Hairpin Packets Research Articles

The structure of turbulence in unsteady flow over urban canopies

The topology of turbulent coherent structures is known to regulate the transport of energy, mass and momentum in the atmospheric boundary layer (ABL). While previous research has primarily focused on characterizing the structure of turbulence in stationary ABL flows, real-world scenarios frequently deviate from stationarity, giving rise to nuanced and poorly understood changes in the turbulence geometry and associated transport mechanisms. This study sheds light on this problem by examining topological changes in ABL turbulence induced by non-stationarity and their effects on momentum transport. Results from a large-eddy simulation of pulsatile open channel flow over an array of surface-mounted cuboids are examined. The analysis reveals that the flow pulsation triggers a phase-dependent shear rate, and the ejection-sweep pattern varies with the shear rate during the pulsatile cycle. From a turbulence structure perspective, it is attributed to the changes in the geometry of hairpin vortices. An increase (decrease) in the shear rate intensifies (relaxes) these structures, leading to an increase (decrease) in the frequency of ejections and an amplification (reduction) of their percentage contribution to the total momentum flux. Furthermore, the size of the hairpin packets undergoes variations, which depend on the geometry of the constituting hairpin vortices, yet the packet inclination preserves its orientation throughout the pulsatile cycle. These observations reinforce the important role non-stationarity holds in shaping the structure of ABL turbulence and the momentum transport mechanisms it governs.

The statistical characteristics and auto-regeneration of backflow in non-Newtonian turbulent pipe flow

The backflow phenomenon in shear-thinning and shear-thickening fluids is investigated in pipe flows at friction Reynolds number Reτ=180 via direct numerical simulations. Conditional average results show that the extreme fluctuation of wall shear stress around the backflow regions is more abrupt under the shear-thinning effect. The statistical characteristics of the backflow at different flow indices from 0.5 to 1.5 show remarkable differences. The probability of the backflow events at the wall increases in both the shear-thinning and the shear-thickening fluids under different mechanisms. The backflow occurs more frequently and exists further away from the wall in the shear-thinning fluids owing to the suppressed near-wall turbulent structures and the laminarization at low flow indices. The increase in the probability of the backflow events in the shear-thickening fluids is caused by increased Q2 and Q4 events in the near-wall region. The variation in the size and the lifespan of the backflow regions with the flow index is very prominent which both increase with the shear-thinning effect and decrease as the flow becomes dilatant. In the weakly turbulent flow of shear-thinning fluid, large backflow regions appear near the leading edge of the turbulent spots where the off-axial turbulent fluctuations are significantly lowered. Observations show the linked evolution between the hairpin vortices and the backflow regions induced underneath the strong spanwise rotations. The backflow follows the auto-regeneration process of the hairpin vortices in a packet which results in coherent streamwise-aligned backflow regions under the hairpin packets confined closer to the wall.

Dynamics and scaling of particle streaks in high-Reynolds-number turbulent boundary layers

Inertial particles in wall-bounded turbulence are known to form streaks, but experimental evidence and predictive understanding of this phenomenon is lacking, especially in regimes relevant to atmospheric flows. We carry out wind tunnel measurements to investigate this process, characterizing the transport of microscopic particles suspended in turbulent boundary layers. The friction Reynolds number$Re_\tau = {O}(10^4)$allows for significant scale separation and the emergence of large-scale motions, while the range of viscous Stokes number$St^+=18$–870 is relevant to the transport of dust and fine sand in the atmospheric surface layer. We perform simultaneous imaging of both carrier and dispersed phases along wall-parallel planes in the logarithmic layer, demonstrating that streamwise particle streaks largely overlap with large-scale low-speed flow regions. The fluid–particle slip velocity indicates that with increasing inertia, the particle streaks outlive the low-speed fluid streaks. Moreover, two-point statistics show that the width of the particle streaks increases linearly with Stokes number, bounded by the size of the coherent flow structures. Finally, the particle-sampled flow topology suggests that particle streaks reside between the legs of hairpin packets. From these observations, we infer a conceptual view of the formation of particle streaks in the frame of the attached eddy model. A scaling for the particle streaks’ width is derived as a function of$Re_\tau$and$St^+$, which reproduces the measured trends and predicts widths${O}(0.1)$m in the atmospheric surface layer, comparable to aeolian streamers observed in the field.

