turbulent flow characteristics and drag over 2d dune shaped structures

8/20/2019 turbulent flow characteristics and drag over 2d dune shaped structures

1/29

Environ Fluid Mech

DOI 10.1007/s10652-013-9312-5

ORIGINAL ARTICLE

Turbulent flow characteristics and drag over 2-D

forward-facing dune shaped structures with twodifferent stoss-side slopes

B. S. Mazumder · K. Sarkar

Received: 27 February 2013 / Accepted: 3 September 2013© Springer Science+Business Media Dordrecht 2013

Abstract The present paper explores the characteristics of turbulent flow and drag over

two artificial 2-D forward-facing waveform structures with two different stoss side slopes of

50◦ and 90◦, respectively. Both structures possessed a common slanted lee side slope of 6◦.Flume experiments were conducted at the Fluvial Mechanics Laboratory of Indian Statistical

Institute, Kolkata. The velocity data were analyzed to identify the spatial changes in turbulent

flow addressing the flow separation region with recirculating eddy, the Reynolds stresses, the

turbulent events associated with burst-sweep cycles and the drag over two upstream-facingbedforms for Reynolds number Reh = 1.44 × 105. The divergence at the stoss side slopebetween the two structures revealed significant changes in the mean flow and turbulence.

Comparison showed that during the flood-tide condition there was no flow separation region

on the gentle lee side of the structure with smaller slope at the stoss side, while for the other

structure with vertical stoss side slope a thick flow separation region with recirculating eddy

was observed at the gentle lee side just downstream of the crest. The recirculating eddy

induced on the lee-side had a strong influence on the resistance that the structure exerts to

the flow due to loss of energy through turbulence. In contrast, a great amount of reduction

in drag was observed in the case of smaller stoss side sloped structure as there was no flow

separation. The quadrant analysis was also used to highlight the turbulent event evolution

along the bed form structures under flood-tide conditions.

Keywords Turbulence · Forward-facing structure · ADV · Flow separation ·Bursting events · Drag reduction

B. S. Mazumder (B) · K. SarkarFluvial Mechanics Laboratory, Physics and Applied Mathematics Unit,

Indian Statistical Institute, Calcutta 700 108, India

e-mail: [email protected]

K. Sarkar

e-mail: [email protected]

1 3


2/29

Environ Fluid Mech

1 Introduction

When the flow past an immovable object or obstacle like a step, shell, pebble or wood

fragment, a complex flow field around the obstacle is usually created by the interaction of

the local flow field with the obstacle. The object/obstacle resists the flow field in a streamchannel and develops a surge at the upstream side of the object accompanied by a series of

vortices at the downstream. Turbulent flow over steps and geometrically regular or irregular

rough surface structures plays a significant role in terms of separating and reattaching flow

phenomenato engineering fields. Separation of flow appears under a variety of flow conditions

such as, flow over the artificial dunes/ripples, the backward and forward facing steps (FFSs),

etc. Several investigations are available for various flow geometries. In particular, some of

the studies have been concentrated on the flow field over moving/rigid bed form structures

in alluvial channels or riverine environments [8,9,32,36,43]. These studies were concerned

with the occurrence of flow separation, reattachment points and turbulence characteristics

due to the ebb flow over such geometries and their impact of sediment transport over such

bed forms. These experiments, simulating the ebb flow over dune type bed forms, face gentle

stoss side slope and steeper lee side slope. Flows over two/three-dimensional backward facing

steps with sharp edges, rounded faces, etc. have received much attention in many engineering

applications such as, hydraulic and aerodynamic devices, combustors, and mixing equipment

[4,6,12,15,27,46]. Recently, Singh et al. [50] have studied the turbulent flow over a backward

facing step of different step angles to determine the separation points and reattachment

lengths.

Investigations had been carried out under controlled conditions in laboratory flumes to

understand the flow separation and reattachment phenomena over FFS immersed in a bound-ary layer flow. Stuer et al. [52] investigated the separation bubble at the upstream side of a

FFS under laminar flow condition using hydrogen bubble technique. They observed that there

was an open three-dimensional separation bubble characterized by span-wise quasi periodic

unsteadiness. The flow characteristics over a FFS and through the sudden contraction of a

pipe were examined by Ando and Shakouchi [3] visualizing the mean and fluctuating com-

ponents using laser Doppler anemometer (LDA). Experiments were carried out to examine

the flow over the FFS with a smooth and rough upper surfaces for various Reynolds num-

bers [11,26,45,47,49]. Experiments showed the existence of two recirculation zones in the

FFS flow: one was just upstream of the sharp edge and the other was just downstream of

the sharp edge. The upstream separation was developed from the adverse pressure gradientdue to the blockage of the flow at the step face. The other separation of flow was developed

at the sharp edge and was characterized by the shedding of vortices which were convected

downstream [22]. The size of separation bubbles and the position of reattachment points

were dependent on Reynolds number and the roughness of the top surface of the structure.

Also the reattachment length X r was observed to be influenced by various flow parameters,

such as the turbulence level, the ratio of boundary layer thickness (δ) to the step height (h),i.e. δ/ h. Addad et al. [1] used a commercial Computational Fluid Dynamics technique forlarge eddy simulation to study the flow over a forward–backward facing step which showed

a good agreement with the previous experimental findings with LDA data. Sherry et al. [49]studied the flow over the FFS for several values of the ratio δ/ h. They categorized thestudy into two groups: for δ/ h > 1, the reattachment length X r was strongly dependent onthe δ/ h and for δ/ h < 1, the X r was weakly affected by the ratio, and usually situatedaround 4–6h. Subsequently, Saleel et al. [48], on investigating the flow over the identicalstructure, verified that immersed boundary method was an active way to determine the flow

field around a forward–backward facing step. Recently, Ren and Wu [47] made a comparative

1 3


3/29

Environ Fluid Mech

study on the turbulent boundary layers (TBLs) over smooth and rough FFSs using particle

image velocimetry. Examining the mean flows, the Reynolds stresses, the turbulent bursting

events and the average span-wise vorticity, they found that the separated flow at downstream

of the step was weakened due to roughness of the top surface of the step, though the flow

structure was independent of the surface roughness ahead of the step.However, investigations into turbulent flow characteristics and bedform dynamics under

flood and tidal flow conditions have been quite rare until the relatively recently and it is an

area of study that is of interest to many researchers. Very recently field studies and numerical

models using Delft3D have been performed to estimate the variation of flow separation zone

over large bedforms during tidal environments [28–30]. In fact, they took the field mea-

surements on seabed bathymetry over a transect line crossing three ebb-oriented primary

bedform structures (see Figs. 2, 6 of [30]) during full tidal cycle and investigated numeri-

cally the flow separation zone due to the bed elevations in the natural environments. They

reported that during the ebb-tide a permanent separation zone occurred on the steep lee sides

(14–23◦) of the ebb-oriented bedforms, whereas during the flood-tide no flow separation zonedeveloped over the gentle slope of flood lee side (3–5◦) except over the steepest (15◦) of thelee side, where a small separation zone was observed [16,29,30]. Here the terms, stoss side

and lee side of the structures, are used conventionally according to the flow direction. They

also reported that the shape of the flow separation zone was not influenced by the changes in

flow velocity or water level rather it was influenced by the bed morphology. It may be noted

that usually ebb-oriented geometry of large-scale bedforms with asymmetric structures is

retained through both ebb and flood portions of the tidal cycle [16,58]. In the Fraser Estuary,

the heights of large dunes change due to tidal cycle, whereas their lengths remain stable

[23], which is comparable to the findings of Ernstsen et al. [16] for both the compound duneand the superimposed dunes with the exception of the crest dune. Kostaschuk and Best [23]

found the dune height to increase with increasing flow velocity due to trough scouring caused

by increased turbulence. The quantitative knowledge on such geometrical structures, their

dynamics, sediment transport and their interaction with turbulent flow is very important for

coastal environments, river planning and restoration, and channel evolution process. In fact,

the flood-tide condition complicates the hydrodynamics of turbulence and sediment transport

phenomena around the bedforms due to variation in flow separation and flow resistances.

