Spanwise Rollers Research Articles

Reynolds number dependence of turbulent flows over a highly permeable wall

Direct numerical simulations of turbulent flows over highly permeable porous walls were performed at various Reynolds numbers to examine the effects of the Reynolds number on permeable wall turbulence. The porous medium consisted of Kelvin cell arrays with porosity $0.95$ , and the permeability Reynolds number $Re_K$ ranged from approximately 7 to 50. Simulations with thin and thick porous walls were performed to investigate the effects of spanwise roller vortices associated with the Kelvin–Helmholtz instability. The results show that the effect of the Kelvin–Helmholtz instability becomes more significant with increasing the permeability Reynolds number, and spanwise rollers, for which length scale is an order of channel height, dominate turbulence when $Re_K \gtrsim 30$ . Spanwise rollers reinforce the negative correlation between the wall-normal and streamwise velocity fluctuations close to the porous/fluid interface, and intensify the turbulent velocity fluctuations away from the porous walls, leading to increased frictional resistance. An investigation of the Reynolds number dependence of the modified logarithmic law indicates that the zero-plane displacement and equivalent roughness height are proportional to the square root of permeability, whereas the von Kármán constant increases with the permeability Reynolds number because of the increased mixing length resulting from the relatively large-scale velocity fluctuations induced by spanwise rollers. We developed a model for the modified log law for permeable wall turbulence based on permeability, and confirmed that the skin friction coefficient obtained from the model reasonably predicts the skin friction coefficient for several types of high-porosity porous media. Hence, permeability is a key parameter that characterizes the logarithmic mean velocity profiles over a variety of porous media with high porosity.

Dissimilar turbulent heat transfer enhancement by Kelvin–Helmholtz rollers over high-aspect-ratio longitudinal ribs

Passive heat transfer enhancement by spanwise rollers associated with the Kelvin–Helmholtz instability was studied through direct numerical simulations of high-aspect-ratio longitudinal ribs at the friction Reynolds number $300$ . The temperature was treated as a passive scalar with Prandtl number unity to discuss the similarity between the heat and momentum transfer. The results reveal that the high-aspect-ratio longitudinal ribs lead to a favourable breakdown of the Reynolds analogy, that is, the enhancement of the heat transfer rate surpasses that of the frictional resistance. The favourable breakdown of the Reynolds analogy can be attributed to the enhanced turbulent heat flux compared with the Reynolds shear stress, whereas the rib-induced secondary flow plays a role in reducing the favourable breakdown of the Reynolds analogy. The conditional average statistics reveal that the high-pressure region accompanied by the spanwise rollers suppresses the spanwise roller-induced sweep and ejection motions, leading to smaller Reynolds shear stress than for the turbulent heat flux.

Role of spanwise rollers by Kelvin–Helmholtz instability in turbulence over a permeable porous wall

Direct numerical simulation over porous walled channel flows with computational domain size constraints were performed to clarify the role of spanwise rollers associated with the Kelvin--Helmholtz instability on turbulent flows over a porous wall. The spanwise rollers contribute to an increase in turbulence inside the porous wall and modify the logarithmic law in the clear flow region.

Resolvent-based predictions for turbulent flow over anisotropic permeable substrates

Abstract

Resolvent-based design and experimental testing of porous materials for passive turbulence control

An extended version of the resolvent formulation is used to evaluate the use of anisotropic porous materials as passive flow control devices for turbulent channel flow. The effect of these porous substrates is introduced into the governing equations via a generalized version of Darcy’s law. Model predictions show that materials with high streamwise permeability and low wall-normal permeability (ϕxy=kxx/kyy≫1) can suppress resolvent modes resembling the energetic near-wall cycle. Based on these predictions, two anisotropic porous substrates with ϕxy>1 and ϕxy<1 were designed and fabricated for experiments in a benchtop water channel experiment. Particle Image Velocimetry (PIV) measurements were used to compute mean turbulence statistics and to educe coherent structure via snapshot Proper Orthogonal Decomposition (POD). Friction velocity estimates based on the Reynolds shear stress profiles do not show evidence of discernible friction reduction (or increase) over the streamwise-preferential substrate with ϕxy>1 relative to a smooth wall flow at identical bulk Reynolds number. A significant increase in friction is observed over the substrate with ϕxy<1. This increase in friction is linked to the emergence of spanwise rollers resembling Kelvin–Helmholtz vortices. Coherent structures extracted via POD analysis show qualitative agreement with model predictions.

