COMPARISONS OF DYE PLUME MIGRATION AT THE NEAR-WALL REGION OF TWO DIFFERENT FLAT BEDS ROUGHENED WITH 7 MM AND 10 MM SYNTHETIC PLEXIGLAS BEADS

The detection of moving particles and the ability of processing the captured images using high-speed cameras can be an effective means of monitoring the sliding, and rolling movement of bed-load sediment along river beds. In this study, two different types of synthetic Plexiglas Beads of size 7mm and 10mm with porosity 0.7125 and 0.8522 respectively were used for the evaluation of the velocity profiles in a flume bath. Potassium permanganate (KMnO4) crystal of molecular weight 158.03 and density 1450 kg/m3 was used as a passive dye-tracer. The cavity region of the flat plate was attached to the oscillatory mechanism in the flume bath where plume activities were monitored. When there is oscillatory flow, the crest of roughness elements induce elevation zones to force (advection) the flow upwards and pull it down at the trough phases as the tracer plume scales over the obstacles, establishing low and high pressure zones in the flow. The enhanced particles in the process mix and dissolve or decay faster with increasing oscillatory frequency, resulting into inter-particle collisions which initiate the conditions of advection and shear dispersion. This phenomenon could be a combination or coupling of the processes of gradient fluctuations enhanced through dispersion due to pressure in the macroscopic pore-fluid field caused by the oscillatory motion. The lightening as the dye-particles cascade in the porous medium is associated with mixing-gain due to the enhanced oscillatory motion. It was observed that the depth of the tracer-blob entrapment is inversely proportional to the friction velocity.


Introduction
The motion of dye plumes as bed load particles is investigated under steady and spatially uniform turbulent flow into and above two flat porous beds with uniform Plexiglas balls of sizes 7mm and 10mm. The experiments were designed to mimic and explore the sediment bed of the coastal zone which exhibits a large variation of sediment sizes. Migration of bed load particles and their respective classification over rough permeable layers on flat beds can be found in Nikora et al (2007b). Several research papers have interpreted the behavior of the cascading particles and transfer mechanisms as having fundamental importance in river morphodynamics, such as resulting from variations of bed materials, particles rolling, and migrating low jump successions (saltations) along the bed of open channels. For instance, Keramaris (2015Keramaris ( , 2017 compared flow experiments in impermeable and permeable beds and found significant changes in the velocity distribution and turbulent characteristics due to porosity differences. Nielson et al (2001) used sand-roughened beds to show the effects of infiltration while studying sediment migration. There is also the contentious claim that hydraulic roughness depends strongly on the velocity profile of the logarithmic region than on bed grain size. However, turbulence measurements of some rivers by Smart (1999) supported those of Nezu and Nakagawa (1993) which show that turbulence intensity is highest near the channel bed but decreases on approaching the water surface. Choi and Waller (1997) observed that turbulence intensity into the depth of porous medium is dependent on the Darcy number of the elements and not related to the Reynolds number (speed) and shape of the velocity profile in the region. Prinos et al (2003) also confirmed that the fluid's kinetic energy penetrating the porous medium increases with the Darcy number which is dependent on the structural geometry of the roughness elements (the pore size of the cavities or gaps between the elements).
Svenson and Rahm (1991) used the benthic sub-layer to study water quality and mass transfer problems due to dispersion mechanisms over thin vertical interfacial layers. Shams et al (2003) investigated the near-edge flow domain of a porous medium by introducing shear-flow across arrays of rods to obtain the flow pattern within, using a PIV. Their work affirms that a secondary motion arises during the shear flow in the square array of rods which is capable of heat and mass transfer between the first and second rows except contaminant is trapped during the flow. Infiltration, according to some researchers (Nielson et al., 2001, Suga andKuwata, 2014;Suga, 2016), has no main effect on the migration direction of bed-sand except to reduce their effective transport. Stansby (2003) observed that in a turbulence based two layer mixing-length model, the horizontal diffusion scale (length scale) is a multiple of the vertical mixing length scale, implying that horizontal and vertical mixings due to applied pressure gradients are responsible for the eddy viscosity. A study involving oscillatory-grid aided turbulence by An and Chen (2004) has also shown the phenomenon of turbulence-driven diffusion. Some researchers (Davis and James, 2003;Shim and Duan, 2017) investigated the role of the interior rows of the porous medium in dissipating energy where it was shown that the slip velocity is dependent on the hydrodynamic resistance of the surface elements and not the inner layers. Pechlivanidis et al. (2012) reported from an open-channel flow experiments using Particle Image Velocimetry, that the velocity is a function of the roughness height and the total flow depth. This study relates to the motion of the fluctuating parcels of dye tracer just above the roughness boundary layer that has been likened to a logarithmic scale, in the interfacial and subsurface sublayers.