In spite of all these studies mentioned above, no experimental studies were performed

to simulate such environmental condition (reverse flow) to examine the mean flow, turbu-

lence characteristics and drag over bedforms with steeper stoss-side slopes, despite the factthat such study in the laboratory has the potential to be useful to the researchers who study

the bedforms in the natural systems, especially those that experience reverse flow condi-

tions [14,34,56]. Therefore, a substantial investigation is required to understand the basic

hydrodynamic phenomena experimentally in a flume over the bedform structures oriented

against the flow. The present study is to identify the spatial changes in turbulence statistics of

flow addressing the recirculation eddies (flow separation regions), the Reynolds stresses, the

turbulent events associated with burst-sweep cycles and the drag coefficients over two artifi-

cial upstream-facing waveform structures. Two isolated waveforms with different stoss-side

slopes oriented against the flow (i.e., facing steeper stoss sides) are considered separatelyunder the identical flow conditions. More precisely, the investigation aims, experimentally in

a flume, at characterizing the turbulent flow over two artificial 2-D bedform structures sep-

arately: (1) asymmetric bedform with 50◦ stoss side angle, and (2) vertical (90◦) stoss sidestructure, facing against the flow with a common gentle lee slope of 6◦, which are akin to theflow over the complex bedform roughness in tidal flows. Essentially, a threshold condition

of development of flow separation zone and circulation eddies on the bedform lee side in

1 3


4/29

Environ Fluid Mech

Fig. 1 Schematic diagram of the hydraulic channel

tidal environments needs to be determined, and hence two different stoss side angles (50◦and 90◦) are considered for these tests. Hitherto it is unclear whether the occurrence of flowseparation region and circulation eddies on the bedform lee side due to reverse flow environ-

ment depends locally on the steepest part of the lee side, or it depends on the increase of stoss

side slope of the bedforms, or both. The velocity data are analyzed to highlight the turbulent

statistics and coherent structures in the flow over such bedforms with different stoss-side

angles, which are not studied earlier. Although the artificial structures with two different

stoss angles are not the correct representation in the natural flood-tide flow regimes, this

study will provide some understanding of the turbulence structures, flow separation regions

and drag on the flow over the bedforms without any added difficulty in measurement in the

tidal flow. The approximation of 2-D static artificial dune structures is justified because thespeed of the sand dunes is small compared with the mean flow [56]. Moreover, the use of

static bedforms allows a high spatial resolution of analysis and sampling very close to the

boundary which is not possible with mobile bedforms in the field.

The description of test channel, experimental method, procedure and flow conditions are

provided in Sect. 2; experimental results including mean flows, Reynolds stresses, quad-

rant analysis and drag reduction are presented in Sect. 3. Discussions and conclusions are

respectively provided in Sects. 4 and 5.

2 Experimentation

2.1 Test channel

Experiments were conducted in a re-circulating ‘closed circuit’ laboratory flume[35,36]espe-

cially designed at the Fluvial Mechanics Laboratory (FML) of the Physics and Earth Sciences

Division, Indian Statistical Institute (ISI), Kolkata. Figure 1 shows the schematic diagram

of hydraulic channel. The experimental channel has the dimension of 10 m length ×0.50 mwidth×0.50 m height. The flume walls were made of Perspex windows over a distance of 8 mproviding a clear view to the flow. A centrifugal pump for flow discharge was located outsidethe main body of the flume. The outlet pipe was fitted with a by-pass and a valve, so that

the flow discharge be adjusted to a desired maximum velocity. An electromagnetic discharge

meter with digital display was fitted with the outlet pipe to facilitate the continuous monitor-

ing of flow. The inlet and outlet pipes were freely suspended from an overhead structure. The

upstream bend of the channel was divided into three sub-channels of equal dimensions, and

a honeycomb cage placed at each end of the sub-channels to ensure smooth and vortex-free

1 3


5/29

Environ Fluid Mech

uniform flow. For identical operating conditions, the water depth and discharge were kept

constant for all experiments.

2.2 Experimental method

In order to ensure the fully developed flow at the sampling station over the smooth rigid

surface, flume experiments were conducted at a flow discharge Q = 0.029m3/s at a con-stant flow depth h (= 0.30 m). The hydraulic slope of the flume was approximately negligi-ble, which was of order 0.0003. Velocity data were collected at three different locations at

the flume central line along downstream using a SonTek 0.05 m down-looking 3-D Micro-

acoustic Doppler velocimeter (ADV) for 5 min (300 s) at a sampling rate of 40 Hz. About 25

vertical sampling positions were used for each longitudinal locations. Data were recorded for

each location starting from the lowest height 0.004 m above the bottom to the highest position

0.22 m. Total 12,000 data points were collected from each vertical position. No velocity data

could be measured near the free surface in the present study. The sampling volume of ADVwas located 0.05 m below the transmitter probe and the precise distance depended on the indi-

vidual probe geometry. The sampling volume was approximately cylindrical oriented along

the transmitter beam axis. The size of the sampling volume of 16 MHz ADV was 9×10−8 m3.The flow Reynolds number Reh (= U m h/ν) and the Froude number Fr (= U m /

√

gh) are

respectively 1.44 × 105 and 0.28, where U m = 0.48 m/s is the maximum velocity observedat the height z = 0.22 m above the flat surface, ν is the kinematic viscosity of water and g isacceleration due to gravity.

Using the phase-space threshold de-spiking method described by Goring and Nikora [18],

the velocity data were analyzed for all three locations to remove noises; and found almost no

change amongst the results of those velocity data, which indicated the steady and uniform

flow at the measuring station. The cut-off level for good-quality velocity data was 93 %, i.e. at

least 93 % of the raw data was remained unaffected after using the de-spiking method. Such

excluded signals were replaced by the data using a cubic polynomial interpolation method.

In turbulent flow, the instantaneous velocity components (u, v, w) in the Cartesian coor-

dinate system ( x , y, z) are given by,

u = U + u ; v = V + v ; w = W + w, (1)where U , V , W are the time-averaged velocities in ( x , y, z)-directions; u, v, w are thefluctuating components of u, v, w. Time-averaged stream-wise (U ) and wall-normal (W )velocity components are defined as,

U = 1n

ni=1

ui , (2)

W = 1n

ni=1

wi . (3)

The root-mean-square (rms) velocity components U r ms , W r ms are defined as,

U r ms =1

n

ni=1

(ui − U )2, (4)

W r ms =1

n

ni=1

(wi − W )2, (5)

1 3


6/29


7/29

Environ Fluid Mech

slope due to tidal flow), and the structures spanned the width of the flume. The first type of

structure, named as SFFS (slanting forward facing structure), had a stoss-side angle 50◦ (up-stream slope due to tidal flow); and the second one, named as VFFS (vertical forward facing

structure), had a stoss-side angle 90◦, which showed a mild change in the crest heights

h = 0.03m for the SFFS case, and h = 0.0335 m for the VFFS case. These resultedthe steepness ratio, h/λ = 0.1 for SFFS case and h/λ = 0.112 for VFFS case, whichare consistent with the steepness values of real dunes in river flows [5,17,20] and in tidal

environments [56]. Each bedform structure was placed opposite to the flow direction (i.e.

in a tidal flow environment) at the same measuring location of the flume bed at about 6m

downstream from the channel inlet. Experiments were conducted separately for each structure

under the identical flow condition to make a comparative study between the two structures

of different stoss angles (50◦ and 90◦) on the mean flows, turbulence characteristics, flowseparation and drag coefficients over the common gentle lee angle of 6◦ at the downstreamface. The bedform structures of two different stoss angles of 50◦ and 90◦ with a commongentle lee angle of 6◦ were considered in the present study, which were closely analogous withthe bedform structures measured in the seabed bathymetry during the tidal environments (see

Fig. 6 of [30]). The observed stoss angles of all three primary bedforms were approximately

at the order of 77◦ and the lee sides were almost gentle slopped (see Fig. 6 of [30]). Therefore,in the present study, the use of steep stoss angles (50◦ and 90◦) with a common gentle leeslope was justified because the slope angles of the structures were of similar order which fall

into the range of those observed in natural environments. The present investigation will focus

here: how the flow structure will be affected if the artificial bedform structures are oriented

against the flow, which are akin to the tidal flow over the ebb-oriented bedforms mentioned

as SFFS and VFFS?Twelve different measuring locations A, B, C, D,…, K and L from upstream to down-

stream forboth SFFS andVFFS caseshadbeen selected(Fig. 3). The respective dimensionless

distances of thelocationswere x /λ = −0.80, −0.40, −0.23, −0.13, −0.06, 0, 0.10, 0.40,

Fig. 3 Two forward facing dune shaped structures (VFFS and SFFS) along with the measuring stations A, B,

C,…, L, M and N. Flow direction is from left to right . Each structure is having a common wavelength λ = 30cm and width = 50 cm

1 3


8/29

Environ Fluid Mech

Table 1 Experimental values of

flow parameters Plane bed

Reynolds number, Reh = U m h/ν 1.44 × 105Maximum flow velocity, U m (m/s) 0.48

Mean flow depth, h (m) 0.30

Froude number, Fr 0.28Friction velocity (from log law), u∗ (m/s) 0.01911Equivalent bed roughness, zo (m) 0.0001

SFFS

Crest height, h (m) 0.03Base length, λ (m) 0.30

Width (m) 0.50

Steepness, h /λ 0.1Lee side angle (◦) 6

Stoss side angle (◦) 50VFFS

Crest height, h (m) 0.0335Base length, λ (m) 0.30

Width (m) 0.50

Steepness, h /λ 0.112Lee side angle (◦) 6Stoss side angle (◦) 90

0.66, 1.00, 1.23 and 2.56. In addition, for the case of VFFS, two more locations M and N

were selected for measurements, and their dimensionless distances were x /λ = 0.2 and 4.0,respectively. The location F of the VFFS case corresponds to the location G of the SFFS,

which were the crest points of the corresponding structures. The Reynolds numbers based on

the crest heights Reh (= U m h/ν) for VFFS and SFFS cases are 1.6 × 104 and 1.44 × 104,respectively. A summery of experimental conditions is provided in Table 1. The velocity

measurements were taken using ADV at all longitudinal locations (A, B,…,L, M, N) sep-

arately under identical flow conditions. In a similar way, the ADV data were processed to

remove the spikes using a phase space threshold de-spiking method described by Goring andNikora [18].

