Wake flow field of a wall-mounted pipe with spoiler on a rough channel bed

This research work focuses on the wake flow region of a cylinder with a spoiler on a rough bed under steady flow conditions. The acoustic Doppler velocimetry was used for the measurement of three-dimensional velocity data for two Reynolds numbers in a fully developed turbulent flow around the cylinder with a spoiler. The mean flow velocities, second-order turbulence structures, and conditional statistics were investigated in the wake region of the spoilered cylinder. The flow was separated from the spoiler with the formation of two shear layers between free surface flow and recirculating flow. It is observed that the flow is reattaching to the bed at 11D irrespective of the Reynolds number. Downstream of the cylinder, the mean velocity distributions are asymmetric due to the wall–wake effect, and the point of inflection is observed for each velocity profile at z = 0.40ẟ. The turbulence intensities, Reynolds stresses, and TKE are highly enhanced in the wake region of the cylinder as compared to their respective upstream values for both runs. The turbulence intensities, Reynolds normal stresses, Reynolds shear stresses, and turbulent kinetic energy are attaining peaks at z = 0.4 ẟ for all the streamwise locations, and the peaks are found to be highest at x = 10D. The quadrant analysis results indicate that the sweeps are dominating bursting events in the inner and intermediate layers, while ejections are dominating in the outer layer of the wake region. As the hole size, H increases ejections stress fraction rises as compared to that of the sweeps in the wake region for z = 0.2–0.7 h.


Introduction
Submarine pipelines, widely used to transport fluids, have been installed on the erodible seabed.These pipelines may be laid on the surface of the seabed or may be buried beneath the seabed.Pipelines are under underexposed conditions when they are laid over the seabed.Free spanning of the pipelines can occur in this situation.Many reasons cause the free spanning of submarine pipelines.The main factors include the scour of ocean currents, uneven seabed topography, human activities, and residual or thermal stress.The pressure difference between the upstream and downstream sides of a pipeline drives a seepage flow underneath the pipe (Sumer et al. 2001).The free spanning of the pipelines could lead to their fatigue, damage, and failure under resonant vortex-induced oscillations causing oil and gas leakage, resulting in huge economic losses and major marine pollution accidents.
To protect the pipelines from possible damage caused by extreme hydrodynamic forces of waves and currents or the human activities of anchor dropping, it is customary to bury pipelines to a certain depth below the seabed.But the cost of artificial trenching and refilling is high, and this expenditure often accounts for a significant proportion of the total budget of a pipeline.Therefore, alternative burial systems ensuring both environmentally friendly and costsaving are essential.In this case, the self-stimulated scouring of the pipeline to bury it underneath the seabed is a very good option.Hulsbergen (1986) and Hulsbergen et al. (1989) were the first ones to find out that the spoiler can aid in increasing the self-burial potential of pipelines.They reported that when a spoiler is attached to the pipeline, it creates a large blockage to the incoming flow, forcing more of the flow downward beneath the pipe, hence increasing the strength of the wake and related scour.They observe five times larger scouring due to a spoiler than scouring due to a plain pipe.Gokce and Gunbak (1991) conducted an experimental study with waves to study the self-burial and stimulated self-burial of the pipeline over the erodible seabed.They observed enhanced scour and burial depths for larger diameter pipes and higher flow velocities.Sagging of the pipe into its erosion hole caused relatively larger scour hole depths and resulted in burial.A deeper and faster burial was achieved with spoilers.Chiew (1993) conducted an experimental study on the spoiler under the pure wave actions to analyze the rate and extent of scouring around the pipeline.He observed the variation in the scour hole profile with changes in the spoiler orientation.The spoiler creates the largest depth and extends in the lee-wake of the pipe when it is attached to the pipeline at an angle in the range of 45°-75°.The maximum lee-wake side scours depth for the spoiler was observed to be 4.5 times the maximum scour depth in the case of the plain pipe.In the study of Chiew and Cheng (2001), they investigated the effect of the spoiler on the velocity profile under the pipe and the bed shear stress distribution.Cheng and Chiew (2003) analyzed the effects of the spoiler on hydrodynamic forces and vortex shedding frequency; they found that the spoiler considerably increases drag and lift forces as well as the flow through the gap between the pipe and the seabed.Zhao and Wang (2009) determined the effects of velocity and spoiler height on bed shear stress.Oner (2009) examined the influence of the spoiler on the separation regions, bed shear stress, and gap flow.Yang et al. (2012a) examined the variation of bottom velocity and dynamic angle of repose for different spoiler heights.Yang et al. (2012b) determined the effects of Reynolds numbers and spoiler heights on the scour depth.In addition to that, they also proposed a formula for the estimation of the scour depth.Zhu et al. (2013) analyzed the effects of Reynolds numbers, spoiler heights, and gap ratios on the flow field and bed scouring around the pipe.They reported that both flow fields around the submarine pipe and seabed scouring are sensitive to the relative spoiler height and gap ratio.Oner (2016) explored the two-dimensional flow field around the pipe at a particular Reynolds number using different numerical models.Kang et al. (2016) estimated the effects of the spoiler heights, Reynolds numbers, and sand size on the self-burial ability.Abbasi et al. (2018) determined the effects of pipe inclination and spoiler heights on the scour depth in the seabed.Lee et al. (2019) conducted laboratory experiments and numerical simulations to clearly understand the self-burial mechanism of subsea pipelines under steady flow conditions.Based on the past literature related to this field, it can be concluded that there is an inadequacy of research on the turbulence of the wake region of the spoilered pipe although turbulence properties play a very important role in the scouring of the seabed.In the present work, the wake region of a circular cylinder with a spoiler attached to it is investigated by conducting experiments for two Reynolds numbers: Re D of 10,800 and 13,800.