Experimental Set-Up with Procedure
Potassium permanganate (KMnO4) crystals of molecular weight 158.03, and density 1450kg/m 3 was used a passive dye-tracer. Some 0.05 g of dry KMnO4 was scooped using a spatula to a flat 9 mm 2 shape of cotton-wool and wrapped into a small ball with a finger tube-grip material (ball diameter < 5mm). The ball is trapped into the porous cavity on a flat plate and the trap position was varied from the top to the near bed as the oscillatory speed is regulated.
Tap water is introduced into the tank and allowed to stabilize and subsequently varied from 20.0cm to 40.0cm. The crystal particles in the tube-grip dissolve and settle onto the bed being denser, prior to inception of the oscillatory movement. The air pressure valve is released, and the speed regulator is set and varied from 0.5m/s start-mark. The oscillatory rig responds at 0.22m stroke length. The two black stripe marks on the external wall of the flat plate (which holds the porous elements) enable the determination of the center of oscillation.
At the 3x7mm plexi-ball stacks, the tracer blob position within the cavity region was variably trapped at distances 0.021m, 0.014m, 0.007m away from the impermeable bed and 0.000 m (i.e., at the bottom). For the 2x10mm stacks, the position was varied by 0.02m, 0.01m and at flume bed (0.000 m), such that the earlier arrangement is 0.001m higher. The porosity of the 7 mm arrangement estimates to 0.7125 and that of 10 mm 0.8522. The Measurements were taken vertically away from the roughness bed region, aided by millimeter-squared graphic transparencies. The flow distances were measured across the longitude of flume cross-section within the cavity area. The velocity record obtained was varied at every oscillatory time interval of 0.5 m/s up to 4.0 m/s. The oscillatory events were also monitored with a stop-clock and recorded. The still water level in the tank was stabilized at a maximum height of 0.40 m.
The Plexiglass frame of the tank opposite the test-window was curtained and the overhead light source dimmed to reduce lighting source that may have direct effect on the CCDC lens by reflection, to account for more contrast of the glass beads. The tube-grip KMnO4 ball was installed initially at the top of the cavity formed with the glass beads and then relocated further vertically down the bed at the completion of each group of experiments. A total of about seventy (70) averaged results were analyzed.
The distribution of the plume particles due the velocity describes the boundary layer thickness. The motion of the plumes tending towards the vertical direction may be considered more rapid compared to those lateral along the bed.

Parameter evaluation and scaling of CCDC plume events
The wavy plume parcels visualized in the free-fluid phase above the roughness elements in the mean direction of oscillatory flow were assumed to represent floating particles of the passive test substance. These images were transferred from the VCR analogue tapes into a Sony DV Camcorder DCR-PC55E and later digitized by copying into computer using i•LINK (IEEE1394) cable connector. The images of the plume parcels were then digitally enhanced and tracked from pre-, and through post-flow initiation stages. The Arc Soft Showbiz 2 software, a professional video image sequencing application, was used to digitally process the CCDC video clips. The motions of the plume parcels were tracked along the vertical flow fields and measured just above the water-porous elements interface aided by millimetre markers on the Plexiglass test-window pane relative to their respective trap-posts. The visual area of interest here is the plume parcel displacement from the trap-posts to and above the interfacial layer. Plume parcels were therefore followed from the trap-posts per complete cycle of oscillation and with increasing flow rates.

Mathematical Analysis
The flume medium has the fluid phase and the porous material-in-fluid region, where 1 h = height of the water only column, 2 h = porous preform (roughness)-in-fluid region medium. The governing equation related to the influx in the roughness medium at steady state may take the Darcy velocity form: for x -z heterogeneous plane of the porous elements, pg  = = pressure head, ( hz = ) = elevation head. Assuming isotropy, K (hydraulic conductivity) is defined as a function of the pressure head ()  K . Such that the boundary conditions in this case relates to a well distributed instantaneous tracer source bounded by The flume medium has the fluid phase and the porous material-in-fluid region. The steady and progressive transfer of mass at the porous-fluid interface may be described by the condition For the initial conditions the mass concentration fields in relation to both regions may be described by their respective compressibility constants as The compressibility constants are assumed equal if tracer mass are found in both mediums (i.e., 1  == ), but 0 or 1 respectively depending on the region tracer mass is present. The velocity describing the mass distribution in first region may be related to the form: The assumed uniform flow profile from the interface to the porous medium takes the form (as in Engelund, 1970):

Fitted Flow Parameters
The cavity region is the visual monitoring area of interest, such that the displacement of the plume parcels along the vertical away from the TP was tracked with time using Arcsoft Showbiz 2. For porosity determination, the flat plate used was partitioned into two panels. Total volume of plate is 1320 m 3 , and for the 7 mm arrangement as example, the width = 98 mm, length = 59 mm, depth = 21mm. So the volume occupied by the Plexiglass balls (pore volume) divided by total volume estimates the porosity to 0.7130.
The measured variables were the variable vertical plume heights, hplm, the maximum velocity, um applied, and time, (T=2t) records. At least five (5) tests were performed on each case and measurements averaged.