3 Experimental results

3.1 Mean velocity components

The verticalprofiles of normalized stream-wise mean velocity (U /u∗) over both the structures

(VFFS and SFFS) from upstream to downstream at different selected locations (A, B,…,L) areplotted against z/ h in Fig. 4. It is observed from the figure that for the SFFS case, the normal-

ized velocity (U /u∗) profiles at all locations along the downstream show almost the identicalpattern like standard log-law [28] except the location G at the crest point, where a reverse

pattern is observed with a maximum normalized velocity (U m /u∗ ≈ 30) at the crest level.Moreover, there is an indication of decrease in mean stream-wise velocity near the bottom

just upstream of the crest position. For the VFFS case, the normalized velocity (U /u∗) looks

1 3


9/29

Environ Fluid Mech

Fig. 4 U /u∗[ x /λ] at the locations A, B, C,…, to L for both SFFS and VFFS cases, where the symbols filled circles and triangles indicate data points of SFFS and VFFS, respectively

like a log-law from locations A to E before the crest point; and then the velocity profiles seem

to be strongly affected by the presence of forward facing structure. Interestingly, different

flow patterns are observed for each case. From the figure, it is observed that stream-wise mean

velocities show reversed flow at E and on the lee side at G, H, and I. Significant flow separationand the recirculating eddy within the separation zone occur just downstream of the crest F on

the gentle lee side; and then the mean velocities are seen to redevelop for the VFFS case, while

for the case of SFFS, the velocity patterns possess a small indication of flow reduction beyond

the crest position G (no flow separation; [16]). The flow separation region with recirculating

eddy induced on the lee-side has a strong influence on the resistance that bedform exerts on

the flow due to energy loss through turbulence [54]. Observations from the VFFS case reveal

that a sharp growth of mean velocity initiates from the crest position F up to the position K that

reaches to a maximum velocity at certain level z / h near bottom and then decreases slowly.

The peak of maximum velocity grows towards the downstream along x /λ.

An indication of strong shear layer within the recirculation region, more akin to the TBL, is observed. Theshear

layer reflects the changes in the velocity gradient between the two overlaying flow regions:

flow reversal region near the boundary and high velocity away from the boundary. The mean

velocity profiles gradually become fully developed at further downstream of the recirculation

region and collapse in the outer flow region, which indicates that the mean flow redevelops

from the perturbation and follows the log-law at a distance of 3.0( x /λ) from the toe point J.

1 3


10/29

Environ Fluid Mech

Fig. 5 Shear velocity, u∗∗[ x /λ] derived from log-law at each of the measuring location for SFFS (with filled circles symbols) and VFFS (with triangles symbols) case. Black dashed vertical line denotes the crest position

G for SFFS and grey dashed vertical line denotes the crest position F for VFFS

A comparative study between the two cases indicates that at the location A the stream-

wise velocity (U /u∗) profiles show a log-law and overlap each other. As it proceeds towardsdownstream, at each location there is an intersecting point of two different velocity profiles.

Below the points of intersections, mean velocity profiles collapse each other up to the location

D at x /λ = −0.13. Further downstream, the mean velocity for the VFFS case seems tobe separated and dramatically reduces with flow reversal at the locations G and H and a

reattachment point at I ( x /λ = 0.66). Above the intersecting points, the mean velocitiesfor the VFFS case seem to increase and differences are becoming much smaller further

downstream at L ( x /λ = 2.56). The distance of the reattachment point from the crest pointF is approximately 6h, which is at the location I ( x /λ = 0.66). It is interesting to note thatthe mean velocity profile at the crest location F of the VFFS case follows a log-law with amaximum velocity (U m,V F F S /u∗ = 29) at the level z/ h = 0.2, and it is concave in shapeat the crest position G for the SFFS case with U m,S F F S /u∗ =30 at the level z/ h = 0.1. It isworthwhile to note that the mean stream-wise velocity is higher for the case of VFFS over

the entire measuring zone than that for the SFFS case.

For the SFFS case, the velocity profiles are tested for log-law with the universal von Kar-

man constant (= 0.40) at all locations except the location G at the crest point (computedlog-law profiles are not shown in the figure), which is similar to results obtained by Lefebvre

et al. [28] for flood tide over the ebb oriented bedforms. The friction velocity u

∗∗computed from respective log-law ranges from 0.022 to 0.035m/s along the flow withdynamic roughness height (≈ 0.00043 m). The computed friction velocity u∗∗ is plot-ted against x /λ except the location G in Fig. 5 (filled circle symbols), which shows

the increase of u∗∗ from A to F up to the head point, and then shows the decreaseof u∗∗ from H to L over the lee-side of the structure. It is observed that the valueof u∗∗ at the toe point J is lower than the other values, where the log-law fitted bet-ter with regression coefficient R2 = 0.99 than the other locations. The upward slopeof u∗∗ before the head point and downward slope over the lee-side represent respec-tively the deceleration and acceleration of flow near the boundary. On the other hand,

for the VFFS case, the stream-wise velocities follow log-law from A to E before thecrest point, and the corresponding values of friction velocity u∗∗ are shown in Fig. 5(triangle symbols). The mean velocity is strongly perturbed by the structure and hence no

log-law is observed until the long distance. Friction velocities for VFFS case show greater

values than that of SFFS case along the flow up to the crest location. The extreme upstream

and extreme downstream locations show approximately same value of u∗∗ for both cases,implying that there is no influence of the structures.

1 3


11/29

Environ Fluid Mech

Fig. 6 W /u∗[ x /λ] at the locations A, B, C,…to L for both SFFS and VFFS cases, where the symbols filled circles and triangles indicate data points of SFFS and VFFS, respectively

The profiles of normalized vertical mean velocity (W /u∗) for both the cases are shownagainst z/ h in Fig. 6 for different stream-wise locations. It is observed that the (W /u∗) at thelocation A for both VFFS and SFFS cases is almost zero, which means that there is no effect

of waveforms. Mean velocity profiles for both the structures (SFFS and VFFS) increase withvertical height near the boundary approximately up to z / h ≤ 0.2 from the location B to thelocation G, and then decrease to zero away from the boundary. It is interesting to note that

the vertical velocity profile at the crest position F for the VFFS case is qualitatively similar

to that for the SFFS case at the position G with about 3.5 times higher in magnitude. Just

after the crest on the lee side, the negative vertical velocity (directed towards the bed) occurs

with a maximum value near the crest level at about z/ h = 0.12 for the VFFS case, whichis associated to the reattachment of the flow to the bed. In addition, the zero-normal mean

velocity for the SFFS case occurs in between K and L, whereas for the VFFS case it is at

point L.To illustrate the visualizations, streamline plots of velocity vector (U , W ) for the both

SFFS and VFFS cases are shown in Fig. 7a, b. Figure 7c is the magnified version of the

separation bubble of the VFFS case. This showed a clear recirculation bubble for the case

of VFFS located just downstream of the crest on the upper lee side, which was comparable

with the observations of [11,47,49], who executed the work with FFS with flat surface. The

extrapolation technique was used for plotting of streamlines. A separation point was obtained

1 3


12/29

Environ Fluid Mech

Fig. 7 Streamline plot of velocity vectors for a SFFS case, b VFFS case, and c magnified version of the VFFS

case

in the x -direction at the upstream of the structure where the stream-wise mean velocity was

nearly equal to zero; and a reattachment point at the downstream of the recirculation bubble

on the lower lee side was attained, where stream-wise mean velocity became nearly equal to

zero. From the results of the Figs. 4, 6 and 7c, it was evident that the flow separated at nearly

x /λ = −0.05 upstream of the case of VFFS case. However, for the case of SFFS, no flowseparation region was observed. According to the observed data, no such reattachment pointwas observed at the vertical face of the VFFS case, i.e. where the vertical velocity component

became nearly equal to zero. Figure 7c shows that the length of the recirculation bubble at

the downstream of the structure, X r is approximately equal to 0.19 m with a bubble center at

x /λ = 0.26, z/ h = 0.112 (exactly at the crest height). The disappearance of recirculationbubble at downstream of the crest for the SFFS case was probably associated with the bed

topography of stoss side, which generated local favorable pressure gradient to prevent any

flow separation. This finding was comparable with Ernstsen et al. [16] and Lefebvre et al.