Hypersonic boundary layer transition on a concave wall induced by low-frequency blowing and suction

Hypersonic boundary layer transitions caused by unsteady blowing and suction are investigated with linear stability analyses and direct numerical simulations (DNS). Three blowing–suction frequencies, i.e., 15, 30, and 45 kHz, are separately utilized to excite a pair of unsteady Görtler instability waves (the first two cases) or first-mode instability waves (the last case). These two primary instabilities, respectively, induce diamond-shaped and Λ-shaped structures through self-interactions. These structures are highly susceptible to high-frequency secondary instabilities, as is demonstrated by global Floquet analyses that take into account both temporal unsteadiness and spanwise spatial variations of the base flow. The secondary instability manifests as hairpin packets riding on the downstream end of the diamond-shaped structures or reside in the outward sides of the two legs of the Λ-shaped structures. The theoretical results quantitatively agree with the DNS results. Energy analyses further reveal that the wall-normal productions dominate the energy transfer for the secondary instability of the unsteady Görtler vortices, while the spanwise productions are crucial to the secondary instabilities in the first-mode oblique breakdown. Quasi-steady analyses based on the “frozen” base flow are also performed, whose results compare favorably with those from Floquet analyses in the lowest-frequency case.

Combined three-dimensional flow field measurements and motion tracking of freely moving spheres in a turbulent boundary layer

A combination of time-resolved tomographic particle image velocimetry, refractive index matching technique and machine vision algorithms was used to measure the translational and rotational motion of freely moving, nearly neutrally buoyant spheres in a fully developed turbulent boundary layer (TBL). Located in the buffer and logarithmic layers, the hydrogel spheres ( $\sim$ 70 inner wall units in diameter) were refractive index matched with the water and tagged by ‘spokes’. Besides translational motion, the spheres exhibited significant rotation. The spheres were surrounded by typical coherent structures observed in TBLs, among them hairpin packets and transverse and longitudinal vortices that induced ejections and sweeps. While the majority of instantaneous sphere Reynolds numbers did not exceed 100, and vortex shedding was not observed, the results showed that the spheres may affect the evolution of hairpin packets in TBLs due to their finite size. The instantaneous rotation-, wall- and shear-induced lift forces, as well as the drag forces, acting on the spheres were estimated using available correlations for the lift and drag coefficients. Results hinted at negative shear-induced lift due to flow separation at a smaller critical Reynolds number than incorporated in the correlations that do not include the effect of ambient turbulence. The results indicated further that the drag force aided by the rotation-induced lift force was instrumental in keeping one of the spheres aloft. For the wall-ward moving spheres, lift forces opposed sphere motion. As a result, the spheres approached the wall with velocities lower than their quiescent settling velocity.

High resolution simulation of film cooling with blowing ratio and inclination angle effects based on hybrid thermal lattice Boltzmann method

A series of high resolution simulations on film cooling with varying blowing ratios and inclination angles are carried out by using in-house code based on hybrid thermal lattice Boltzmann method. Three blowing ratios ranging from 0.2-0.8 and four inclination angles from 15? to 60? are chosen for the simulations. The evolutionary mechanism of coherent structure in three domains of film-covering region is studied from the view of space and time. Besides, the influencing mechanism of blowing ratio and inclination angle on flow and heat transfer features of film cooling is uncovered. Results show that hairpin vortex, hairpin packet, and quasi-streamwise vortex appearing in rotating domain play a key role in heat transfer process of film cooling. The strong ejection, sweep and vortex rotation resulted from these vortices enhance the convective heat transfer. It is also found that the size of coherent structure varies significantly with blowing ratio and its integral form shows a strong dependence on inclination angle. Moreover, inclination angle of coolant jet has a significant impact on turbulence fluctuation intensity. The influence of blowing ratio on the attachment of coolant film and film-cooling performance is more obvious than that of inclination angle. It is believed that all of these are related closely to the variation of streamwise and wall-normal jet velocity in the case of various blowing ratios and inclination angles.