Comparisons of the Test Cases at the 7mm and 10mm walls
The estimated porosity for the 7mm category is 0.7125 and that of 10 mm category is 0.8522. Estimates from the governing parameters from the experiments using CCDC shows that as the position of the tracer blob is shifted through the porous preforms from the top towards the bottom the friction velocity increases with the oscillatory velocity.
Tracer blob trapped at 0.021m above bed level of the 7mm arrangement The averaged relative heights of the plume, plm w hH (dimensionless) varied from 0.013 to 0.025 during the period of oscillation, as the velocity was regulated from 4 m/s to 0.3 m/s respectively. The curve in Figure 1a illustrates that the flow near the bed may be controlled by quasiequilibrium in turbulent kinetic energy (TKE) which balances the dissipation in the rough cavity. This implies that TKE rises to a maximum as the velocity becomes higher being sustained by diffusion. This behavior increases the length scale with distance away from the near-wall region. The averaged maximum velocity within the confidence interval estimates to 2.033±0.439m/s. The The estimated amplitude Reynolds number in this case was 2.367 x 10 3 with a mean value within the confidence interval estimate (WCIE) as 3961.1±652.30. The Froude, number, Fr, is 5.7783 x 10 -3 with a mean varying WCIE as 0.0024±0.0008, obtained from the experiments. The mean velocity input also from experimentation was 0.076 m/s. The ratio of the roughness height to the friction length, k + is shown in Figure 1a, indicating fully rough flow, with Darcy permeability WCIE as 0.00023±2.5x10 -5 m/s.
The profile of the curve shows the influence of the effect of rough bed material region as it moves away towards the outer regions. At the bed region the curve seem to deviate from the logarithmic behaviour. A repeat of this characteristic behaviour is also likely as the plume approaches reasonable heights above the roughness elements unto the near surface regions. Figure 1a also shows this influence of the rough elements as the time averaged velocity profiles increase with distance along the vertical cross-section of the rough cavity domain, that is, away from the surface of the rough elements. The reality of this situation is seen from the fitted curve as it intersects the plume axis at some finite value ( plm w hH = 0.26) close to the roughness surface where the velocity profile loses its direct proportionality character with the vertical plume-axis. The reduced magnitude of velocity profiles at the near-surface region is an indication of turbulent shear stress penetration affecting the porous medium which becomes weaker as Darcy permeability also decreases (3.175x10 -4 to 9.75x10 -5 ).
The reduction in the Darcy accounts that plume permeability was affected by the oscillatory velocity profile. At the porous interface the flow is generally assumed to show some semblance of mixing layer type than that of boundary layer, according to Prinos et al (2003).
At some point along the roughness surface the velocity profile shifts away from the interfacial curve to a position where momentum or the velocity deviates from the logarithmic law (Raupach  et al 1991, Prinos et al, 2003). This shifting in the mean position of the velocity relative to the vertical axis has been referred to as the beginning of the logarithmic layer which portrays the dampening effects of the roughness elements on the horizontal oscillatory shear flow (Prinos et  al, 2003). The Froude number increased WCIE to 0.0012±0.0004 with the amplitude Reynolds number varying by 6056.8±918.2. In comparison to the case with the 0.021m roughness height of 0.007m diameter spheres, the Reynolds and Froude numbers were seen to increase, which may be due to pore-size differences. The mean velocity from the distance-time graph was 0.134m/s. constant stress region are clearly seen in the limit of increasing velocity record in the free stream.
In Figure 2b, the * u u is an order of magnitude greater than the mean velocity record plot in Figure   1b. The curve describes how turbulence evolves with the mean oscillatory velocities near the bed and continues across the developing boundary layer from the roughness surface. At some critical point near to flow reversal, the energetic/turbulent plume in the free stream approach a uniformly distributed flow stream.
Tracer blob trapped at trough position 0.014m of the 7mm bed The velocity profiles show identical characteristic curve shapes compared with the former. The fluctuating velocity profiles of the plume parcels tracked relative to the vertical axis due to the oscillatory plate is shown in Figure 3a. The variation of plume heights,  (Figure 3a), also indicates fully rough flow but the roughness parameter k + slumped to show the effect of the difference in the roughness height in comparison to the case in Figure 1a. In comparison with Figure 2a, the graph shown in Figure  4a seems to demonstrate late appearance of the developing logarithmic boundary layer which subsequently describes the approach to flow reversal following the uniformly distributed plume in the fluid stream. The increase in the velocity below the interface is described by the Reynolds value and may be attributed to the developing constant stress across the free-stream. Tracer blob at trough position 0.01m of the 10mm bed The profile of the velocity was identical to the previous cases where the characteristic curve deviates from linearity on approach to the near-wall region (Figure 6b). The shift in the mean position of the velocity relative to the vertical axis shows the dampening effects of the roughness elements on the horizontal oscillatory shear flow. The depth to source is accounted such that the depth averaged plume heights plm w hH range from 0.038 -0.058 with the maximum mean stream oscillatory velocity regulated between 4m/s to 0.3m/s respectively.  Figure 6, that compares reasonably well with the mean velocity profile plot in Figure 8. The behaviour of the plume in this case may be due to the position of the blob further away from the interface where the velocity within the porous spheres increases. velocity at close to the permeable region, almost a roughness height away from the roughness surface. The constant stress layer compares well with the previous cases. The friction factor at the roughness bed region was also plotted against the ratio of the particle amplitude in the oscillatory flow and the roughness size as shown in Figure 10a. The profiles in Figures 8b depict reasonably corresponding distribution of the velocity profiles. The early appearance of the viscous sub-layer from the surface of the roughness elements and the developing constant stress region are clearly represented as described by the curves. In both cases the curves describe how turbulence evolves with the mean oscillatory velocities near the bed and continues across the developing boundary layer from the roughness surface. At some point near to flow reversal however, the plumes in the free stream approach a uniformly distributed flow stream. Figure 7b describes the normalized velocity distribution and plume height in wall units for the positions 0.02 and 0.01m of the entrapment tracer blob. The curves show that the velocity distribution curves approach constant stress at increasing wall-coordinate heights. The heights in wall unit are about an order of magnitude more than the distributions described in Figure 0a. This development may be attributable to the porosity differences due to roughness material sizes of the respective beds. The paths of the curves narrate the history of the developing logarithmic regions above the viscous sub-layer of the roughness surfaces up to the free stream. The trend of the friction factor at the roughness bed region for the 10.0mm case follow identical pattern compared to the 7.0mm bed. The friction factor decreased progressively with increasing s a k as shown in Figure   10b The friction factor or wall friction as it may be referred is calculated from the maximum value of