[30].

3.2 Turbulence intensities

The plots of normalized stream-wise turbulence intensity ( I u ) are shown along downstream

in Fig. 8 for both SFFS and VFFS cases. It is observed that the pattern of turbulence intensity

( I u ) is almost identical through out the depth z/ h except near the boundary from the locations

A to E for both cases. In fact, as it proceeds towards downstream leading from the location

1 3


13/29

Environ Fluid Mech

Fig. 8 Plots of normalized stream-wise intensity for: a SFFS case and b VFFS case. Flow direction is from

left to right

A, there are successive increments of intensity near the boundary up to location E, then from

the crest F of VFFS a drastic growth of intensity with a maximum value I u = 9.95 at F isobserved. It may be pointed out that beyond the crest F of VFFS within the recirculation

region on the lee side, I u increases sharply and reaches a maximum value at each locationat a level of z/ h ≈ 0.15 and finally decreases and coincides with the intensity profiles of SFFS case. The position of the maximum intensity for the case of VFFS moves toward the

free surface further downstream, which is opposite to the result achieved by Mazumder et

al. [36] who conducted experiments with isolated scalene waveform structure; and similar to

the observation of [13]. The magnitude of stream-wise intensity profiles for the case of SFFS

is much smaller than that of the VFFS case near the boundary leading from the location E

up to the location L. The intensity I u attains its maximum value over the crests for both the

cases. It is noted that the zones of high turbulence intensity are characterized by low mean

velocity. The presence of a peak in the vicinity of crest level indicates the presence of a shearlayer, which is caused by a separation of the flow.

The normalized vertical turbulence intensity ( I w) is shown along the flow in Fig. 9 for

both SFFS and VFFS cases. The profiles of I w along the stream-wise locations show the

similar trend as I u with smaller in magnitude. The intensity I w is seen to be more prominent

at the downstream of the crest for the VFFS case and this effect persists for a longer distance

than that in the case of I u for both the cases. For the VFFS case, a slight increase in I w is

1 3


14/29

Environ Fluid Mech

Fig. 9 Plots of normalized wall-normal intensity for: a SFFS case and b VFFS case. Flow direction is from

left to right

observed while approaching the forward face, which is about 5 % of the U m∗ . This change in I w is due to the vertical forward face and it is more prominent compared to I u . It is observed

that I w for the case of VFFS is higher than that of the SFFS along the stream-wise locations,

and after the crest G of VFFS case within the recirculation region, I w increases sharply andreaches a maximum value at each location at a level of z/ h ≈ 0.2 and finally decreasesgradually towards the main flow.

3.3 Reynolds shear stress

The dimensionless Reynolds shear stress (τ uwdi m = −uw/u2∗) is shown against z/h for allstream-wise locations in Fig. 10 for the both SFFS and VFFS cases for comparison. It is noted

from the figures that the magnitude of turbulence shear stress (τ uwdi m ) is almost identical

through out the depth z/

h from the locations A to E for the both VFFS and SFFS cases, whileat the crest F of VFFS case shear stress τ uwdi m initiates to increase due to change in velocity.

At the location G of the immediate downstream of the crest F of VFFS case and at the crest

G of the SFFS, a small region of negative Reynolds shear stress is observed, indicating the

outward flux of momentum. Further downstream, especially in the case of VFFS, a large

region of high positive Reynolds shear stress is seen within the region z/ h ≤ 0.5 with aclear peak near the boundary. Interesting to note that the maximum shear stress falls at a

1 3


15/29

Environ Fluid Mech

Fig. 10 τ uwdi m [ x /λ] at the locations A, B, C,…to L for both SFFS and VFFS cases, where the symbols filled circles and triangles indicate data points of SFFS and VFFS cases, respectively

distance within 0.50 ≤ x /λ ≤ 0.66, where the reattachment point exists. Furthermore, theposition of the maximum τ uwdi m moves toward the free surface and decreases gradually as

it proceeds towards the downstream, which has the evident in the open channel flow overdunes [13]. Reynolds shear stress profiles collapse in the upper part of the flow within the

range 0.3 ≤ z/ h ≤ 0.6. Close to the bottom, the Reynolds shear stress profiles are greatlyperturbed and the development of a shear layer is confirmed by the presence of peaks.

3.4 Quadrant analysis of Reynolds shear stress

The observations reveal that the TBL is directly associated with large-scale coherent struc-

tures, occurring irregularly. Coherent structures with large flux events have been proposed to

explain the ‘bursting’ phenomena responsible for resistance to motion, transport processes,turbulence production, and hence mixing. These coherent structures are quasi-periodic and

occupy the total boundary layer depth. The turbulence over the bedform structures against the

flow is examined through quadrant analysis to estimate the major turbulent events characteriz-

ing the coherent structures. The analysis clearly indicates the impact of the chosen structures

on the dominant Reynolds shear stress. The quadrant threshold technique for direct estima-

tion of observed data of conditional statistics of Reynolds shear stress is presented briefly.

1 3


16/29

Environ Fluid Mech

The longitudinal and vertical velocity components U and W are aligned along x and z direc-

tions, respectively and Reynolds shear stress τ = −ρuw is the inward flux of stream-wisemomentum.

The quadrant analysis is originally devised to sort out the contributions to τ from each

quadrant of instantaneous values on the uw– plane. The quadrants are usually referredby the following names: (a) outward interactions (i = 1; u > 0, w > 0), Quadrant-1(Q1), (b) ejections (i = 2; u < 0, w > 0), Quadrant-2 (Q2), (c) inward interactions(i = 3; u < 0, w < 0), Quadrant-3 (Q3) and (d) sweeps (i = 4; u > 0, w < 0),Quadrant-4 (Q4). This method of quadrant decomposition is similar to that used in some

of the previous researches like [31,36,39,47,57]. The existing quadrant analysis is used to

analyze how the ebb oriented bedform structures under flood-tide conditions influence the

turbulent events. The analysis essentially highlighted the turbulent event evolution along the

bedform structures. Each velocity pair from ADV data may be investigated either through

examining the entire signal data or filtering those data above a threshold value (i.e., excluding

a Hyperbolic region of size H ) defined as,

H = |uw|/ [(U r ms ) (W r ms )] . (10)At any point in a turbulent flow, the contribution of the total Reynolds stress from quadrant

i, excluding the region H , is defined as,

uwi, H = limn→∞

1

n

n 0

u(t )w(t ) I i, H [u, w]dt , (11)

where n is the total number of measurements and the angle brackets denote a conditional

average and the indicator function I i, H is defined as,

I i, H (u, w) =

1, if (u, w) is in i th quadrant andif |uw| ≥ H [(U r ms ) (W r ms )] ,

0, otherwise.

(12)

Here, H is the threshold parameter in the Reynolds stress signals by which one can

extract the values of u w from the whole set of signal data, which are greater than H times

[(U r ms ) (W r ms )

] value. In the Eq. 12, the expression

|uw

| ≥ H

[(U r ms )(W r ms )

] is used as

a filter which cancels out all those data whose strength is less than H times [(U r ms ) (W r ms )].The stress fraction [31,36] by ith quadrant is defined as,

S i, H = uwi, H [(U r ms )(W r ms )]

, (13)

which gives the Reynolds shear stress fraction associated with each of the turbulent events. By

definition, S 1, H , S 3, H 0, and for H = 0, S 1,0 + S 2,0 + S 3,0 + S 4,0 = 1.The space fraction [47,57] gives the fraction of space , i.e., fraction of total observations

(n) contributing to the instantaneous Reynolds shear stress by each of the quadrant events for

a given H , is attained by using

N i, H (u, w) =

I i, H

n, (14)

where I i, H is the indicator function (Eq. 12) and n is the total number of observations.

For comparison, contributions of stress fraction S i, H were computed for the both SFFS

and VFFS for H = 0 and 4 for all the four quadrant events.