Experimental setup and methodology
Experiments were performed in a rectangular laboratory flume of 12 m long, 0.91 m wide, and 0.70 m deep.A constant longitudinal bed slope of 0.023% was provided throughout the flume length.The flume has see-through glass sidewalls at the test section to facilitate the visual observations.A cylinder with a diameter of 6 cm with a spoiler of a height (h s ) of 1.35 cm (h s = 0.2D) was mounted horizontally on the bed at a distance of 6.5 m downstream of the flume as shown in Fig. 1.The spoiler height, h s, was taken in the range of the optimal height which causes maximum scouring over the erodible under given approach flow conditions as reported by Yang et al. 2012a, b.The flow entering the flume is controlled by a valve at the storage tank and metered by a calibrated V-notch weir located in the stilling basin.The flow depth, h, for all the experimental runs was kept equal to 0.30 m.The flow depth in the flume was regulated by adjusting the tailgate height, and it is measured by a point gauge with an accuracy of ± 0.1 mm on a Vernier scale attachment.The flow was stabilized and straightened by the flow straightener provided upstream of the flume inlet.The flume bed was prepared by pasting a thin layer of uniform sand of median size, d 50 = 2.54 mm to generate roughness.The sediment size was chosen similar to occurring in the natural stream by following the research work of Ghani and Azamathulla 2014.The x, y, and z-axes are oriented in the longitudinal, spanwise, and vertical directions, respectively.The origin of the coordinate system was located at the bottom point (nadir) of the cylinder at the central vertical plane in the situation of the bed.
Two approach flow free-stream velocities of 0.18 and 0.23 m/s were maintained corresponding to two Reynolds numbers of 10,800 and 13,800.The experimental conditions are selected systematically after reviewing all available papers on this topic.The Reynolds numbers of the present experiments that are completely different from the existing literature and are similar to those occurring in the natural water streams.The approach flow conditions of both runs are summarized in Table 1.The Reynolds number based on approach flow free-stream velocity, U ∞ , and cylinder diameter, D, was calculated as Re ∞ = U ∞ D/υ, where υ is the kinematic viscosity of the water.The corresponding flow Froude numbers [Fr = U ∞ /(gh) 0.5 , where g is the acceleration due to gravity] were estimated as 0.11 and 0.13 for SP1 and SP2, respectively.The friction velocity of the approach, u ⁎, was obtained by extrapolating the Reynolds shear stress (RSS) distribution onto the wall and was used as the velocity scale for non-dimensionalizing the turbulence properties.The friction velocities are 7.1 and 9.2 mm/s for SP1 and SP2, respectively.
The instantaneous three-dimensional velocity components recorded by acoustic doppler velocimetry (ADV) are denoted u (= ū + u′), v (= v̄ + v′), and w (w = w̄ + w′), and they are decomposed into their time-averaged and fluctuating components using Reynolds decomposition.Here over bar denotes the time-averaged velocities, while apostrophe indicates fluctuating components of velocity.Velocity profiles were measured along the centerline of the flume in the xz plane at nine streamwise locations for each run.The x = − 4D is located upstream of the cylinder, and it represents the approach flow.The location of the cylinder is x = 0.All other measurement locations are in the wake of the cylinder.
A four-receiver down-looking ADV probe, Vectrino plus manufactured by Nortek (Nortek AS, Vangkroken 2, NO-1351 RUD, Norway), working with an acoustic frequency of 10 MHz, was employed to capture the velocity components with a sampling rate of 100 Hz.The cylindrical sampling volume had a 6 mm diameter and a changeable height of 1-4 mm.A measurement duration of 300 s was used.The signal-to-noise ratio (SNR) and signal correlation  Following the recent research works (Taye et al. 2019;Sharma and Kumar 2019;Sharma et al. 2021;and Ghasempour et al. 2022), the uncertainty analysis of ADV data was done by recording 10 data samples of the velocity at 10 mm away from the flume bed.The uncertainty of the velocity gradient (∂ū/∂z), the streamwise velocity (ū), the vertical velocity (w), the streamwise turbulence intensity ( , and the Reynolds shear stress (τ xz ) are 2.5%, 2%, 0.5%, 0.5%, 2%, and 1%, respectively.The uncertainty of the mean velocity and turbulence properties are within ± 5% which validate the data measured by the ADV probe.