Conclusion
Two types of porous bed setting with synthetic spherical beads (7mm and 10mm) were investigated in a flume bath. The dye tracer plume just above the roughness boundary layer and the cavity region (interfacial and subsurface sub-layers) of the flat plate attached to the oscillatory mechanism in the flume bath was monitored during the experiments. During the oscillatory flow, the crest of roughness elements induce elevation zones to force (advection) the flow upwards and pull it down at the trough phases as the tracer plume scales over the obstacles, establishing low and high pressure zones in the flow. The enhanced particles in the process mix and dissolve or decay faster with increasing oscillatory frequency, resulting into inter-particle collisions which initiate the conditions of advection and shear dispersion. Several authors (Smart, 1999;Nezu and Nakagawa, 1993;Choi and Waller, 1997;Prinos et al, 2003) have shown their findings with regard to the build-up of pressure relative to the behavior of the tracer plume as a consequence of the oscillatory mechanism. However, in the 10mm preform the velocities relatively reduced inside the roughness which may be attributed to the larger pore size of the troughs and lower roughness height. In a study Prinos et al (2003) affirmed that the fluid's kinetic energy penetrating the porous medium increases with the Darcy number which is dependent on the structural geometry of the roughness elements (the pore size of the cavities or gaps between the elements).
The study viewed the phenomenon as a combination or coupling of the processes of gradient fluctuation enhanced through dispersion due to pressure forcing in and out of the macroscopic pore-fluid field caused by the oscillatory motions. The lightening as the dye-particles cascade in the porous medium can be associated to mixing-gain due to the enhanced oscillatory motion. Hydraulic conductivity was considered to increase with increasing pore-size and rates of tracer particle interactions within the cavities (Itugha, 2008).
The difference in the porosity between the 10mm and 7mm beds changes the velocity distribution and the turbulent characteristics of the flow. For instance, the velocities over the 10mm bed had greater penetration of flow, hence were relatively higher in comparison with the flow over the 7mm preform. The velocities of the different porous beds increased due to the high turbulence inside the roughness trough in comparison to the roughness height region (which is the distance from the roughness tops to roughness trough). Hydraulic conductivity was considered to increase with rates of tracer particle interactions within the cavities at the 10mm pore-size.