Low-speed Streaks Research Articles

Characteristics of shear stress fluctuations in polymer solutions and their relation to turbulent structures in channel flows

In this study, the wall shear stress in the channel flow of polyacrylamide polymers was investigated through electrochemical experiments, and the effects of the polymer concentration were evaluated at different Reynolds numbers. The objective was to explore the relationship between the changes in the drag reduction and near-wall turbulence structure induced by the polymer. The experiments were conducted using polymer concentrations of 0, 20, 50, 100, and 150 ppm, and a drag reduction of approximately 23% was achieved at a bulk Reynolds number of Reb = 18 750. In the electrochemical method, the working electrode was arranged spanwise, and simultaneous measurements were performed for eight electrodes to discuss the scale of the near-wall low-speed streaks and burst events. A comprehensive analysis of the correlation of the wall shear stress in the streamwise direction and the cross-spectrum of two points in the spanwise direction revealed that large streamwise and spanwise scales of near-wall low-speed streaks were generated at high polymer concentrations. Furthermore, the results obtained using the variable interval time averaging technique indicated that polymer incorporation suppressed the wall shear stress fluctuations and weakened both the intensity and frequency of the bursting events.

A numerical study on the turbulence characteristics in an air–water upward bubbly pipe flow

A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are $Re_{bulk}= u_{bulk} D/\nu _w = 5300$ and $Re_{bub}= (\langle u_{bub}\rangle - u_{bulk}) d_{eq}/\nu _w = 533\unicode{x2013}1000$ , respectively, where $u_{bulk}$ is the water bulk velocity, $\langle u_{bub}\rangle$ is the overall bubble mean velocity, $D$ is the pipe diameter and $\nu _w$ is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to $\bar {\psi }(r)^{0.4}$ , where $\bar {\psi } (r)$ is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all radial locations including near the wall. Rising bubbles near the wall mostly bounce against the wall rather than slide along the wall or hang around the wall without collision. Low-speed streaks observed in the near-wall region in the absence of bubbles nearly disappear due to the bouncing bubbles. These bouncing bubbles generate counter-rotating vortices in their wake, and increase the skin friction by sweeping high-speed water towards the wall. We also suggest an algebraic Reynolds-averaged Navier–Stokes model considering the interaction between shear-induced and bubble-induced turbulence. This model provides accurate predictions for a wide range of liquid bulk Reynolds numbers.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

Rainbow Imaging Of 3-D Microbubble Distribution Clustered Inside A Turbulent Boundary Layer

Microbubbles dispersed in a turbulent boundary layer spatially developing along a flat plate is investigated experimentally. The aim of study is to find out visually how microbubbles interact with turbulent eddies to achieve frictional drag reduction on a wall. For stream Reynolds number up to 3×104 , microbubble suspended at Stokes number smaller than 10 − 3 is measured. Stream-wise vortices in the boundary layer were visualized by flake optics, of which spacing expands with injection of microbubbles. 3-D microbubble distributions were measured by a color-coded volumetric illumination applied to the boundary layer. The result showed preferentially accumulated microbubble clouds to low-speed streaks close to viscous sublayer and to hair-pin vortices in the buffer layer.

Direct numerical simulation of supersonic boundary layer transition induced by gap-type roughness