1 3


17/29

Environ Fluid Mech

Fig. 11 Contour plots of stress fraction |S i, H | for each quadrant for H = 0: a SFFS case and b VFFS case.Flow direction is from left to right

Figure 11a, b shows the contribution of all four quadrant events to the Reynolds shear

stress i.e., stress fraction |S i, H | for i = 1–4 for the threshold parameter H = 0 over theboth SFFS and VFFS cases. These figures show a trend that the contributions of ejections

and sweeps to the shear stress are much higher than that of the outward and inward inter-

actions, though there are some conflicts regarding the statement at some locations which

might be the point of interests. In the vicinity of the crest position of the SFFS case and ata distance just downstream of the crest for the VFFS case, it is interesting to note that the

contributions of ejections and sweeps are negligible, whereas outward and inward interac-

tions dominate equally at the referred locations for both of the cases. Contour plots show

that contributions from ejections and sweeps to the shear stress are almost same for the

case of SFFS at the downstream of the crest, where no recirculation region is formed. On

the other hand, for the case of VFFS, sweeps have larger effects to the shear stress in the

1 3


18/29

Environ Fluid Mech

Fig. 12 Contour plots of stress fraction

|S i, H

| for each quadrant for H

= 4: a SFFS case and b VFFS case.

Flow direction is from left to right

recirculation region. Further downstream near the bed, sweeps overshadow the ejections

for the VFFS case. In addition, larger contributions of ejections to the Reynolds shear

stress are distributed at a slightly away from the bedform structure which is similar to

the observation of Ren and Wu [47]. At the interface of ejections and sweeps over the

trough region, kolk–boils phenomenon is observed [40,41]. A kolk phenomenon is asso-

ciated with an ejection when rapidly rushing fluid passes the forward face (stoss side) of

the structures [33,43]. Existence of upward tilting stream-wise vortex motion in the flowis known as kolk; while boils are the structures like circular or oval shaped patch lift

up from the kolk on the water surface, which dissipate or merge with the surroundings

[40,41].

Figure 12a, b shows contributions to Reynolds shear stress from all the four quadrants for

H = 4 for the both SFFS and VFFS cases. It is obvious that other than the most strong events,all will filter out. Only inward interactions contribute notably in the vicinity of crest region of

1 3


19/29

Environ Fluid Mech

Fig. 13 Contour plots of the ratio |S 2,0|/|S 4,0| : a SFFS case and b VFFS case. Flow direction is from left toright

SFFS case. Over the crest for VFFS, intense ejections largely contribute to the shear stress.

As we go further downstream, on the surface of the structure in the recirculation bubble,

sweeps contribute most as in the case of H = 0. Away from the surface at the downstreamof the crest of the VFFS case, intense ejections largely dominate over sweeps similar to theobservation of [40,41]. In the case of SFFS, contributions from ejections and sweeps vanish

as compared to the case of H = 0.Figure 13a, b depicts the ratio of ejections to sweeps (|S 2,0|/|S 4,0|) that contributes to

the Reynolds shear stress. This figure verifies the previous statements about the positions

where the sweeps have greater contributions to the Reynolds shear stress and where the

ejections overshadow it. If the ratio |S 2,0|/|S 4,0| < 1 at any position, the sweeps are moreprominent than the ejections at that position; and if |S 2,0|/|S 4,0| > 1 at any point, the ejectionsovershadow the contributions of the sweeps to the shear stress at that point. Just in the vicinity

of the crest and in the recirculation region sweeps exceed ejections by approximately a factorof 1.4 for the VFFS case. Typically contributions of ejections exceed that of sweeps in further

vertical distance and downstream by a factor ranging between 1.13 to 2.5. However, for the

SFFS case in the vicinity of the crest position, contributions of sweeps exceed that of ejections

by a factor of 2.4 approximately.

The space fractions N i, H (u, w) occupied by all the four quadrants for H = 0 are shown

in Fig. 14a, b for both SFFS and VFFS. Clearly, Q1 and Q3 events (interactions) have low

probability to occur in near bed region and the events generally increase above the bed

z/ h > 0.25. In contrast, the percentage of space occupied by ejections Q2 and sweeps Q4

is high near the bed and decreases slowly toward the water surface. In the vicinity of thecrest for the SFFS case, outward and inward interactions occupy around 30 % of the space,

while for the case of VFFS at the same location, sweeps overshadow the other three. Near

the surface of the structure in the recirculation region for the VFFS case, ejections are seen

to occupy higher space about 40% than sweeps which is about 25%. Sweeps occupy the

larger space just at the upper regions of recirculation bubble and go on increasing further

downstream.

1 3


20/29

Environ Fluid Mech

Fig. 14 Contour plots of space fraction N i, H to each quadrant for H = 0: a SFFS case and b VFFS case. Flow

direction is from left to right

3.5 Flow resistance and drag reduction

There were several approaches to deduce the flow resistance, i.e. total boundary shear stress

and hence the overall drag. Flow resistance due to the form drag exerted by bedforms is

important to quantify its influence on water surface fluctuation. In general, vertical profiles

of stream-wise velocity measured over the waveform structures were used to calculate theboundary shear stresses. The profiles may be either locally derived or by means of spatial

averaging. Smith and McLean [51], McLean et al. [37] preferred the latter procedure. There

were several ways to construct a spatial average: (1) averaging over constant elevations

above the waveform structure, (2) averaging along streamlines of constant velocities, or

(3) averaging the velocity data at constant values of z above the surface along the stream-

wise direction. The last procedure was applied for our present study.

1 3


21/29

Environ Fluid Mech

Fig. 15 Spatially averaged mean stream-wise velocity profiles (U ) for a SFFS case and b VFFS case, wherethe symbols filled circles and triangles indicate data points of SFFS and VFFS cases, respectively

Spatial averages of mean stream-wise velocity along the flume centerline, U were com-puted for both the SFFS and VFFS cases using the third procedure of spatial averaging as

stated earlier and plotted in Fig. 15a, b. As recommended in [37], velocity average excluded

those data in the separation zone. Spatially averaged profile near the bed was characterizedby shear velocity associated with the skin friction. The spatially averaged velocity profiles

for both the cases follow log-law with coefficient of regression, R2 ≈ 0.98 and are given by,

U = 7.713 log( z/ h) + 54.46 (for VFFS), (15)

and

U = 5.493 log( z/ h) + 52.98 (for SFFS). (16)

The corresponding shear velocities, u

∗T associated with the fitted log-law and hence the

total boundary shear stresses, τ T (= ρ u2∗T ) are given by 0.0309m/s and 0.9518 N/m2 for theVFFS case and 0.0220m/s and 0.4828 N/m2 for SFFS case, respectively. It is notable that

mean flow resistance over the VFFS case is much larger than that of the SFFS case.

Again, it can be argued that, rather than comparing τ T , drag coefficient can be compared

according to [55], but as the flow discharge was constant for all the experiments, i.e. steady

flow condition was maintained, the flow resistance can be thought of only dependant on the

waveform shape. Drag coefficient C D is defined here as, C D = (u∗/U )2, where u∗ is theshear velocity calculated by extrapolating the Reynolds stress profiles at each stream-wise

locations and U is the depth averaged mean stream-wise velocity. Stream-wise values of drag

coefficients for both SFFS and VFFS cases are plotted in Fig. 16. Therefore, it is seen that inthe flow reversal region on the waveform there is an increase in drag and it is much higher for

the case of VFFS than that of SFFS. So, by reducing the stoss-side angle, we can minimize the

overall flow resistance. Thus the reduction in drag occurs. It can be concluded that waveform

shape with different stoss-side slopes against the flow (forward facing to the flow) plays an

important role for controlling the mean flow resistance and hence the movement of sediments

in a fluvial channel.

1 3


22/29

Environ Fluid Mech

Fig. 16 Drag coefficient over the two structures SFFS and VFFS along the stream-wise direction, where the

symbols filled circles and triangles indicate data points of SFFS and VFFS, respectively. Flow direction is

from left to right

4 Discussion

The flow structure generated over forward-facing dunes/obstructions has many important

implications to the bedform dynamics, bed shear stress and flow resistance due to form drag

in the tidal flow situation. The above considerations motivated the need to investigate the

role of forward-facing dune-shaped structures to the flow field. Study of flow associated

with these structures in the tidal environment is inherently difficult since it is usually hard tomeasure the near-bed flow and hard to quantify the nature of turbulence over these structures.

The current paper presents the experimental data for the mean flow, the turbulence and the

resistance due to drag associated with these bedform structures, which could be thought of

as a bluff body or object in unidirectional flow or a relic bedform subjected to a tidal bore

oriented in the opposite direction (i.e. in reverse flow condition). The novelty of this study is

the execution of the flume experiments to characterize the turbulent flow over two forward-

facing bed form structures, which are akin to the tidal flow environments, and to make the

necessary comparative discussions with the field and numerical investigations of dynamics

of dunes in tidal environments [16,29,30]. Moreover, the test data are used to analyze the

turbulent statistics of flow over such bedforms with different stoss-side angles, which werenot studied earlier. Thus the results were evaluated in terms of turbulence characteristics

and the coherent structures in the perturbed flow region. This study showed that there were

significant changes in the turbulence, especially in the near-bed area and in the vicinity of

the crest position due to different geometries, i.e. difference in stoss-side angle.