On the origin of drag increase in varying-phase opposition control

This study investigates the physics underlying the drag increase in a low Reynolds number turbulent channel flow due to varying-phase opposition control by means of direct numerical simulation and modal analysis. The drag increase occurs for an extended region of the parameter space and we consider a controller with a positive phase shift in Fourier domain between sensor measurement and actuator response as a representative example for this regime. Analyses of instantaneous flow fields as well as spatial power spectra show that the structure of drag-increased flows is remarkably different from that of drag-reduced and canonical flows. In particular, the near-wall region is dominated by structures of short streamwise and large spanwise extent. Isolation of a representative control scale shows that these energetic structures can be characterized as spanwise rollers, which induce strong ejection and sweep motions and lead to drag increase. The presence of rollers, and therefore drag increase, in the full nonlinear system correlates well with the presence of an amplified eigenvalue in the eigenspectrum of the linearized Navier–Stokes operator. It is further shown that the scales responsible for drag increase at positive phase shifts are inactive at negative phase shifts and do not contribute to drag reduction. These scales can therefore be excluded from a controller aimed at drag reduction, which relaxes the spatial resolution requirements on the control hardware. The eigenspectrum may be used as a computationally cheap tool to identify such detrimental scales during an early design stage.

Spanwise Cylinder Wake Hydrodynamics and Fish Behavior

AbstractFlows generated near hydro‐engineering structures are characterized by energetic three‐dimensional flow structures that are markedly different from naturally occurring fish habitats. The current study evaluated the interaction of Nile tilapia (Oreochromis niloticus) with spanwise rollers in the turbulent wake of a cylinder in both the wake bubble and the vortex shedding further downstream. The flow field hydrodynamics were measured using an acoustic Doppler velocimeter for Reynolds number (ReD) regimes ranging from 3,730 to 33,590, over a streamwise length of six diameters downstream of the cylinder, and revealed a pair of alternating vortices rotating about a spanwise axis, which were rendered asymmetric by the bed boundary proximity. Fish avoided areas where vorticity, turbulence intensity, turbulent kinetic energy, eddy size, and Reynolds shear stress were highest. Events of stability loss, referred to as spills, were significantly correlated to the turbulence integral length scale relative to fish standard length, with the peak number of spills occurring when the eddy length approached 45% to 50% of the fish length. Spill events significantly depended on ReD, Reynolds stress, and vorticity and varied according to fish length and weight. Among zones of similar Reynolds stress and vorticity magnitude, spills were most frequent when Reynolds shear stress was positive, downward acting and eddies rotated clockwise, which highlights the importance of direction and orientation of flow structures in determining the hydrodynamic forces that affect fish swimming stability. Recommendations are made for the inclusion of these metrics in the design and refinement of hydro‐engineering schemes.

Asymmetric wake of a horizontal cylinder in close proximity to a solid boundary for Reynolds numbers in the subcritical turbulence regime

The near wake dynamics developed behind a horizontal cylinder with wall proximity effects are elucidated from laboratory experiments and Large-Eddy Simulations (LES). Fixed vertical gap to diameter (G/D) ratios of 0.5 and 1.0 were investigated for Reynolds numbers equal to 6,666, 10,000 and 13,333. The LES results agreed well with the experimental measurements for the time-averaged flow quantities and captured the upward flow motion developed over the lower half of the flow depth as a consequence of the near-wall effect. The presence of a narrow gap between the cylinder and the bed, i.e. G/D = 0.5, significantly influenced the dynamics of the vortex generation and shedding which, in consequence, led to an increasingly pronounced asymmetric wake distribution with increasing Reynolds number. In the wider gap case of G/D = 1.0, the wake remained relatively symmetrical, with reduced impact of ground proximity. Kelvin-Helmholtz instabilities developed in the upper and lower shear layers were shown to be decoupled as their instantaneous laminar-to-turbulent transition occurred at different downstream distances at any given time. Spanwise rollers were shown to form with an undulating pattern and presented irregularly located vortex dislocations. Furthermore, a ground-vortex induced during the early stages of the lower roller’s generation in the wake lifted off the ground and merged with the vortices to form a single vortical structure. For G/D = 0.5, a positive upwards force was present, and experimental and LES Strouhal number values ranged between 0.28–0.32, while computed drag coefficient values were lower than those typical for unbounded cylinder flows. As for G/D = 1.0, Strouhal numbers decrease to a 0.26–0.30 range whilst drag coefficient increases, further demonstrating the effects on the cylinder wake structure dynamics due to the proximity to a solid boundary.