Results and discussions
The wake region of the cylinder with the spoiler will be assessed in terms of its mean and turbulence properties.Vertical distributions of non-dimensional mean flow velocities, turbulence statistics, and quadrant analysis along the wake region of the cylinder with spoiler will be analyzed in the different sub-headings of this section.

Mean velocity field
The 2D velocity has a magnitude, U = (ū 2 + w̄2) 0.5 , and direction, θ = tan −1 (w/ū).The dimensionless resultant 2D velocity is calculated as U + = U/u ⁎ .From the non-dimensional 2D velocity vector field of the flow in Fig. 2, it is observed that the flow is separated from the spoiler attached to the cylinder.In the immediate downstream of the cylinder, in nearbed region, the flow reversal takes place, where the velocity vectors are pointed in the direction opposite to the flow direction.The height of the recirculation region is 0.3 h for both runs, indicating that the vertical extent of the recirculation region is not changing with a change in the approach flow conditions.As moving in the streamwise direction away from the cylinder, the vertical extent of the recirculation region decreases, and the separated shear layer attached to the bed somewhere between x = 10D and x = 12D for both Runs, so it can be concluded that the length of the separated region is not changing from one Reynolds number to another Reynolds number.
A separated shear layer with a strong velocity gradient (∂ū/∂z) is located between the recirculation region and the outer flow on the free surface.The blue dashed line represents the lower shear layer, along which the streamwise flow velocity is zero.The green dotted line indicates the upper boundary of the separated shear layer.After flow reattachment to the bed, the separated shear layer starts as a new boundary layer and it begins recovering to its undisturbed condition and velocity distribution becomes positive throughout the flow depth.Within the streamwise domain of this research, flow is not recovered to its approach flow conditions.The wake region is located between the upper shear layer and the lower shear layer.
Vertical distributions of the streamwise velocities on (a) inner scaling and (b) outer scaling for both runs are analyzed using Fig. 3.The velocity profiles downstream of the cylinder exhibit an upward concavity in their profiles.This asymmetry in the velocity profiles is caused by the presence of the channel bed.Immediate downstream of the cylinder, negative streamwise velocities are observed in the near-bed region of the flow for both scales due to backflow.These negative velocities are persisting up to x = 10D, and the velocity profile becomes positive throughout the flow depth at x = 12D for both runs.So, it can be concluded that the flow is reattaching to the bed somewhere between x = 10D and x = 12D (refer to Fig. 2).The vertical extent up to which the negative streamwise velocity is occurring, decreases while moving away from the cylinder in the streamwise direction since the separated flow momentum is reducing, and it is bending toward the bed for reattachment.The null points of streamwise velocity distribution are moving toward the bed with an increase in the streamwise distance, x.In the downstream of the cylinder, the points of inflection (d 2 u/dz 2 = 0) are observed for each profile at z = 0.40ẟ (refer Fig. 3b).This location is similar to the location of the point of inflection by Dey et al. (2018), Devi et al. (2021a), Devi et al. (2022) for a wall-mounted horizontal cylinder and Nepf and Ghisalberti (2008) for a dense canopy of vegetation.On inner scaling, the streamwise velocity distributions are not showing any effects of the Reynolds numbers.But on outer scaling, the velocity for SP2 is higher in magnitude than the velocity of SP1 for z above the inflection points (refer Fig. 3b).Whereas for z below the inflection point, the streamwise domain of the study, the velocity profiles are overlapping each other.The free-stream velocity in the wake region is higher than the corresponding approach flow velocity for both runs, due to the upward deflection of the flow.At x = 2D, the free-stream velocities are 25% and 38% higher than their approach flow free-stream velocity for SP1 and SP2, respectively.In near free surface region, the velocity profiles attain almost the same gradient (du/dz) respective of their streamwise locations and Reynolds numbers since in this region the effects of the spoilered cylinder become negligible.
A close examination in Fig. 4, which displays the vertical distribution of the non-dimensional mean vertical velocity (w/U ∞ ) for SP1 and SP2, shows that mean vertical velocity has a large positive value of 0.6 U ∞ just above the cylinder throughout the flow depth as the flow is deflected in the upward direction due to separation from the spoiler.Whereas when moving further downstream of the cylinder at x = 2D, the velocity profiles are attaining two peaks (refer to Fig. 4).Similar trends persist up to x = 4D with flattened peaks compared to that of x = 2D.Two peaks, one lower and one upper peaks at x = 2D, are located at vertical distances of z = 0.35ẟ and 0.6ẟ, with values of 0.1U ∞ and 0.15U ∞ , respectively.
The occurrence of two peaks with a positive velocity profile immediate downstream of the cylinder is similar to the observations of Devi et al. (2021b) for a wall-mounted cylinder over a sand bed and a gravel bed.From x = 6D-12D,