Shear layers generated along flow in the SFFS case had a much smaller velocity than the

velocity from the characteristics of shear layer generated by the flow separation in the case

of VFFS. Turbulence production associated with the VFFS case was dominated by eddies

generated along the shear layer, which produced high horizontal and vertical velocities and

large Reynolds stresses in this region.For the SFFS case, the velocity profiles followed log-law [28] with the universal von

Karman constant (= 0.40) at all locations except for the location G at the crest point. Onthe other hand, for the VFFS case, the log-law was observed from A to E before the crest

point; and then log-velocity was strongly perturbed by the structure; and hence no log-law

was observed until far away from the crest. Interesting to note that the mean velocity profile

at the crest F of the VFFS case followed a log-law, while the shape of the velocity profile

1 3


23/29

Environ Fluid Mech

with vertical hight was concave at the crest G for SFFS case. The vertical velocity profile at

the crest F for the VFFS case was qualitatively similar to that for the SFFS case at the crest

position G with about 3.5 times higher in magnitude.

The bedform structure with forward-facing vertical stoss side (VFFS case) acquired a thick

flow separation region with a prominent recirculating eddy on the gentle lee side, whereasthere was no indication of flow separation or flow reduction on the lee side of the forward-

facing bed form structure (SFFS case). The flow separation induced wakes that grew and

transported downstream occupying the outer flow towards the free surface. The length of the

recirculation bubble at the downstream of the structure was about 0.19 m with a bubble center

exactly at the crest height for the VFFS case (Fig. 7c). The disappearance of recirculation

bubble at downstream of the crest for the SFFS case was probably due to the topography

of slanted stoss face, which prevented flow separation (Fig. 7a). Similarly, in the numerical

study by Lefebvre et al. [29], for bedform nos. 2 and 3, there was no flow separation zone

during the reverse flow; whereas, permanent flow separation zones were achieved during the

ebb flow condition. The bedform structures considered in the present study are analogous to

the natural dune structures measured in the seabed bathymetry during the tidal environments.

It is interesting to determine the threshold condition of the development of flow separation

zone and recirculation bubbles in lee side of the bedform structures; and the dependence of

stoss and lee angles to turbulence parameters, drag coefficients during the tidal conditions.

Therefore, the implication of this study is to understand the turbulence phenomena, what

occur in the natural dunes. Mazumder et al. [36] reported experimentally that during the ebb-

tide flow a permanent separation zone occurred on a sharply sloping lee side (50◦) for theebb-oriented bedforms, whereas in the present study during the flood-tide no flow separation

zone developed over the gentle slope of flood lee side (6◦), that agrees well with the ebbflow condition in the work of Kostaschuk and Villard [25], Best and Kostaschuk [10] and

Paarlberg et al. [44], which confirmed the occurrence of permanent flow separation on the lee

side slope of greater than 10◦. Importantly, for ebb flow condition, flow separates at the crestpoint [29,36] but in the present study, there was a flow separation for only VFFS case which

occurred at about x /λ = 0.05 upstream of the structure. For VFFS case, the flow patternswere classified as the boundary layer development region before the crest point; the flow

recirculation and the reattachment on the lee-side, and the boundary layer redevelopment

region along the flow. No definite recirculation bubble was observed at the upstream side

of the structure for either cases, which is contrary to the previous result using a FFS and a

forward–backward facing step [11,47].A high turbulence intensity was characterized by low flow in the flow reversal region,

while the outer flow region was characterized by high velocity and lower turbulence intensity.

Vertical normalized intensity seemed to be more prominent at the downstream of the crest

than the stream-wise intensity and the effect persisted for a longer distance. The intensity

I u attained its maximum value over the crest for both the cases. In contrast, the vertical

intensity I w attained its maximum over the lee slope at about x /λ = 0.66 distance from thecrest for the VFFS case and interestingly for the SFFS case the maximum of it was observed

in the vicinity of the crest position. Whereas, for the ebb flow condition over such SFFS,

Mazumder et al. [36] concluded that both the I

u and I

w attained their maximum at about x /λ = 0.70 distance from the crest. Again, comparison with Mazumder et al. [36] showedthe disappearance of definite peak in I u . As in the case of reverse flow, the maximum I uwas always obtained at lower-most point at 0.004 m above the bed. The maximum value of

stream-wise intensity I u at the crest F of the VFFS case was about two times greater than that

of I w at I, which was about 4.5 for the VFFS. For ebb flow condition over the same structure

as our SFFS, according to the study of [36] maximum I u is about three times greater than I w,

1 3


24/29

Environ Fluid Mech

whereas for our case in reverse flow condition, I u was measured to be five times greater than

I w. For the SFFS case, the maximum of I u is nearly equal to 25% of the U m∗ (= U m /u∗).Again, at downstream of the crest region, I u greatly reduces to 12 % compared to that of

the VFFS case, and that value is lower than the value obtained by Ren and Wu [ 47]. The

maximum of I u for VFFS case attained about 39% of the normalized maximum velocityU m∗ (= U m /u∗) which agreed reasonably well with the earlier studies by Agelinchaab andTachie [2] (≈ 30–40 %), Ren and Wu [47] (≈ 30 %) and Sherry et al. [49] (≈37–45 %). Justdownstream of the crest F, a high increment in I w is observed in the layer near the boundary,

where the negative vertical velocity occurred. In this region, for the VFFS case, I w is found

to have magnitude of about 18% of U m∗ . In the case of SFFS, maximum intensity is observedabove the crest region which is just about 4 % of U m∗ . It diffuses towards the outer region aswell as the bottom boundary further downstream. Due to the presence of waveform structure,

enhancement of turbulence intensity occurred which was more prominent in the case of VFFS

due to significant flow separation, recirculation and development of a thin shear layer. The

recovery of I u at the flat surface beyond the downstream of the toe was much faster than I wfor both the cases which was qualitatively similar with the study of [36].

A change in the Reynolds shear stress was noticed due to the local flow conditions at

different locations relative to the structural geometry. A strong enrichment was observed

between the locations G and J for the VFFS case compared to that of the SFFS, which

revealed a greater flow perturbation in that region. A clear peak in the vicinity of the crest

height ( z/ h ≈ 0.13) for the VFFS case was observed, which was similar to the turbulent flowover dunes using numerical technique obtained by Mendoza and Shen [38]. For our VFFS

case, the maximum τ uwdi m achieved was about 15 times greater than that for the SFFS case.

Comparison with the study by Mazumder et al. [36] showed that for ebb flow condition, themaximum τ uwdi m is about two times greater than that for reverse flow condition over SFFS

as in our case. The recovery of the shear stress was much faster in the SFFS case than that of

the VFFS. The significant scattered points at the recirculation region just beyond the crest for

the VFFS case were noticed, which were due to the sudden change in the depth. For SFFS

case, the profiles of Reynolds shear stress were almost identical in pattern for all locations

along the flow.

A quadrant decomposition technique was adopted to explain the ‘bursting’ phenomena

responsible for most turbulent production. The contributions of ejections and sweeps have

greater influence to the Reynolds shear stress overall except at the crest locations indicating

that the momentum transfer between the flow and the channel bed is mostly carried bythese two events. The crest locations can be treated as rough edges and hence it verifies that

contributions to the Reynolds shear stress by the outward and inward interactions become

significant and dominate over the other two events at the rough surfaces as reported by Kaftori

et al. [21]. It is in contrary with the findings of [36] in ebb flow condition, whose study showed

ejections and sweeps to be always dominant over and beyond the structure and have greater

influences to the Reynolds shear stresses than the other two interactions. Large-scale vorticity

is manifested as ejection event and arises both along the shear layer and at flow reattachment.

It should be noted that for the VFFS case the relative intensity of each event (specially

ejections and sweeps) for H >

0 is significantly greater as compared to the SFFS case. Thisis probably due to relatively high turbulence level. As a result, the relative importance of

contributions of the turbulent events to the shear stress for VFFS case is much higher than

that for SFFS case. Contribution of ejections is clearly the most responsible event for moving

sediment particles away from the bed, and sweeps provide an avenue for entraining particles.

In the vicinity of the crest region for the SFFS case, outward and inward interactions

occupy around 30% of the space, while in the case of VFFS at the same location, sweeps

1 3


25/29

Environ Fluid Mech

overshadow the other three. Although near the surface of the structure in the recirculation

region for the VFFS case, ejections are seen to occupy higher space about 40 % than sweeps

which is about 25%. However, the sweeps and ejections extract energy from the mean flow to

create turbulence near the bed, which are considered to be more important than the interaction

events. In this region sweeps contribute more to the Reynolds shear stress than ejections aswe have discussed earlier. That emerges the fact that in this region, duration of sweeps are

larger.