The transition of the supersonic boundary layer induced by roughness is a highly intricate process. Gaining a profound understanding of the transition phenomena and mechanisms is crucial for accurate prediction and control. In this study, to delve into the flow mechanisms of a transition in a supersonic boundary layer induced by the medium gap-type roughness, direct numerical simulation is employed to capture and analyze the transition process. Research indicates that as the flow over the flat plate passes the gap, the spanwise convergence effect leads to the formation of both upper and lower counter-rotating vortex pairs. As the flow progresses, these counter-rotating vortex pairs in the central region exhibit attenuation, with streamwise vortices developing on both sides. At a certain downstream distance, the boundary layer becomes unstable, triggering the formation of streamwise vortex legs. These streamwise vortex legs undergo further evolution, transforming into hairpin vortices and leg-buffer vortices. The formation of the central low-speed zone downstream of the roughness element is mainly attributed to the lift-up effect of the low-speed flow propelled by the central counter-rotating vortex pairs. The low-speed streaks on both sides are primarily influenced by the streamwise vortices. Through a meticulous analysis of the turbulent kinetic energy distribution and its generation mechanisms during the transition phase, this study infers that the primary sources of turbulent kinetic energy are the hairpin vortices, leg-buffer vortices, and their consequent secondary vortices. Combined with modal analysis, the study further elucidates the generation and breakdown of hairpin and leg-buffer vortices.

Understanding Low-Speed Streaks and Their Function and Control through Movable Shark Scales Acting as a Passive Separation Control Mechanism.

The passive bristling mechanism of the scales on the shortfin mako shark (Isurus oxyrinchus) is hypothesized to play a crucial role in controlling flow separation. In the hypothesized mechanism, the scales are triggered in response to patches of reversed flow at the onset of separation occurring in the low-speed streaks that form in a turbulent boundary layer. The two goals of this investigation were as follows: (1) to measure the reversing flow occurring within the low-speed streaks in a separating turbulent boundary layer; (2) to understand the passive flow control mechanism of movable shark skin scales that inhibit reversing flow within the low-speed streaks. Experiments were conducted using digital particle image velocimetry (DPIV). DPIV was used to analyze the flow in a turbulent boundary layer subjected to an adverse pressure gradient formation over both a smooth flat plate and a flat plate on which shark skin specimens were affixed. The experimental analysis of the flow over the smooth flat plate corroborated the findings of previous direct numerical simulation studies, which indicated that the average spanwise spacing of the low-speed streaks increases in the presence of adverse pressure gradients upstream of the point of separation. However, the characteristics of the flow over the shark skin specimen more closely resemble that of a zero-pressure gradient turbulent boundary layer. A comparative analysis of the width and velocity of the reversed streaks between flat plate and shark skin cases reveals that the mean spanwise spacing decreases, and thus, the number of streaks increases over the shark skin. Additionally, the reversed streaks observed over shark scales are thinner and the highest negative velocity within the streaks falls within the range required to bristle the scales.

Sub-filter-scale shear stress analysis in hypersonic turbulent Couette flow

Direct numerical simulations of hypersonic turbulent Couette flows are performed for top-wall Mach numbers of 6, 7 and 8, inspired by non-reactive high-enthalpy wind tunnel free-stream conditions, with the goal of analysing the physical processes driving the sub-filter-scale (SFS) stresses to inform development of large-eddy simulation techniques for hypersonic wall-bounded flows. Semi-local scaling laws collapse mean profiles and second-order turbulent statistics well, in spite of the strong wall-normal gradients of temperature and density. On the other hand, the SFS shear stresses exhibit an unexpected profile characterized by a region of pronounced shear stress deficit, which becomes more pronounced for higher Mach numbers. Instantaneous visualizations suggest that the SFS shear stress deficit is induced by the counter-gradient resolved momentum transport driven by residual velocity motions at the interface between high-density low-speed streaks being ejected away from the wall, and low-density high-speed ones replacing the displaced fluid, qualifying this as a compressibility effect. It is shown that the SFS shear stresses are primarily driven by second-order interactions between residual velocities, in spite of their triply nonlinear nature. This, in turn, motivated a statistical quadrant analysis revealing the presence of a SFS shear stress deficit, that is, SFS processes driving momentum transport of the resolved field towards the top wall. Additionally, higher-Reynolds-number simulations reveal that there is an upper limit of spatial filter widths to resolve large-scale structures, and such deficit is observable at any Reynolds number when a reasonable spatial filter is applied.