Resolvent Analysis for Turbulent Channel Flow with Riblets

This paper extends the resolvent formalism for wall turbulence to account for the effect of streamwise-constant riblets. Under the resolvent formulation, the Navier–Stokes equations are interpreted as a forcing-response system: the nonlinear convective term is interpreted as a feedback forcing on the remaining linear terms, which generates a velocity and pressure response. A gain-based decomposition of the linear forcing-response transfer function—the resolvent operator—yields highly amplified velocity and pressure modes, which can be considered key building blocks of the turbulent flow field. Previous work has shown that these high-gain modes provide substantial insight into turbulence statistics, structure, and control of smooth-walled flows. To introduce the effect of riblets within this framework, a linear spatially varying body force is added to the governing equations. In other words, volume penalization is used to approximate the surface features. Predictions for spanwise-periodic and streamwise-constant riblets show that specific high-gain modes identified from the modified governing equations reproduce observations made in prior direct numerical simulations with limited computation. The deterioration in performance with increasing riblet size is predicted well and so is the emergence of spanwise rollers resembling Kelvin–Helmholtz vortices. This new modeling framework is also used to pursue limited riblet shape optimization.

Large-eddy simulation of an open-channel flow bounded by a semi-dense rigid filamentous canopy: Scaling and flow structure

We have carried out a large-eddy simulation of a turbulent open-channel flow over a marginally dense, fully submerged, rigid canopy. The canopy is made of a set of rigid, slender cylinders normally mounted on a solid wall. The flow in the canopy is resolved stem-by-stem by means of an immersed boundary method. It is found that the flow behavior can be categorized according to the velocity distribution into two separate spatial regions: the canopy itself and the outer region above it. Within the region occupied by the canopy elements, the velocity magnitude is found to be related to the local shear stress. Outside the canopy, a logarithmic velocity profile matching the canonical turbulent open-channel flow over rough walls is recovered albeit the strong manipulation exerted by the canopy on the buffer layer. In the innermost layer, the presence of the stems is responsible for redistributing the local momentum fluctuations from a streamwise to a spanwise leading component, inhibiting the survival of the wall streamwise velocity streaks. On the other hand, the outer region presents a structure very similar to the well-known logarithmic boundary layer with the presence of large and energetic streamwise velocity streaks generated by a system of quasistreamwise vortices. These vortices strongly contribute to the intracanopy fluctuations through vigorous sweep and ejection events that affect all the region occupied by the stems. Consistent with the results of previous investigations [H. Nepf, “Flow and transport in regions with aquatic vegetation,” Annu. Rev. Fluid Mech. 44, 123–142 (2012)], it is found that the inflection point in the mean velocity profile, produced by the drag discontinuity at the canopy tip, promotes the appearance of another system of spanwise oriented vorticity structures. However, different from previous results reported in the literature [J. Finnigan, “Turbulence in plant canopies,” Annu. Rev. Fluid Mech. 32, 519–571 (2000)], in our simulations, the presence of alternating head up–head down hairpin vortices generated by a mutual induction of the counter-rotating spanwise vortices is not observed. Instead, we advocate that the modulation of the spanwise coherent vorticity is due to the action of the external logarithmic layer structures (i.e., the outer streamwise vortices that penetrate the canopy) rather than by upwash and downwash motions induced by the mutual interaction of the spanwise rollers.

Role of jet spacing and strut geometry on the formation of large scale structures and mixing characteristics

