impulse, but is dependent on the direction of the impulsive body force. All of these vortex-streak structures are attached to the wall, and their Reynolds stresses collapse when scaled by distance from the wall, consistent with Townsend's attached eddy hypothesis. †

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“…Also, some studies cast doubts on the very idea that hairpin vortices are a prominent feature of high Reynolds number turbulence (see e.g. Jeong et al 1997;Eitel-Amor et al 2015). Indeed, an alternative explanation of the origin of large-scale motions is currently emerging, which conjectures that these motions are sustained by a mechanism similar to the self-sustained process (SSP) proposed by Hamilton et al (1995).…”

Section: Mechanisms Sustaining Streaky Motionsmentioning

confidence: 99%

On the self-sustained nature of large-scale motions in turbulent Couette flow

et al. 2015

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Large-scale motions in wall-bounded turbulent flows are frequently interpreted as resulting from an aggregation process of smaller-scale structures. Here, we explore the alternative possibility that such large-scale motions are themselves self-sustained and do not draw their energy from smaller-scale turbulent motions activated in buffer layers. To this end, it is first shown that large-scale motions in turbulent Couette flow at Re = 2150 self-sustain even when active processes at smaller scales are artificially quenched by increasing the Smagorinsky constant C s in large eddy simulations. These results are in agreement with earlier results on pressure driven turbulent channels. We further investigate the nature of the large-scale coherent motions by computing upper and lower-branch nonlinear steady solutions of the filtered (LES) equations with a Newton-Krylov solver, and find that they are connected by a saddle-node bifurcation at large values of C s . Upper branch solutions for the filtered large scale motions are computed for Reynolds numbers up to Re = 2187 using specific paths in the Re − C s parameter plane and compared to large-scale coherent motions. Continuation to C s = 0 reveals that these large-scale steady solutions of the filtered equations are connected to the Nagata-CleverBusse-Waleffe branch of steady solutions of the Navier-Stokes equations. In contrast, we find it impossible to connect the latter to buffer layer motions through a continuation to higher Reynolds numbers in minimal flow units.

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Hairpin vortices in turbulent boundary layers

Cited by 27 publications

References 37 publications

Hairpin-like optimal perturbations in plane Poiseuille flow

Hairpin-like optimal perturbations in plane Poiseuille flow

Coherent structures in the linearized impulse response of turbulent channel flow

On the self-sustained nature of large-scale motions in turbulent Couette flow

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