Reynolds stresses
The velocity scale, u ⁎ 2 , is the most commonly used scaling to non-dimensionalize the RSS, but there is no record of the appropriate scaling parameter for the RNSs.In most of the past wake region investigations, u ⁎ 2 was applied to nondimensionalize the normal stresses as well.For normalizing the RNSs, the u ⁎ 2 , U ∞ 2 , and mixed scale (u ⁎ U ∞ ) are used as velocity scales while for normalizing the vertical distance, z, and boundary layer thickness, ẟ, have been used as the length scale.The RSS distribution is nonlinear for channel flows, and the linearity occurs only for flow depth above the peak as stress decays from its maximum near the boundary to the free surface (Afzalimehr et al. 2011).The RSS per unit mass,τ uw ( = −u � w � ) was non-dimensionalized using u ⁎ 2 as the velocity scale and it is written as The vertical distribution of RSS is determined to define the momentum diffusion mechanism using Fig. 5.It can be observed that RSS at the upstream undisturbed location, increases toward the bed and obtains maximum value somewhere near the bed and then declines with a further decrease in distance from the bed.The RSS is drastically enhanced downstream of the cylinder and attains its peak at z = 0.4ẟ (refer to Fig. 5).The locations of the peak in the RSSs profiles are corresponding to the locations of the points of inflection (d 2 u/dz 2 = 0) in the velocity distributions.The results obtained in this study are similar to those of Dey et al. (2018) and Devi et al. (2021a).The magnitudes of the peaks increase with the increase in the streamwise distance downstream of the cylinder up to the flow reattachment point.The RSS distributions for this scaling in the wake region are changed significantly due to changes in the Reynolds numbers.The scatter in the RSS profiles at x = 6D and 8D is attributed to vortex shedding which increases with Reynolds number.
The streamwise, σ uu ( = u � u � ), and vertical, σ ww ( = w � w � ), RNSs in non-dimensional form are written as σ uu + = σ uu /u ⁎ 2 and σ ww + = σ ww /u ⁎ 2 , and their analysis in the wake region of a cylinder with a spoiler is performed using Figs.6 and  7, respectively.The RNSs are highly enhanced downstream of the cylinder in the wake region due to increased velocity fluctuations caused by the high turbulence mixing nature of the separated flow.The RNSs are drastically enhanced downstream of the cylinder.They are attaining their peak values at z = 0.40ẟ (refer to Figs. 6 and 7).The magnitudes of peaks decrease as moving away from the cylinder in the streamwise direction up to x = 10D.Then, flow reattached to the bed and starts to recover, and its momentum deficit starts reducing.These observations are consistent with the observations of Devi et al. (2021b), who found that peak values of RNSs increased in the recirculation and decreased in the reattachment regions along the flow direction.The RNSs distributions are showing the Reynolds number effects for z < 0.5ẟ on all scales as for this flow region at a particular streamwise location, and the profiles are not overlapping each other.It can be said that with a change in the Reynolds number, the magnitudes of non-dimensional RNSs at a particular streamwise location also change for all scales.The peak value is highest at x = 10D with magnitudes of 0.14 U ∞ 2 and 0.06 U ∞ 2 , respectively, for the streamwise and vertical RNSs.At all streamwise locations, the value of streamwise RNSs is twice the vertical RNSs approximately indicating highly anisotropic turbulence flow in the wake region of the cylinder.