The present study primarily focuses on the effect of the jet spacing and strut geometry on the evolution and structure of the large-scale vortices which play a key role in mixing characteristics in turbulent supersonic flows. Numerically simulated results corresponding to varying parameters such as strut geometry and jet spacing (Xn = nDj such that n = 2, 3, and 5) for a square jet of height Dj = 0.6 mm are presented in the current study, while the work also investigates the presence of the local quasi-two-dimensionality for the X2(2Dj) jet spacing; however, the same is not true for higher jet spacing. Further, the tapered strut (TS) section is modified into the straight strut (SS) for investigation, where the remarkable difference in flow physics is unfolded between the two configurations for similar jet spacing (X2: 2Dj). The instantaneous density and vorticity contours reveal the structures of varying scales undergoing different evolution for the different configurations. The effect of local spanwise rollers is clearly manifested in the mixing efficiency and the jet spreading rate. The SS configuration exhibits excellent near field mixing behavior amongst all the arrangements. However, in the case of TS cases, only the X2(2Dj) configuration performs better due to the presence of local spanwise rollers. The qualitative and quantitative analysis reveals that near-field mixing is strongly affected by the two-dimensional rollers, while the early onset of the wake mode is another crucial parameter to have improved mixing. Modal decomposition performed for the SS arrangement sheds light onto the spatial and temporal coherence of the structures, where the most dominant structures are found to be the von Kármán street vortices in the wake region.

Self-sustaining turbulent wake characteristics in fluid–structure interaction of a square cylinder

We present a numerical study on the fluid–structure interaction of a square cylinder at subcritical Reynolds numbers 1400≤Re≤10,000. Variation in spatial and temporal structures during the self-sustaining regeneration cycle are investigated via a three-dimensional Navier–Stokes flow coupled with a freely vibrating square cylinder at relatively low mass ratio. We employ a variational fluid–structure interaction formulation based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model. To begin, we assess the response amplitudes, the synchronization regimes and the vortex shedding patterns against the experimental measurements for the flow-induced vibration of a square cylinder at zero incidence angle. Of particular interest is to predict and analyze the synchronization regimes and the associated wake structures for a range of reduced velocity. The vibration of the cylinder provides an avenue for the merging of smaller eddies in the vicinity of the cylinder and there are relatively more clustered spanwise rollers and streamwise ribs as compared to the stationary counterpart. We provide a comparative assessment of Reynolds stress distributions in the near-wake region between the VIV lock-in case and its stationary counterpart. We find that the spatial symmetry of the shearing process in the wake shifts to the temporal symmetry of Reynolds stress when the cylinder is free to vibrate. Consequently, in the vibrating case, the competition between the mean shear growth and damping results in a relatively lower frequency shearing as compared to the stationary cylinder. We introduce a representative control volume in the near-wake region to assess the kinetic energy and enstrophy evolution for the stationary and vibrating configurations. We examine the core reason of the matching of periodic wake frequency with the vibrating cylinder frequency through the development of near-wake flow structures and the kinetic energy evolution. By combining these results with the self-sustained process of coherent vortex structure development, we finally explain the formation of intermediate hairpin-like structures in close proximity to the vibrating cylinder and the absence of them in the stationary cylinder.

Reynolds-number dependence of wall-pressure fluctuations in a pressure-induced turbulent separation bubble

Direct numerical simulations are used to examine the behaviour of wall-pressure fluctuations$p_{w}$in a flat-plate turbulent boundary layer with large adverse and favourable pressure gradients, involving separation and reattachment. The Reynolds number$Re_{\unicode[STIX]{x1D703}}$based on momentum thickness is equal to 300, 600 and 900. Particular attention is given to effects of Reynolds number on root-mean-square (r.m.s.) values, frequency/power spectra and instantaneous fields. The possible scaling laws are also examined as compared with the existing direct numerical simulation and experimental data. The r.m.s. value of$p_{w}$normalized by the local maximum Reynolds shear stress$-\unicode[STIX]{x1D70C}\overline{uv}_{max}$(Simpson et al. J. Fluid Mech.vol. 177, 1987, pp. 167–186; Na &amp; MoinJ. Fluid Mech.vol. 377, 1998b, pp. 347–373) leads to near plateau (i.e.$p_{w\,rms}/-\unicode[STIX]{x1D70C}\overline{uv}_{max}=2.5\sim 3$) in the adverse pressure gradient and separated regions in which the frequency spectra exhibit good collapse at low frequencies. The magnitude of$p_{w\,rms}/-\unicode[STIX]{x1D70C}\overline{uv}_{max}$is however reduced down to 1.8 near reattachment where good collapse is also obtained with normalization by the local maximum wall-normal Reynolds stress$\unicode[STIX]{x1D70C}\overline{vv}_{max}$. Near reattachment,$p_{w\,rms}/-\unicode[STIX]{x1D70C}\overline{vv}_{max}=1.2$is attained unambiguously independently of the Reynolds number and pressure gradient. The present magnitude (1.2) is smaller than (1.35) obtained for step-induced separation by Ji &amp; Wang (J. Fluid Mech.vol. 712, 2012, pp. 471–504). The reason for this difference is intrinsically associated with convective nature of a pressure-induced separation bubble near reattachment where the magnitude of$p_{w\,rms}$depends essentially on the favourable pressure gradient. The resulting mean flow acceleration leads to delay of the r.m.s. peak after reattachment. Attention is also given to structures of$p_{w}$. It is shown that large-scale spanwise rollers of low pressure fluctuations are formed above the bubble, whilst changing to large-scale streamwise elongated structures after reattachment. These large-scale structures become more prominent with increasing$Re_{\unicode[STIX]{x1D703}}$and affect$p_{w}$significantly.