Manipulation of a turbulent boundary layer using sinusoidal riblets

We investigate experimentally the effects of micro-grooves on the development of a zero pressure gradient turbulent boundary layer at two different values of the friction Reynolds number. We consider both the well-known streamwise aligned riblets as well as wavy riblets, characterized by a sinusoidal pattern in the mean flow direction. Previous investigations by the authors showed that sinusoidal riblets yield larger values of drag reduction with respect to the streamwise aligned ones. We perform new particle image velocimetry experiments on wall-parallel planes to get insights into the effect of the sinusoidal shape on the near-wall organisation of the boundary layer and the structures responsible for the friction drag reduction and the turbulence generation. Conditional averages, aimed at identifying the topology of the low-speed streaks in the turbulent boundary layer, reveal that the flow is highly susceptible to wall manipulation. This is particularly evident in the cases that are associated with greater values of drag reduction. The results suggest a fragmentation and/or weakening of the streaks in the sinusoidal cases, that is triggered by the larger values of the wall-normal vorticity found at the streaks’ edges. The results are also confirmed by applying the variable interval spatial averaging events eduction technique. The turbulent kinetic energy budget also shows that the sinusoidal geometry significantly attenuates the turbulence production, hence supporting the idea of the manipulation of the turbulence regeneration cycle.

On the generation of near-wall dilatational motions in hypersonic turbulent boundary layers

Dilatational motions in the shape of travelling wave packets have been identified recently to be dynamically significant in hypersonic turbulent boundary layers. The present study investigates the mechanisms of their generation and their association with the solenoidal motions, especially the well-recognized near-wall self-sustaining process of the regeneration cycle between the velocity streaks and quasi-streamwise vortices. By exploiting the direct numerical simulation databases and orchestrating numerical experiments, we explore systematically the near-wall flow dynamics in the processes of the formation and transient growth of low-speed streaks. We conclude via theoretical ansatz that the nonlinearity related to the parallel density and pressure gradients close to the wall due to the restriction of the isothermal boundary condition is the primary cause of the generation of the dilatational structures at small scales. In fully developed turbulence, the formation and the existence of healthy dilatational travelling wave packets require the participation of the turbulence at scales larger than those of the near-wall regeneration cycles, especially the occurrence of the bursting events that generate vortex clusters. This is proven by the less intensified dilatational motions in the numerical experiments in which the Orr mechanism is alleviated and the vortical structures and turbulent bursts are weakened.

Drag reduction of the turbulent boundary layer over divergent sawtooth riblets surface with a superhydrophobic coat

Energy conservation and environmental protection have become pivotal components of the green economy. In recent years, underwater drag reduction technology has garnered significant interest. This study discusses a novel composite surface that combines divergent riblets with a superhydrophobic coating (D-rib&SHS) to enhance the drag reduction rate. Alongside this new surface, a riblet surface with a superhydrophobic coating (rib&SHS, without yaw angles) and a smooth surface are used as comparison groups. The turbulent boundary layer flow of these three surfaces is measured using a two-dimensional particle image velocimetry system. The results indicated that the maximum drag reduction rate of D-rib&SHS is approximately 27% higher than that of rib&SHS, and the drag reduction range is increased to Reθ≈4100 compared to rib&SHS (Reθ≈2200). Using correlation algorithms, it observed that the spacing between low-speed streaks over D-rib&SHS is larger than that of rib&SHS and the smooth surface. This finding suggested that the spacing between the hairpin vortex legs of D-rib&SHS is wider. The increased spacing between the hairpin vortex legs reduces the likelihood of vortex head formation between the two quasi-streamwise vortices, ultimately suppressing the auto-generation of hairpin vortices. Consequently, the development of hairpin vortex packets over D-rib&SHS is also inhibited. These phenomena observed over D-rib&SHS can be attributed to the combined effects of velocity slip on the superhydrophobic coating and the secondary flow over the divergent riblets near the wall. In addition, unlike divergent riblets that are not covered with a superhydrophobic coating, where the drag reduction effect is more pronounced with a yaw angle of 30° compared to 10°, D-rib&SHS with a 10° yaw angle demonstrated a superior drag reduction effect compared to D-rib&SHS with a 30° yaw angle. This innovative composite surface enhances the drag reduction effect and expands the drag reduction Reynolds number range, offering a new approach to mitigating drag in turbulent boundary layer flows.