Data-driven enhancement of coherent structure-based models for predicting instantaneous wall turbulence

Predictions of the spatial representation of instantaneous wall-bounded flows, via coherent structure-based models, are highly sensitive to the geometry of the representative structures employed by them. In this study, we propose a methodology to extract the three-dimensional (3-D) geometry of the statistically significant eddies from multi-point wall-turbulence datasets, for direct implementation into these models to improve their predictions. The methodology is employed here for reconstructing a 3-D statistical picture of the inertial wall coherent turbulence for all canonical wall-bounded flows, across a decade of friction Reynolds number (Reτ). These structures are responsible for the Reτ-dependence of the skin-friction drag and also facilitate the inner-outer interactions, making them key targets of structure-based models. The empirical analysis brings out the geometric self-similarity of the large-scale wall-coherent motions and also suggests the hairpin packet as the representative flow structure for all wall-bounded flows, thereby aligning with the framework on which the attached eddy model (AEM) is based. The same framework is extended here to also model the very-large-scaled motions, with a consideration of their differences in internal versus external flows. Implementation of the empirically-obtained geometric scalings for these large structures into the AEM is shown to enhance the instantaneous flow predictions for all three velocity components. Finally, an active flow control system driven by the same geometric scalings is conceptualized, towards favourably altering the influence of the wall coherent motions on the skin-friction drag.

Outer-layer structure arrangements based on the large-scale zero-crossings at moderate Reynolds number

The structural arrangements in the outer layer of turbulent boundary layer flows were explored with large-field time-resolved particle image velocimetry measurements at moderate Reynolds number. The large- and small-scale structures were reconstructed by the modes of multiscale proper orthogonal decomposition. The association between hairpin packets and uniform momentum zones (UMZs) was examined by the conditional averaging results based on the large-scale positive-to-negative/negative-to-positive (PN/NP) zero-crossings. The scale arrangements provided the spatial evidence that the intense small-scale swirling motions are aligned in the confined internal shear layers along the backside of the large-scale, low-speed region, which was characterized by hairpin vortex packets. The uniform momentum zones (UMZs) conditioned on the large-scale PN/NP zero-crossings were detected from the histograms of the instantaneous streamwise velocity. The attached eddy behavior was consolidated based on the conditional events, by presenting the joint probability of UMZs thickness and wall-normal location. A close agreement of the conditional averaging raw velocity and modal velocity was examined. Moreover, the conditional averaging results of the UMZs interface probability exhibited a similar spatial distribution as the small-scale turbulent kinetic energy and swirling strength, which manifests the coincidence between the hairpin heads and the UMZs interfaces. This result was confirmed by the distribution of the wall-normal locations corresponding to the maximum value of interface probability and small-scale representations, which performs a streamwise inclination angle of 15°. The statistical spatial feature demonstrated the association between hairpin packets and uniform momentum as proposed by Adrian et al. [“Vortex organization in the outer region of the turbulent boundary layer,” J. Fluid Mech. 422, 1–54 (2000)].

Drag reduction and hairpin packets of the turbulent boundary layer over the superhydrophobic-riblets surface

Drag reduction and hairpin packets of the turbulent boundary layer over the superhydrophobic-riblets surface

Low- and mid-frequency wall-pressure sources in a turbulent boundary layer

Abstract

Cross-term events of scale-decomposed skewness factor in turbulent boundary layer at moderate Reynolds number

This study reports the observation of cross term events of scale-decomposed skewness factor in turbulent boundary layer at moderate Reynolds number. The large field-of-view particle image velocimetry was utilized to measure the flow fields. By the approach of multi-scale proper orthogonal decomposition (mPOD), the large- and small-scale structures were reconstructed by the mPOD modes relevant to the predefined frequency bands. Then, the cross term of the scale-decomposed skewness was observed, which was proposed in the previous works by Schlatter and Örlü [Phys. Fluids 22, 051704 (2010)] and Mathis et al. [Phys. Fluids, 23, 121702 (2011)]. The cross term events are featured by both the large and small scales, which were consolidated by the linear fitting of correlation coefficients with different slope angles. The characteristic length of the local intense cross term events is around 0.1δ (δ is the boundary layer thickness), which is comparable with that of the swirling structures related to hairpin vortice in the form of hairpin packets. The conditional averaging results presented the arrangement that the local cross term event appears underneath the hairpin vortex in the statistical viewpoint. Based on the hairpin vortex model, it was proposed that the local intense cross term events are associated with the local low-speed fluids induced by the hairpins through the ejection process. Especially, in the wake region, the cross term events are promoted, and also well-correlated with the swirling structures. This kind of configuration was attributed to the combination of the vortex induction and the entrainment process relative to the turbulent/non-turbulent intermittency.