Analysis and comparison between rough channel and pipe flows

Direct numerical simulations of turbulent channel and pipe flows are presented to highlight the effect of roughness at low Reynolds number (Reτ = 180 − 360). Several surfaces are reproduced with the immersed boundaries method, allowing a one-to-one comparison of the two canonical flows. In general, all rough surfaces produce the same effect on the flow in pipes and channels, with small differences in the roughness function, RMS velocities and spectral energy density of pipes and channels. The only exception is for the rough surfaces made of longitudinal bars. In particular, the triangular bars (riblets) show drag reduction in the channel and drag increase in the pipe. This behaviour is linked to the development of spanwise rollers and wide u-structures near the plane of the crest of the pipe.

Enhanced secondary motion of the turbulent flow through a porous square duct

Direct numerical simulations of the fully developed turbulent flow through a porous square duct are performed to study the effect of the permeable wall on the secondary cross-stream flow. The volume-averaged Navier–Stokes equations are used to describe the flow in the porous phase, a packed bed with porosity${\it\varepsilon}_{c}=0.95$. The porous square duct is computed at$\mathit{Re}_{b}\simeq 5000$and compared with the numerical simulations of a turbulent duct with four solid walls. The two boundary layers on the top wall and porous interface merge close to the centre of the duct, as opposed to the channel, because the sidewall boundary layers inhibit the growth of the shear layer over the porous interface. The most relevant feature in the porous duct is the enhanced magnitude of the secondary flow, which exceeds that of a regular duct by a factor of four. This is related to the increased vertical velocity, and the different interaction between the ejections from the sidewalls and the porous medium. We also report a significant decrease in the streamwise turbulence intensity over the porous wall of the duct (which is also observed in a porous channel), and the appearance of short spanwise rollers in the buffer layer, replacing the streaky structures of wall-bounded turbulence. These spanwise rollers most probably result from a Kelvin–Helmholtz type of instability, and their width is limited by the presence of the sidewalls.

Plane jet excited by disturbances with spanwise phase variations

Evolution of the near-field structures of a plane jet excited by temporal periodic disturbances with spanwise phase variations was investigated with stereoscopic particle image velocimetry. The three-dimensional vorticity distributions were reconstructed by using Taylor’s frozen field hypothesis. When ϕ, the temporal phase difference of disturbances in the spanwise direction was π; chain-link-fence type structures were formed. The $$\Uplambda$$ vortices in the chain-link-fence structures were then distorted into an $$\Upomega$$ shape, and the head of the vortex was detached and reconnects to form a vortex ring, or reconnects to the adjacent V-shaped vortices to form an A-shaped vortex. After the reconnection stage, the flow field was occupied by uniformly distributed fine scale eddies. Here, the overall turbulent kinetic energy and shear stress were suppressed, and the jet width was narrower than that of the unexcited case and other forced cases. In the case of ϕ = π/2, spanwise rollers and rib structures were formed near the nozzle exit after the first vortex pairing. However, further vortex pairing did not occur downstream, and the rate at which the jet widened was reduced.

Large-eddy simulation of turbulent open-channel flow over three-dimensional dunes

A large-eddy simulation study has been undertaken to investigate the turbulent structure of open-channel flow over three-dimensional (3D) dunes. The governing equations have been discretized using the finite volume method, with the partial cell treatment being implemented in a Cartesian grid form to deal with the 3D dune topography. The simulated free surface elevations, mean flow velocities and Reynolds shear stress distributions have been compared with experimental measurements published in the literature. Relatively close agreement has been obtained between the two sets of results. The predicted mean velocity field and the associated turbulence structure are significantly different from those observed for flows over two-dimensional dunes. The effects of dune three-dimensionality are reflected in spanwise variations of mean flow fields, secondary currents and different distributions of vertical profiles of the double-averaged velocity. Furthermore, large-scale vortical structures, such as spanwise rollers and hairpin-like structures, are predicted in the simulations, with most of them being generated in the concave regions of the 3D dunes.