The Interaction of Turbulent Spots With Low-Speed Streaks

Abstract Turbulent spots are regions of turbulence surrounded by laminar flow that appear during the late stages of boundary layer transition. While turbulent spots are often studied in isolation, they usually occur near low-speed streaks and other disturbances during transition. This paper investigates the interaction between a turbulent spot and a subcritical low-speed streak using direct numerical simulations. The results, analyzed from streak instability and vorticity points of view, reveal mechanisms of the destabilization of the streak by the spot and provide insights into spot evolution in a realistic environment. Additional simulations involving intentional local control of portions of the streak provide further insight into the interaction mechanisms and potential transition mitigation strategies.

Turbulent–turbulent transient concept in pulsating flows

The turbulence behaviour of current-dominated pulsating flows has been investigated. Direct numerical simulations have been carried out for Stokes lengths over a range of $l_s^+=5\unicode{x2013}26$ , and amplitudes spanning 90 % of the current-dominated regime, about a mean flow of $\overline {Re}=6275$ . The results show that the turbulence response in intermediate and low-frequency pulsations is governed by a multistage turbulent–turbulent transition process, which bears a strong similarity to the multistage response of non-periodic acceleration. During the early acceleration period, the flow enters a pretransition stage, in which a new laminar perturbation boundary layer forms at the wall, and the streamwise velocity streaks are stretched. If the low-speed streaks destabilise prior to the deceleration period, then the flow enters a transition stage in which the perturbation boundary layer undergoes a bypass-like transition process. A unique feature of pulsating flows is the ongoing mechanism of turbulence decay, which initiates during the deceleration period and constitutes the main transient turbulence mechanism for much of the cycle. For high-frequency pulsations, the perturbation boundary layer fails to reach the pretransition stage prior to the deceleration period. Instead, the flow alternates between two inertial stages which are characterised by two layers of amplified viscous force; one growing at the wall, and one detached and moving towards the core.

Preferential accumulation of finite-size particles in near-wall streaks

The preference for particles to accumulate at specific regions in the near-wall part is a widely observed phenomenon in wall-bounded turbulence. Unlike small particles more frequently found in low-speed streaks, finite-size particles can accumulate in either low-speed or high-speed streaks. However, mechanisms and influencing factors leading to the different preferential concentration locations still need to be clarified. The present study conducts particle-resolved direct numerical simulations of particle-laden turbulent channel flows to provide a better understanding of this seemingly puzzling behaviour of preferential accumulation. These simulations cover different particle-to-fluid density ratios, particle volume fractions, particle sizes and degrees of sedimentation intensity. We find that the large particle size is the crucial factor that results in particles accumulating in high-speed streaks. Large particles not only are difficult to be conveyed by the quasi-streamwise vortices to low-speed streaks but also can escape from the near-wall region before moving spanwisely out from high-speed streaks. The sedimentation effect allows particles to gather closer to the channel wall and stay longer in the near-wall regions, reinforcing the sweeping mechanism of quasi-streamwise vortices that transport particles from high- to low-speed streaks. As a result, sedimenting particles tend to accumulate in the low-speed streaks.