On the H-type transition to turbulence—Laboratory experiments and reduced-order modeling

A series of experiments were conducted to understand the sources of local, high-amplitude velocity fluctuations produced at the late stages of boundary-layer flow transition to turbulence. The laboratory experiments considered the controlled injection of Tollmien–Schlichting (TS) waves into a nearly zero pressure gradient, laminar boundary layer, resulting in H-type transition to turbulence. Proper orthogonal decomposition (POD) was used to extract the energetic coherent structures within the transitional flow field obtained with particle image velocimetry. The first three modes were observed to feature spatial mode shapes consistent with a cross-section of a canonical hairpin vortex structure and were associated with time-dependent amplitudes having consistent peak frequencies with the fundamental TS wave frequency. Higher-order modes exhibited a combination of sub- and super-harmonics of the TS wave frequency and were attributed to flow interactions produced by a hairpin packet. A conditional averaging method was used to establish a reduced-order model for the overshoot phenomena in Reynolds shear stress and turbulence kinetic energy observed at the late transition stage. The lower portion of the large-scale hairpin vortex structure was observed to be primarily responsible for the overshoot mechanisms, which was well captured in a reduced-order model of the velocity field. The first four POD modes were used to create this reduced-order model, which, while only consisting of ≈15% of the total turbulence kinetic energy of the original velocity field, was able to capture ≈85% of the peak Reynolds stress amplitude across the overshoot region.

Tomographic particle image velocimetry flow structures downstream of a dynamic cylindrical element in a turbulent boundary layer by multi-scale proper orthogonal decomposition

This study reports the modification of large and small scales in a turbulent boundary layer (TBL) perturbed by a dynamic cylindrical element (DCE). Tomographic particle image velocimetry (Tomo-PIV) was utilized to measure the flow fields downstream of the dynamic perturbation. By the approach of multi-scale proper orthogonal decomposition (mPOD), the coherent modes relevant to the predefined frequency bands were extracted from the Tomo-PIV dataset. Then, a method was developed to construct the large- and small-scale structures and the DCE-perturbed structure based on the mPOD modes. The DCE impact on the large- and small-scale structures was elaborated by comparing with the unperturbed TBL case. The two-point correlation analysis indicated that large-scale structures appear downstream of the DCE perturbation in a short streamwise length scale. More importantly, the scale rearrangements were further examined by presenting the modulation coefficients between the large scales and small-scale energy. It revealed that even though the DCE perturbation alters the level of correlation, three different types of interaction scenario can still be observed. In the near-wall region, the large-scale structures have an amplitude modulation effect on the small-scale energy with the lower positive coefficients. The reversal scale arrangement was observed at the wall-normal height around the DCE amplitude, which could be attributed to the fluid exchange caused by the new-generated turbulent structures. In the log region, it confirmed that the inclined shear layer resides along the low-speed regions, which supported the robustness of the conceptual model of hairpin packets in the current DCE-perturbed TBL.

Experimental measurement of coherent structures in turbulent boundary layers using moving time-resolved particle image velocimetry