The interactions between the turbulent coherent structures at different flow layers are

associated with the kolk–boils phenomena. These coherent flow structures are advected with

the mean flow, often reaching the free surface and erupting as surface ‘boils’. The origin

of kolks and boils in the fluvial systems has been vigorously attributed to the interface of

ejections and sweeps over the trough region [40,41]. Existence of upward tilting stream-wise

vortex motion in the flow is known as kolk [33,43]; while boils are the structures like circular

or oval shaped patch lift up from the kolk on the water surface, which dissipate or merges with

the surroundings. Boils indicate the presence of macro-turbulence structures generated by the

dunes at the bed [19,24]. The formation of such macro-turbulent structures conceives from

the flow separation during high flows. Overall, sweeps are seen to have greater contribution

to the shear stress near the top surface in the case of VFFS and ejections largely contribute

at a slightly higher vertical height.

Bed forms in alluvial channels exerts flow resistance according to their shapes and sizes

and hence can greatly influence the sediment transport process. It is revealed from this study

that slope of the upstream-facing stoss-side has an effect on the flow resistance due to drag

and hence the sediment transport rate similar to the findings of [7,28,53]. So, it is an important

issue and of great importance in the filed for river engineering to predict channel evolutionprocess, river planning and restoration in the reverse flow condition/tidal flow. The flow

resistance is calculated from spatially averaged stream-wise velocity profiles for both the

cases and it is concluded that with increase in the stoss-side slope, there is an increase in

overall flow resistance and the drag.

5 Conclusions

The purpose of the present study was to ascertain the effect of different stoss-side slopes of

forward-facing bedform structures on the mean flow, turbulence and flow resistance/drag;and thus to simulate of flow over such bedforms in tide/flood environments. Two isolated

rigid bedform structures with a common lee-side angle were considered under identical flow

conditions. An ADV was used to collect the velocity data at different horizontal locations to

examine the time-mean velocities, Reynolds stresses and contributions of burst-sweep cycles

to the Reynolds shear stress.

Comparative study shows that there were substantial changes in the turbulence properties

and drag coefficients associated with different stoss-side slopes especially in the near-bed

area and in the vicinity of the crest positions. Although the artificial rigid isolated upstream-

facing bedform structure is not the exact representative situation in the riverine environment,

this study provides a knowledge of flow characteristics and resistance due to form drag over

the structures in reverse/tidal flow condition. Several conclusions can be drawn from the

present experimental simulations:

– The longitudinal velocity profiles for the bedform with smaller stoss-side angle (SFFS

case) follow the log-law (except at the crest location), similar to the observation of

1 3


26/29

Environ Fluid Mech

Lefebvreet al.[28]. However, forthe structure with vertical stoss face (VFFS), thevelocity

profiles follow the log-law up to just upstream of the corresponding crest location.

– A permanent flow separation region with a recirculating eddy is observed at just down-

stream of the crest of the bedform with vertical stoss-side (VFFS case), while no flow

separation zone is observed over the bedform with smaller stoss-side angle (SFFS case).Comparison with previous studies for ebb flow condition readily showed that the size and

the location of flow reversal zone are influenced by changes in bed geometry during the

tidal/flood flow condition. The threshold condition of the development of flow separation

zone in lee side of the bedform structures; and the dependence of stoss and lee angles

to turbulence parameters, drag coefficients during the tidal conditions are worthy of this

study.

– Maximum value of the longitudinal and vertical turbulence intensities for the SFFS case

and the longitudinal turbulence intensity for VFFS attained at the vicinity of the respective

crest locations. However, the vertical turbulence intensity for VFFS case attained its

maximum at some distance downstream of the crest over the lee portion.

– Maximum longitudinal intensity was five times greater than the maximum vertical inten-

sity for the structure with smaller stoss-slope (SFFS case) for the case simulating a tidal

flow condition, which is greater in comparison with ebb flow condition [ 36] over similar

structure.

– Greatly affected Reynolds shear stress was noticed due to different structural geometries

enhancing different local flow conditions. The maximum normalized Reynolds shear

stress for the structure with smaller stoss-slope is just about half of that for the ebb flow

condition [36] over the similar structure.

– A quadrant decomposition technique was adopted to discriminate the turbulent events dueto different structures. Importantly in the vicinity of the crest locations for both structures,

inward and outward interactions were mostly contributed to the Reynolds shear stress.

Other-wise sweeps and ejections were the two most dominant events.

– Near the bottom region, adjacent to the lee face, the sweeps have greater contributions

to the Reynolds shear stress for the structure with vertical stoss-face (VFFS), which

contributed to enhance the avenue of entraining particles and for the other structure

(SFFS), it was the ejections which is responsible for movement of sediment particles.

– A great enhancement in flow resistance due to the structure with vertical stoss-face (VFFS

case) was observed and hence a reduction in overall drag was achieved in the case of

smaller stoss side sloped structure (SFFS case) as there is no flow separation.

This study could provide a better understanding of turbulence, if there would be a bed

covered by such waveforms rather than an isolated feature. It is of future interest to improve

our understanding of turbulence and resistance due to form drag over a series of forward-

facing bedform structures in the flood-tide condition; and to study the effect of different stoss

side angles of bedform structures. Detailed investigations are important to formulate a better

modelling of three-dimensional flow structures for different Reynolds numbers associated

with a series of forward-facing dunes oriented against the flow for a wide range of parameters,

which will help the researcher to understand the mean flow, turbulence and drag in the fields

of geology, geophysics, hydraulics and river engineering.

Acknowledgments One of the authors (BSM) would like to express his sincere thanks to Professor Stephen

G. Monismith, Director of Environmental Fluid Mechanics Laboratory (EFML), Stanford University, USA for

suggesting the problem and constructive technical discussions on the work during BSMs visits to the EFML,

Stanford University, California, USA. The authors would like to acknowledge the Department of Science

and Technology (DST), New Delhi for the financial support for this research work at the Fluvial Mechanics

1 3


27/29

Environ Fluid Mech

Laboratory (FML), Indian Statistical Institute, Kolkata, India; and many thanks to two anonymous referees

and Associate Editor, Professor Hubert Chanson for their detailed and constructive input on the paper.

References

1. Addad YD, Laurence CT, Jacob MC (2003) Large eddy simulation of a forward–backward facing step

for acoustic source identification. Int J Heat Fluid Flow 24:562–571

2. Agelinchaab M, Tachie M (2008) PIV study of separated and reattached open channel flow over surface

mounted blocks. ASME J Fluids Eng 130(6):061206–061214

3. Ando T, Shakouchi T (2004) Flow characteristics over forward facing step and through abrupt contraction

pipe and drag reduction. Res Rep Fac Eng Mie Univ 29:1–8

4. Armaly BF, Durst F, Pereira JCF, Schonung B (1983) Experimental and theoretical investigation of

backward-facing step flow. J Fluid Mech 127:473–496

5. Ashley GM (1990) Classification of large-scale subaqueous bedforms: a new look at an old problem.

J Sediment Petrol 60:160–172

6. Barkley D, Gomes M, Henderson R (2002) Three-dimensional instability in flow over a backward-facing

step. J Fluid Mech 473:167–190

7. Bennett JP (1997) Resistance, sediment transport, and bedform geometry relationships in sandbed chan-

nels. In: Proceedings of the U.S. Geological Survey (USGS) sediment, workshop, 4–7 Feb

8. Bennett SJ, Best JL (1995) Mean flow and turbulence structure over fixed, two-dimensional dunes:

implications for sediment transport and bedform stability. Sedimentology 42:491–513

9. Best J (2005) The fluid dynamics of river dunes: a review and some future research directions. J Geophys

Res 110:F04S02. doi:10.1029/2004JF000218

10. Best J, Kostaschuk RA (2002) An experimental study of turbulent flow over a low-angle dune. J Geophys

Res 107(C9):18(9)–18(19). doi:10.1029/2000JC000294

11. Camussi R, Felli M, Pereira F, Aloisio G, Marco AD (2008) Statistical properties of wall pressure fluc-

tuations over a forward-facing step. Phys Fluids 20(7):075113

12. Casarsa L, Giannattasio P (2008) Three-dimensional features of the turbulent flow through a planar sudden

expansion. Phys Fluids 20(1):015103

13. Cellino M, Graf WH (2000) Experiments on suspension flow in open channels with bed forms. J Hydraul

Res 38(4):289–298

14. Dinehart RL (2002) Bedform movement recorded by sequential single-beam surveys in tidal rivers.

J Hydrol 258:25–39

15. Eaton JK, Johnston JP (1981) A review of research on subsonic turbulent flow reattachment. AIAA

J 19:1093–1100

16. Ernstsen VB, Noormets R, Winter C, Hebbeln D, Bartholoma A, Flemming BW, Bartholdy J (2006)

Quantification of dune dynamics during a tidal cycle in an inlet channel of the Danish Wadden Sea.