Scaling and mechanism of the propagation speed of the upstream turbulent front in pipe flow

The scaling and mechanism of the propagation speed of turbulent fronts in pipe flow with the Reynolds number has been a long-standing problem in the past decades. Here, we derive an explicit scaling law for the upstream front speed, which approaches a power-law scaling at high Reynolds numbers, and we explain the underlying mechanism. Our data show that the average wall distance of low-speed streaks at the tip of the upstream front, where transition occurs, appears to be constant in local wall units in the wide bulk-Reynolds-number range investigated, between 5000 and 60 000. By further assuming that the axial propagation of velocity fluctuations at the front tip, resulting from streak instabilities, is dominated by the advection of the local mean flow, the front speed can be derived as an explicit function of the Reynolds number. The derived formula agrees well with the speed measured by front tracking. Our finding reveals a relationship between the structure and speed of a front, which enables a close approximation to be obtained of the front speed based on a single velocity field without having to track the front over time.

Boundary layer transition due to distributed roughness: effect of roughness spacing

The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation and global stability analysis, and compared with isolated roughness elements at the same Reynolds number $Re_h=U_eh/\nu$ ( $U_e$ is the boundary layer edge velocity, h is roughness height and $\nu$ is the kinetic viscosity of the fluid). Small spanwise spacing ( $\lambda _z=2.5h$ ) inhibits the formation of counter-rotating vortex pairs (CVP) and, as a result, hairpin vortices are not generated and the downstream shear layer is steady. For $\lambda _z=5h$ , the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. The temporal periodicity of the primary hairpin vortices appears to be independent of the streamwise spacing. Distributed roughness leads to a lower critical roughness Reynolds number for instability to occur and a more significant breakdown of the boundary layer compared with isolated roughness. When the streamwise spacing is $\lambda _x=5h$ , the high-momentum fluid barely moves downward into the cavities and the wake flow has little impact on the following roughness elements. The leading unstable varicose mode is associated with the central low-speed streaks along the aligned roughness elements, and its frequency is close to the shedding frequency of hairpin vortices in the isolated case. For larger streamwise spacing ( $\lambda _x=10h$ ), two distinct modes are obtained from global stability analysis. The first mode shows varicose symmetry, corresponding to the primary hairpin vortex shedding induced by the first-row roughness. The high-speed streaks formed in the longitudinal grooves are also found to be unstable and interact with the varicose mode. The second mode is a sinuous mode with lower frequency, induced as the wake flow of the first-row roughness runs into the second row. It extracts most energy from the spanwise shear between the high- and low-speed streaks.

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.

Effects of the direction of rotation axis on turbulent flows in rectangular ducts

The effects of the direction of rotation axis on flows in rectangular ducts are studied using direct numerical simulation. The rotation axis lies in the cross section of the duct. The angle of the rotation axis relative to the bottom edge of the cross section is altered from 0° to 90°. A series of cases are considered, including three Reynolds numbers Reτ = 300, 454, and 900, three rotation numbers Roτ = 2, 4, and 8, and two cross-sectional aspect ratios ar = 1.0 and 2.0. The results show that as the angle increases, the bulk velocity remains almost constant in the square duct while it decreases monotonically in the duct with ar = 2.0. When the angle increases from 0° to 45°, turbulence is significantly or even completely suppressed, while the secondary flow is gradually enhanced. Furthermore, with the same rotation number, turbulence is more strongly suppressed at a lower Reynolds number. As the angle further increases from 45° to 90° in the cases with ar = 2.0, the intensity of turbulence is recovered to some extent and the secondary flow gradually weakens. With the angle increasing from 0°, the Ekman layer is formed above the pressure wall and gradually strengthens, resulting in a drastic wall-normal variation of the mean flow direction and a tilting of the low-speed streaks near the wall, which may cause the weakening of the turbulence. In addition, in the flow fields where turbulence is severely suppressed, periodic structures are observed in the corner of the duct, which needs further study.