Turbulent kinetic energy (TKE)
Turbulent kinetic energy (TKE) is obtained from the mean values of turbulent eddies, which serves as an essential parameter to quantify turbulence and form a three-dimensional velocity dataset, and it is estimated as k = 0.5 u � u � + v � v � + w � w � by following the work of (Przy- borowski et al. 2019).It is normalized using the approach flow free-stream velocity, and it is written as k/U ∞ 2 .Figure 8 presents the vertical profiles of non-dimensional turbulent kinetic energy (k/U ∞ 2 ) over the vertical plane for SP1 and SP2.An examination of the distributions unveils that TKE is very small at the upstream undisturbed location throughout the flow depth.In the wake region of the flow, TKE values are highly enhanced as compared to their respective upstream values for both runs due to higher velocity fluctuations caused by enhanced turbulence mixing.The cylinder causes the flow separation and formation of the wake region, which acts as a source of increased turbulence.Therefore, TKE in the wake region is very high as compared to that in the upstream undisturbed region.The TKE attains its peak at z = 0.4ẟ for all the streamwise locations for both runs (refer to Fig. 8).From the separation point to the reattachment point, however, the peak of the TKE increased with an increase in the streamwise distance from the cylinder.
The highest value of TKE in the present work is 0.15 U ∞ 2 which is approximately the same as obtained by Ampadu-Mintah and Tachie (2015) in the case of a backward-facing step.
The highest TKE value is approximately equal to the streamwise RNSs.This observation implies that the contribution of streamwise RNSs to TKE is equal to the combined contribution of the vertical and transverse RNSs since flow is highly anisotropic in the wake region.The TKE distribution on this scale (U ∞ 2) is showing significant effects of the Reynolds numbers, and they are collapsing over each other at a particular streamwise location.In the free surface region, the value of the TKE becomes very small due to the damping of velocity fluctuations.The variation of TKE in the vertical central plan is similar to the variation of the streamwise Reynolds normal stresses.