Dynamics of vortical structures in cylinder/wall interaction with moderate gap ratio

The interaction between the wake of a transverse circular cylinder and the underlying flat-plate boundary layer with a moderate gap ratio G/D=1.0 is investigated using both hydrogen-bubble-based and PIV-based visualization techniques. The spanwise rollers in the cylinder wake are found to be capable of inducing secondary vortices in the near-wall region. The mutual induction from the counter-clockwise rollers, which are closer to the wall, plays a primary role, so that these secondary vortices present linear lift-up motion at first. Their subsequent evolution dominantly determines the characteristics of the wake/boundary-layer interaction. Two different vortex interaction scenarios are observed: the secondary vortices can be either entrained into the rollers or pushed down towards the wall. This leads to a rapid three-dimensional destabilization process, through which streamwise vortices are generated. And it is suggested that these streamwise vortices are the dominant structures to promote the following boundary layer transition.

Interactions of an Array of Finite Span Synthetic Jets and a Crossflow

The formation of secondary flow structures due to the interaction of an array of three finite span synthetic jets with a crossflow was investigated experimentally over a finite swept-back wing (NACA 4421, , sweep angle of 30 deg, Reynolds number of ). Stereoscopic particle image velocimetry data were collected in the midspan section of the wing, where the effects of the jets’ combinations and their blowing ratios were analyzed based on the three-dimensional flowfield using time- and phase-averaged statistics. The focus of the present work was to capture the formation and advection of secondary flow structures in the vicinity of the synthetic jets for different combinations of jets, including 1) only the center jet activated, 2) two synthetic jets off the middle jet activated, and 3) all three synthetic jets actuated. An angle of attack of 13.5 deg was selected, in which the boundary layer was either attached (in the vicinity of the middle jet) or partially separated (in the vicinity of the jet closer to the wing tip). The time-averaged total velocity fields exhibited secondary streamwise structures that were formed along the jets orifice span. Furthermore, the effect of the synthetic jet(s) was felt at spanwise locations (toward the wing tip) away from the point of activation. From the phase-averaged flowfield, it was shown that, during the blowing portion of the synthetic jet cycle, quasi-two-dimensional pairs of counter-rotating spanwise rollers were formed at the jet exit plane. Each pair was advected downstream as time progressed, bent and tilted toward the tip, and eventually broke down into smaller structures farther downstream, which resulted in the formation of secondary streamwise structures.

Role of coherent structures in multiple self-similar states of turbulent planar wakes

AbstractWe study the nature of archetypal, incompressible, planar splitter-plate wakes, specifically the effects of the exit boundary layer state on multiple approximate self-similarity. Temporally developing direct numerical simulations, at a Reynolds number of 1500 based on the volume-flux defect, are performed to investigate three distinct wake evolution scenarios: Kelvin–Helmholtz transition, bypass transition in an asymmetric wake, and an initially fully turbulent wake. The differences in the evolution and far-wake statistics are analysed in detail. The individual approximately self-similar states exhibit a relative variation of up to 48 % in the spread rate, in second-order statistics, and in peak values of the energy budget terms. The multiplicity of self-similar states is tied to the non-universality of the large-scale coherent structures. These structures maintain the memory of the initial conditions. In the far wake, two distinct spanwise-coherent motions are identified: (i) staggered, segregated spanwise rollers on either side of the centreplane, dominant in wakes transitioning via anti-symmetric instability modes; and, (ii) larger spanwise rollers spanning across the centreplane, emerging in the absence of a near-wake characteristic length scale. The latter structure is characterized by strong spanwise coherence, cross-wake velocity correlations and a larger entrainment rate caused by deep pockets of irrotational fluid within the folds of the turbulent/non-turbulent interface. The mid-sized structures, primarily vortical rods, are generic for all initial conditions and are inclined at ∼$\pm 3{3}^{\circ } $ to the downstream, shallower than the preferential $\pm 4{5}^{\circ } $ inclination of the vorticity vector. The spread rate is driven by the inner-wake dynamics, more specifically the advective flux of spanwise vorticity across the centreplane, which depends on the large-scale coherent structures.