Intermittent behavior of a bypass transition of boundary layers over an axisymmetric body of revolution

A transitional boundary layer developing over the forebody of a SUBOFF model subject to high free-stream turbulence (FST) was experimentally measured using both laser induced fluorescence and time-resolved two-dimensional particle image velocimetry. Typical coherent structures in the bypass transition, including low-speed streaks, hairpin-like vortices and vortex packets, are clearly visualized. Continue wavelet transform analysis on the time-frequency characteristics of instantaneous Reynolds shear stress (RSS) indicates that the intermittent behavior is mainly confined in mild-to-high-frequency domain, whereas low-frequency component is attributed to the Klebanoff mode. A wavelet-based approach was proposed to detect multi-scale turbulent events from wavelet coefficients of RSS, and the spatial evolution of the multi-scale intermittency factor was then calculated. Furthermore, the conditional sampling of laminar and turbulence events provides a new perspective on the route of the disturbance growth in the bypass transition. It is clearly shown that FST-introduced disturbances with moderate-to-high frequency are unable to penetrate the near-wall region; meanwhile, multi-scale characteristics inside the boundary layer evolve spontaneously from the Klebanoff mode.

Physical Model of Gusty Coherent Structure in Atmospheric Boundary Layer

AbstractCoherent structure is an important phenomenon in the fluid field, and also exists in atmospheric boundary layer. For example, after the passage of a cold front in spring in northern China, there is a rather regular gusty wind with a period of approximately 3 min superimposed on the basic strong wind, and the gusty wind possesses a coherent structure: the vertical velocity is upward when horizontal velocity is in the valley phase, but downward when horizontal velocity is in the peak phase. The coherence makes transport of momentum and matter more effective. It was later found that this gusty coherent structure is a phenomenon of mechanical turbulence, which occurs in weakly stable, neutral and unstable stratification. However, research on the physical mechanism of this coherent structure is still lacking. This paper shows that the gusty coherent structure can be explained by quasi‐streamwise vortex pairs and high and low speed streaks induced by quasi‐streamwise vortexes. The coherent structure can be obtained from the three‐dimensional Navier‒Stokes (N‒S) equations. The maximum intensities of vortices and streaks are located at 20.7% and 12.1% of the boundary layer heights respectively, which are consistent with the observed results at 200 and 120 m.

Numerical study of the hydrodynamic stability of a wind-turbine airfoil with a laminar separation bubble under free-stream turbulence

The interaction of several instabilities and the influence of free-stream turbulence on laminar-turbulent transition on a 20% thick wind-turbine blade section with a laminar separation bubble (LSB) are investigated with wall-resolved large-eddy simulations (LES). Turbulence intensities (TI) of 0%, 2.2%, 4.5%, 8.6%, and 15.6% at chord Reynolds number 105 are considered. Linear receptivity occurs for the most energetic disturbances; high-frequency perturbations are excited via non-linear mechanisms for TI≥8.6%. Unstable Tollmien–Schlichting (TS) waves appear in the inflectional flow region for TI≤4.5%, shifting to inviscid Kelvin–Helmholtz (KH) modes upon separation and forming spanwise rolls. Sub-harmonic secondary instability occurs for TI=0%, with rolls intertwining before transition. Streaks spanwise modulate the rolls and increase their growth rates with TI for TI≤4.5%, reducing separation and shifting transition upstream. The TI=4.5% case presents the highest perturbations, leading to the smallest LSB and most upstream transition. Earlier inception of TS/KH modes occurs on low-speed streaks, inducing premature transition. However, for TI=8.6%, the effect of the streaks is to stabilize the attached mean flow and front part of the LSB. This occurs due to the near-wall momentum deficit alleviation, leading to the transition delay and larger LSB than TI=4.5%. This also suppresses separation and completely stabilizes TS/KH modes for TI=15.6%. Linear stability theory predicts well the modal evolution for TI≤8.6%. Optimal perturbation analysis accurately computes the streak development upstream of the inflectional flow region but indicates higher amplification than LES downstream due to the capture of low-frequency, oblique modal instabilities from the LSB. Only low-amplitude [O(1%)] streaks displayed exponential growth in the LES since non-linearity precludes the appearance of these modes.