A moving time-resolved particle image velocimetry (MTRPIV) system was designed to measure the turbulent boundary layer (TBL). The combination of time-resolved particle image velocimetry and a translational moving system enables the MTRPIV to track the coherent structures with a long period and high temporal resolution. Based on the MTRPIV, the time-evolving of coherent structures within the TBL was measured and analyzed. The observation of the large-scale sweep collision with ejection shows that the strong collision causes the large-scale high- and low-speed coherent structures to break down. The time-evolving process of the hairpin packets shows that the low-speed fluid mass under the hairpin vortices is important for the generation of a whole hairpin packet. The small-scale low-speed structures increase their spatial scales by merging so that the independent hairpin vortices can be organized by merged larger-scale structures. The shear layer exceeding the length of 0.7–0.8 δ (δ is thickness of TBL) or 350–400 υUτ (υ and Uτ denote the kinematic viscosity and friction velocity, respectively) is unstable, and it will roll-up to generate a hairpin vortex. In the hairpin packet growth process, the inclination angle of the hairpin packet decreases from ∼13° to 8° in a time duration of 120 υUτ2, and the underlying low-speed fluid is elongated and then split. The analysis of the uniform momentum zones (UMZs) shows that the topmost UMZ has a relatively stable wall-normal position and convection speed. The lower UMZ is quasi-periodically generated and tends to move upward to merge with the upper UMZs. The hairpin packets impact the lower UMZs by inducing large-scale low-speed fluid mass to modulate the probability density function distribution of instantaneous streamwise velocity. The evolution of UMZs with velocity less than 0.5U∞ (U∞ denotes the free-stream velocity) is the result of the interaction of large- and small-scale streamwise fluctuation velocity.

Space–time formation of very-large-scale motions in turbulent pipe flow

We examine the origin of very-large-scale motions (VLSMs) in fully developed turbulent pipe flow at friction Reynolds number, $\mathit{Re}_{\unicode[STIX]{x1D70F}}=934$, using data from a direct numerical simulation. The VLSMs and the packet-like large-scale motions (LSMs) found in this study are very similar to those found in earlier studies. Three-dimensional time-evolving instantaneous fields show that one component of the process leading to the large streamwise length of VLSMs is the concatenation of adjacent streamwise LSMs caused by the continuous elongation of LSMs due to the strain component of the mean shear. Spatial organization patterns of the VLSMs and LSMs and their properties are studied by separating auto-correlation of the streamwise velocity fluctuations into the components of the VLSM and the LSM defined by low-pass/high-pass filtering in the streamwise direction. The structures of the two-point spatial correlations of the streamwise velocity component of the VLSMs and the LSMs in the streamwise-azimuthal plane are characterized by multiple maxima and complex patterns that beg explanation in terms of patterned coherent arrangements of the LSMs. Using proper orthogonal decomposition (POD), it is found that the X-shape correlation pattern of the VLSMs results from the superposition of very long helically inclined structures and streamwise-aligned structures. Further explanation of the patterns in the correlations of the VLSMs and LSMs is provided through the study of synthetically constructed arrangements of simple hairpin packet models of the LSM. Head-to-tail alignment of the model packets along streamwise and helical directions suggested by the eigenvalues of the POD creates a pair of long roll-cells centred above the logarithmic layer, and bracketing the LSMs. These roll-cells are pure kinematic consequences of the induction within the LSM packets, but they may also serve to organize smaller packets.

Wavelet Coherency Structure in Open Channel Flow

Many studies based on single-point measurement data have demonstrated the impressive ability of wavelet coherency analysis to catch the coherent structures in the wall-bounded flows; however, the question of how the events found by the wavelet coherency analysis relate to the features of the coherent structures remains open. Time series of velocity fields in x–y plane of the steady open channel flow was obtained from a time-resolved particle imaging velocimetry system. The local wavelet spectrum found shows that one of the main energetic scales in open channel flows is 3h motions. The wavelet coherent coefficients of u and v series from the same measurement points successfully detected the occurrence and the scale of these 3h motions, and the phase angle indicates their inside velocity structure is organized by the Q2 and Q4 events. The wavelet coherency analysis between different measurement points further reveals the incline feature of the 3h scale motions. All the features of this 3h motion found by the wavelet coherency analysis coincide well with the flow field that is created by the passing of hairpin packets.