Quadrant analysis
The main target of the quadrant analysis is to quantify the bursting events as they play a very important role in sediment transport (Willmarth and Lu 1972;Lu and Willmarth 1973;Nakagawa and Nezu 1977).RSS which is a product of instantaneous velocity fluctuations u' and w' governs the momentum transfer.Therefore, a quadrant analysis is carried out based on the fluctuating velocity components of streamwise and vertical directions, u′ and w′, respectively, to properly understand the momentum transport.Wallace et al. (1972) developed the quadrant decomposition method for quantification of the instantaneous events of RSS.Nezu and Nakagawa (1993) found that strong events are the only contributing events to the Reynolds shear stress.The quadrant analysis was performed to analyze the turbulence of the cylinder wake by quantifying the bursting events using u′ and w′ plots on the u′-w′ plane (Lu and Willmarth 1973).According to the signs of u′ and w′, the bursting events are defined by four-quadrant as outward interactions, Q1(q = 1; u′, w′ > 0), ejections, Q2(q = 2; u′ < 0, w′ > 0), inward interactions, Q3(q = 3; u′, w′ < 0), and sweeps, Q4(q = 4; u′ > 0, w′ < 0).
The turbulent burst is created only because of the extreme events.These extreme bursting events which are responsible for bursts are separated from low-level events using arbitrarily defined hole size, H.The hyperbolic hole size, H, is defined as ‫|‬u′w′‫|‬ = H(u′ 2 ) 0.5 (w′ 2 ) 0.5 (Nezu and Nakagawa 1993).The hole size, H = 0, indicates that all events weaker and stronger are contributing to total RSS.Using this technique, larger shear stress contribution to total RSS can be selected leaving behind the smaller ones that lie within the hole.Therefore, the hole size demarcates the boundary between the strong and the weak events for a particular hole size, H.The contributions from a specific quadrant to the total RSS at a location and for a particular value of hole size, H, are obtained using Eq.(1) as written below: where T is the sampling duration, and λ q,H (t) is the discriminating function indicator which is.
λ q,H (t) is defined (Hanmaiahgari et al. 2017) in Eq. ( 2) as follows: The stress fraction, S q,H, is the relative contribution of each event to the total RSS, and it indicates the strength of (1) the individual event.Therefore, the stress fraction is estimated using Eq. ( 3) as expressed below: The value of S q,H is positive for ejection and sweep events, while it is negative for outward and inward interactions.Figure 9 illustrates the vertical profiles of the stress fraction, S 0,H, from all four quadrants at H = 0 for SP1 and SP2.It is observed from S 0,H distributions that in the approach flow, the stress fraction has small negative values for Q 1 and Q 3, while it has positive large values for Q 2 and Q 4 throughout the flow depth for both runs.From this observation, it can be concluded that ejections and sweeps are the main quadrant events contributing to the bursting, which is similar to the finding of Khan et al. (2021).
Variation of stress fraction from different quadrants for H = 0, 2, and 4 along the central vertical plane (xz-plane) is displayed in Fig. 10.It is observed from the distribution that outward interactions and inward interactions are negative, while ejections and sweeps are positive for H = 0 and 2 throughout the flow depth.The values of stress fraction are higher in magnitude for the ejections and sweeps as compared to that of the outward interactions and inward interactions.For H = 4, the stress fraction of the outward interactions and inward interactions becomes insignificant in magnitude, while its values for the ejections and sweeps become very small.Furthermore, the comparison of stress fraction for different values of hole size, H, illustrates that with an increase in the hole size, from H = 0 to 4, the stress fraction of each event declines sharply, indicating that stronger event's contributions to RSS are very small.
To further analyze the variation of stress fraction with a variation in hole size, H, Fig. 11 presents the distribution of stress ratios with H for four streamwise locations for SP1 and SP2.Out of the selected four streamwise locations, three are taken from the recirculation region (x/D = 3, 6, and 10), and one is taken from the redeveloping region (x/D = 12).For each selected streamwise location, 3 points (one in the inner layer, one in the intermediate layer, and one in the outer layer) each at a different vertical distance from the bed are taken into consideration.An examination of the distributions unveils that the stress fraction at all the streamwise locations throughout the flow depth is decreasing with an increase in the hole size, H, as is already noticed in Fig. 10.In addition to that, it is also seen that the stress fractions of the sweeps and ejections are higher as compared to that of outward and inward interactions throughout the flow depth at all streamwise locations.In the inner layer, the stress fraction of all events is highest for x/D = 3, and after this location, the stress fraction decreases considerably and remains almost the same for the other two downstream locations also.The stress fraction profiles of individual quadrant events in the inner layer are self-similar in the wake region, respective to the flow Reynolds numbers.In the intermediate region, the stress fraction profiles of a quadrant event at a fixed streamwise location are overlapping each other except at x/D = 3.At x/D = 3, SP1 has a higher stress fraction of the ejection event, while SP2 has a higher stress fraction of the sweep event.Throughout the streamwise domain of the study, there is not much variation in the stress fraction profiles of an event with a change in the x.The stress fraction profiles are self-similar irrespective of the streamwise distance.In the outer layer of the flow, the stress fraction is increased drastically along the streamwise direction for a particular value of the H.In this layer, the stress fraction of a particular event for a value of H at the fixed streamwise location is higher for SP1 as compared to SP2 except for ejection events at x/D = 3 and outward events at x/D = 6.
From the aforementioned discussion in Fig. 11, it is clear that the sweeps and ejections are the main contributing events to the RSS.Therefore, to understand their contributions in-depth, the ratio of stress fraction of sweep to ejection vertical profiles for different hole sizes, H, in the case of SP1 for four streamwise locations: x/D = 3, 1 3 6, 10, and 12 is displayed in Fig. 12.It is observed from stress ratio distributions that for all streamwise locations, and the contribution of ejection events increases sharply as compared to sweeps stress ratio for z/h = 0.2-0.7 with an increase in the hole size, H. From the above-mentioned discussions, it can be concluded that ejections are the main contributing events in the intermediate region (z/h = 0.2-0.7) at H = 2 and 4, while at H = 0 both ejections and sweeps have a comparable stress ratio.