Geo-Mar Lett 26(3):151–163

17. Gabel SL (1993) Geometry and kinematics of dunes during steady and unsteady flows in the Calamus

River, Nebraska, USA. Sedimentology 40(2):237–26918. Goring DG, Nikora VI (2002) Despiking acoustic Doppler velocimeter data. J Hydraul Eng 128(1):

117–126

19. Jackson RG (1976) Sedimentological and fluid-dynamic implications of the turbulent bursting phenom-

enon in geophysical flows. J Fluid Mech 77:531–560

20. Julien PY, Klaassen GJ (1995) Sand-dune geometry of large river during floods. J Hydraul Eng

121(9):657–663

21. Kaftori D, Hetsroni G, Banerjee S (1998) The effect of particles on wall turbulence. Int J Multiphase

Flow 24(3):359–386

22. Kiya M, Sasaki K (1983) Structure of a turbulent separation bubble. J Fluid Mech 137:83–113

23. Kostaschuk RA, Best JL (2005) The response of sand dunes to variations in tidal flow. J Geophys Res

110:F04S04. doi:10.1029/2004JF000176

24. Kostaschuk RA, Church MA (1993) Macroturbulence generated by dunes: Fraser River, Canada. SedimentGeol 85:25–37

25. Kostaschuk RA, Villard PV (1996) Flow and sediment transport over large subaqueous dunes: Fraser

River, Canada. Sedimentology 43:849–863

26. Largeau J, Moriniere V (2007) Wall pressure fluctuatings and topology in separated flows over a forward-

facing step. Exp Fluids 42(1):21–40

27. Le H, Moin P, Kim J (1997) Direct numerical simulation of turbulent flow over a backward-facing step.

J Fluid Mech 330:349–374

1 3

http://dx.doi.org/10.1029/2004JF000218http://dx.doi.org/10.1029/2004JF000218http://dx.doi.org/10.1029/2000JC000294http://dx.doi.org/10.1029/2000JC000294http://dx.doi.org/10.1029/2004JF000176http://dx.doi.org/10.1029/2004JF000176http://dx.doi.org/10.1029/2004JF000176http://dx.doi.org/10.1029/2000JC000294http://dx.doi.org/10.1029/2004JF000218


28/29

Environ Fluid Mech

28. Lefebvre A, Ernstsen VB, Winter C (2011) Influence of compound bedforms on hydraulic roughness in

a tidal environment. Ocean Dyn 61(12):2201–2210

29. Lefebvre A, Ernstsen VB, Winter C (2013) Estimation of roughness lengths and flow separation over

compound bedforms in a Natural Tidal inlet. Cont Shelf Res 61–62:98–111

30. Lefebvre A, Ferret Y, Paarlberg AJ, Ernstsen VB, Winter C (2013) Variation of flow separation over large

bedforms during a tidal cycle. In: Marine and river dune dynamics MARID IV, Bruges, Belgium, 15 and16 April, pp 169–175

31. Lu SS,Willmarth WW (1973) Measurements of thestructure of theReynolds stressin a turbulent boundary

layer. J Fluid Mech 60:481–512

32. Lyn DA (1993) Turbulence measurements in open channel flows over artificial bed forms. J Hydraul Eng

119(3):306–326

33. Mao Y (2003) The effects of turbulent bursting on the sediment movement in suspension. Int J Sediment

Res 18(2):148–157

34. Martinius AW, Gowland S (2010) Tide-influenced fluvial bedforms and tidal bore deposits (Late Juras-

sic Lourinha Formation, Lusitanian Basin, Western Portugal). Sedimentology. doi:10.1111/j.1365-3091.

2010.01185.x

35. Mazumder BS, Ray RN, Dalal DC (2005) Size distributions of suspended particles in open channel flow

over bed materials. Environmetrics 16(2):149–16536. Mazumder BS, Pal DK, Ghoshal K, Ojha SP (2009) Turbulence statistics of flow over isolated scalene

and isosceles triangular-shaped bedforms. J Hydraul Res 47(5):626–637

37. McLean SR, Wolfe SR, Nelson JM (1999) Spatially averaged flow over a wavy boundary revisited.

J Geophys Res 104(C7):15743–15753

38. Mendoza C, Shen HW (1990) Investigation of turbulent flow over dunes. J Hydraul Eng 116(4):459–477

39. Nakagawa H, Nezu I (1981) Structure of space–time correlations of bursting phenomena in an open-

channel flow. J Fluid Mech 104:1–43

40. Nezu I, Nakagawa H (1993a) Three-dimensional structures of coherent vortices generated behind dunes

in turbulent free-surface flows. Refined flows modelling and turbulence measurements. In: Proceedings

of the 5th international symposium, Paris, pp 603–612

41. Nezu I, Nakagawa H (1993b) Turbulence in open channel flows. IAHR monograph. Balkema, Rotterdam.

ISBN 90-5410-118-042. Nezu I, Rodi W (1986) Open-channel measurements with a laser Doppler anemometer. J Hydraul Eng

112(5):335–355

43. Ojha SP, Mazumder BS (2008) Turbulence characteristics of flow region over a series of 2-D dune shaped

structures. Adv Water Resour 31:561–576

44. Paarlberg AJ, Dohmen-Janssen CM, Hulscher SJMH, Termes P (2009) Modelling river dune evolution

using a parameterization of flow separation. J Geophys Res 114:F01014

45. Pearson DS, Goulart PJ, Ganapathisubramani B (2011) Investigation of turbulent separation in a forward-

facing step flow. In: 13th European turbulence conference. J Phys Conf Ser 318. doi:10.1088/1742-6596/

318/2/022031

46. Poole RJ, Escudier MP (2003) Turbulent flow of a viscoelastic shear-thinning liquid through a plane

sudden expansion of modest aspect ratio. J Non-Newton Fluid Mech 112:1–26

47. Ren H, Wu Y (2011) Turbulent boundary layers over smooth and rough forward-facing steps. Phys Fluids23(4):1–17

48. Saleel CA, Shaija A, Jayaraj S (2011) Numerical simulation of fluid flow over a forward–backward facing

step using immersed boundary method. Int J Eng Sci Technol 3(10):7714–7729

49. Sherry MJ, Jacono DL, Sheridan J (2010) An experimental investigation of the recirculation zone formed

downstream of a forward facing step. J Wind Eng Ind Aerodyn 98:888–894

50. Singh AP, Paul AR, Ranjan P (2011) Investigation of reattachment length for a turbulent flow over a

backward facing step for different step angle. Int J Eng Sci Technol 3(2):84–88

51. Smith JD, McLean SR (1977) Spatially averaged flow over a wavy surface. J Geophys Res 82(12):

1735–1746

52. Stuer H, Mass HG, Virant M, Becker J (1999) A volumetric 3D measurement tool for velocity field

diagnostic in microgravity experiments. Meas Sci Technol 10:904–913

53. Toyama A, Shimizu Y, Yamaguchi S, Giri S (2007) Study of sediment transport rate over dune-coveredbeds. In: 5th IAHR symposium on river, coastal and estuarine morphodynamics. University of Twente,

Enschede

54. Vanoni V, Hwang LS (1967) Relation between bed form and friction in streams. J Hydraul Div Am Soc

Civ Eng 93(HY3):121–144

55. Venditti JG (2007) Turbulent flow and drag over fixed two- and three-dimensional dunes. J Geophys Res

112:F04008

1 3

http://dx.doi.org/10.1111/j.1365-3091.2010.01185.xhttp://dx.doi.org/10.1111/j.1365-3091.2010.01185.xhttp://dx.doi.org/10.1111/j.1365-3091.2010.01185.xhttp://dx.doi.org/10.1088/1742-6596/318/2/022031http://dx.doi.org/10.1088/1742-6596/318/2/022031http://dx.doi.org/10.1088/1742-6596/318/2/022031http://dx.doi.org/10.1088/1742-6596/318/2/022031http://dx.doi.org/10.1111/j.1365-3091.2010.01185.xhttp://dx.doi.org/10.1111/j.1365-3091.2010.01185.x


29/29

Environ Fluid Mech

56. Winter C, Ferret Y, Lefebvre Y, Ernstsen VB (2013) Geometric properties of hydraulically-relevant tidal

bedforms. In: Marine and river dune dynamics MARID IV, Bruges, Belgium, 15 and 16 April, pp 337–338

57. Wu Y, Christensen KT (2006) Reynolds-stress enhancement associated with a short fetch of roughness

in wall turbulence. AIAA J 44(12):3098–3106

58. Zarillo GA (1982) Stability of bedforms in a tidal environment. Mar Geol 48:337–351

turbulent flow characteristics and drag over 2d dune shaped structures

Documents

Transcript of turbulent flow characteristics and drag over 2d dune shaped structures