Large-scale turbulence structures in a laboratory-scale boundary layer under steady and gusty wind inflows

Experiments on turbulence structures and features of a wind field under steady inflow and gusty wind inflows were implemented in a straight-through wind tunnel. Streamwise and wall-normal velocity components were measured using a streamline constant temperature anemometer (streamline CTA). Power spectra analyses revealed the existence of very large-scale motions (VLSMs) under both steady and gusty wind inflows; but new gusty scale motions (GSMs) were revealed under only gusty wind inflows. The GSMs might originate from an ordered external driving force that forces hairpin packets to align coherently in groups with a length scale related to the gust inflow condition. The streamwise wavelength of VLSMs is independent of inflow conditions, while the turbulent energy of VLSMs is associated with the wall-normal height and local mean streamwise velocity. In particular, the streamwise wavelength of GSMs increases linearly with the average value and period of sinusoidal gusty wind inflows, and the turbulent energy of GSMs is sensitive to the wall-normal height and all characteristic parameters of gusty wind inflows, including the average value, amplitude and period. Considerable wall-normal airflows induced by gusty wind inflows were detected and these are negatively correlated with the variation in gusty streamwise velocity, and root mean square (RMS) values of the gusty wall-normal velocity tended to increase linearly with the average value and amplitude of gusty wind inflows.

The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

Partially filled pipes: experiments in laminar and turbulent flow

Pressure-driven laminar and turbulent flow in a horizontal partially filled pipe was investigated using stereoscopic particle imaging velocimetry (S-PIV) in the cross-stream plane. Laminar flow velocity measurements are in excellent agreement with a recent theoretical solution in the literature. For turbulent flow, the flow depth was varied independently of a nominally constant Reynolds number (based on hydraulic diameter, $D_{H}$; bulk velocity, $U_{b}$ and kinematic viscosity $\unicode[STIX]{x1D708}$) of $Re_{H}=U_{b}D_{H}/\unicode[STIX]{x1D708}\approx 30\,000\pm 5\,\%$. When running partially full, the inferred friction factor is no longer a simple function of Reynolds number, but also depends on the Froude number $Fr=U_{b}/\sqrt{gD_{m}}$ where $g$ is gravitational acceleration and $D_{m}$ is hydraulic mean depth. S-PIV measurements in turbulent flow reveal the presence of secondary currents which causes the maximum streamwise velocity to occur below the free surface consistent with results reported in the literature for rectangular cross-section open channel flows. Unlike square duct and rectangular open channel flow the mean secondary motion observed here manifests only as a single pair of vortices mirrored about the vertical bisector and these rollers, which fill the half-width of the pipe, remain at a constant distance from the free surface even with decreasing flow depth for the range of depths tested. Spatial distributions of streamwise Reynolds normal stress and turbulent kinetic energy exhibit preferential arrangement rather than having the same profile around the azimuth of the pipe as in a full pipe flow. Instantaneous fields reveal the signatures of elements of canonical wall-bounded turbulent flows near the pipe wall such as large-scale and very-large-scale motions and associated hairpin packets whilst near the free surface, the signatures of free surface turbulence in the absence of imposed mean shear such as ‘upwellings’, ‘downdrafts’ and ‘whirlpools’ are present. Two-point spatio-temporal correlations of streamwise velocity fluctuation suggest that the large-scale coherent motions present in full pipe flow persist in partially filled pipes but are compressed and distorted by the presence of the free surface and mean secondary motion.

Coherent instability in wall-bounded shear

The mechanism underlying the coherent hairpin process in wall-bounded shear flows is studied. An algorithm for the identification and analysis of flow structures based on morphological operations is presented. The method distils the topology of the flow field into a discrete data set and enables the time-resolved sampling of coherent flow processes across multiple scales. Application to direct simulation data of transitional and turbulent boundary layers at moderate Reynolds number sheds light on the flow physics of the hairpin process. The analysis links the hairpin to an exponential instability which is amplified in the flow distorted by a negative perturbation in the streamwise velocity component. Linear analyses substantiate the connection to an inviscid instability mechanism of varicose type. The formation of packets of hairpins is related to a self-similar process which originates from a single patch of low-speed fluid and describes a recurrence of the dynamics that leads to the formation of an individual hairpin. Analysis of the evolution of several thousand turbulent hairpins provides a statistical characterization of the principal dynamics and yields a time-resolved average of the hairpin process. Comparisons with the transitional hairpin show qualitatively consistent trends and thus support earlier hypotheses of their equivalence. In terms of the causality of events, the results suggest that the hairpin is a manifestation of the varicose instability and as such is a consequence rather than a cause of the primary perturbations of the flow.