Conclusions
Two laboratory experiments were performed for the statistical analysis of the mean flow and two-dimensional turbulence structures in the wake region of a wall-mounted horizontal cylinder with a spoiler on a fixed sand bed for a fully developed approach flow.The ADV was used to measure the three-dimensional velocity vector around the cylinder.
Main conclusion of the present research work is that the wake region of the spoilered cylinder is highly turbulent as compared to the approach flow region since turbulence properties are drastically enhanced in the wake region.The flow is separated from the spoiler which is attached to the cylinder and immediately downstream of the cylinder, near the bed region, and flow reversal is observed with the formation of two shear layers.One shear layer is located below the free surface potential flow and another shear layer with a strong velocity gradient (∂ū/∂z) is located between the recirculation region and the outer flow on the free surface.The vertical extent of the recirculation region at a streamwise location is unaffected by a change in Reynolds number.With an increase in streamwise distance from the cylinder, the vertical extent of the recirculation region decreases, since flow is bending toward the flume bed.It is observed that the flow is reattaching to the bed at 11D irrespective of the Reynolds number.Downstream of the cylinder, the mean velocity distributions are asymmetric due to the wall-wake effect, and the point of inflection (d 2 u/dz 2 = 0) is observed for each velocity profile at z = 0.40ẟ.The streamwise mean velocity distribution on inner scaling is independent of Reynolds numbers up to z = 0.5ẟ and shows significant  The turbulence intensities, Reynolds stresses, and TKE are highly enhanced in the wake region of the cylinder as compared to their respective upstream values for both runs.The turbulence intensities, Reynolds normal stresses, Reynolds shear stresses, and turbulent kinetic energy are attaining peaks at z = 0.4ẟ for all the streamwise locations in both runs.The peaks of the turbulent intensities, Reynolds normal stresses, Reynolds shear stresses, and turbulent kinetic energy increase along the streamwise direction in the recirculation region and decrease in the redeveloping region, and the peaks are found to be highest at x = 10D.The highest value of TKE in the present work is observed as 0.15 U ∞ 2 which is similar to the experimental values found on the backward-facing step.The highest TKE value in the present work is approximately equal to streamwise RNSs, implying that the contribution of streamwise RNSs to TKE is equal to the combined contribution of the vertical and transverse RNSs.The value of streamwise RNSs is approximately twice the vertical RNSs indicating a highly anisotropic turbulence flow in the wake region of the cylinder with spoiler.
The Reynolds stresses and TKE are higher for higher Reynolds number flows.
From the quadrant analysis, it is concluded that the ejections and sweeps are major contributing events to RSS for both runs.For all events, the stress fraction becomes either negligible or zero for H ≥ 6.The sweeps are dominating bursting events in the inner and intermediate layers, while ejections are dominating in the outer layer of the wake region.As the hole size, H, increases, ejections stress fraction rises as compared to that of the sweeps in the wake region for the intermediate layer (z = 0.2-0.7 h) which indicates the ejections are the main contributing events in the intermediate layer for H ≥ 2.

Declarations
Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
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Fig. 1
Fig. 1 Schematic diagram (not to scale) of the experimental setup used for the present study

Fig. 2
Fig. 2 2D velocity vector of dimensionless resultant velocity (U. + ) along the vertical plane of the flume for a SP1 and b SP2

Fig. 3
Fig. 3 Vertical distributions of non-dimensional mean streamwise velocity: a on inner variables and b on outer variables for SP1 and SP2

Fig. 4
Fig. 4 Vertical distributions of non-dimensional mean vertical velocity (w/U ∞ ) over the central vertical (xz) plane for SP1 and SP2

Fig. 9
Fig. 9 Vertical distributions of stress fraction, S 0,H : a Q 1 , b Q 2 , c Q 3 , and d Q 4 in the wake of the cylinder for SP1 and SP2 at H = 0

Fig. 10
Fig. 10 Vertical profiles of fraction contribution of different quadrant events to RSS in the wake of the cylinder with H = 0, 2, and 4 for SP1

Table 1
(Goring and Nikora 2002;Wahl 2003;Mori et al. 2007ing experimental datasets maintained above their threshold values of 17 and 70%, respectively.A MATLAB subroutine developed by Nobuhito Mori (Disaster Prevention Research Institue, Kyoto University) was used to exclude spike noise from acoustic doppler velocimetry (ADV) data using the phase space method(Goring and Nikora 2002;Wahl 2003;Mori et al. 2007) which considers first and second derivatives of time series signal. were