ENERGY LOSSES IN MEANDERING CHANNELS WITH FLAT AND NATURAL BEDS FOR OVERBANK FLOWS

Shiono, K., Spooner, J., Rameshwaran, P. and Chandler, J.H.

Department of Civil and Building Engineering, Loughborough University, UK

Address: Ashby Road, Loughborough, Leicestershire, LE11 3TU, UK

Tel: +44 (0)1509 222936, Fax: +44 (0)1509 223981, E-mail: k.shiono@lboro.ac.uk

Abstract: Measurements of mean velocity and secondary flow, in meandering channels with flat bed and natural formed bed for overbank, were carried out using Laser Doppler Anemometer. Bed-forms were also measured using automated digital photogrammetry. This enabled the evolution of secondary flow to be identified within the meandering channel. Detailed measurements of secondary flow along a sand bar were also carried out for understanding the interaction between secondary flow and the bed form caused by floodplain flow. A comparative study of flow structures in the meandering channels with flat and mobile beds for overbank flows, was carried out using layer-averaged velocities, longitudinal mean velocities and secondary flow vectors along the meandering channel. The Reynolds stresses on the horizontal plane at bankfull level were measured in order to calculate energy loss owing to turbulence. Energy losses due to secondary flow, turbulence and boundary friction within the main channel were estimated. This result demonstrated significant energy losses due to secondary flow and boundary friction for the natural formed bed case. However, for the flat bed case boundary friction loss is dominant and turbulence loss is relatively significant, but secondary flow loss is small.

Keywords: meandering channel, flat bed, mobile bed, flow structure, energy loss, turbulence

1 INTRODUCTION

There are many meandering channel sections with floodplains along a river system, which frequently becomes inundated. Numerous studies on compound straight and meandering channels with flat bed for overbank flow have been carried out, e.g. Shiono and Knight (1991), Nezu (1994) for straight channels and Shiono and Muto (1998) and Shiono et. al. (1999) for meandering channels. A few studies on straight main channels with mobile bed for overbank flow have been carried out, e.g. Knight and Brown (2001). Flow structures in meandering channels with artificially designed bed for overbank flow, were observed by Willets and Hardwick (1993) and Rameshwaran and Willets (1999). Recently Rameshwaran el. al. (1999) have undertaken flow and bed-form measurements at the FCF, HR Wallingford to show secondary flow and bed-form in the meandering channel for overbank flow. Shiono et. al. (1999) investigated mean energy losses due to boundary friction, secondary flow and turbulence at the bankfull level along the meandering channel with flat bed for overbank flows using the turbulence flow data. Relative magnitudes of those parameters were obtained and they showed that the dominant mechanism for energy loss varies according to the relative depth and sinuosity. However, mechanisms of mean energy loss in the meandering channel with mobile bed have not been studied yet. The interaction between the main channel and floodplain flows and bed-form in the main channel has therefore not been fully understood. This paper attempts to show different mechanisms of energy loss in the main channels with flat and mobile beds for overbank flow through the measurements of secondary flow, velocity and bed form in small meandering two stage channels using a Laser Doppler Anemometer (LDA) and automated digital photogrammetry.

2 EXPERIMENTS

Brief descriptions of experimental apparatus and data collections are given below. The test flume is 2.4m wide, 13m long, and 0.3m deep, has a slope of 1/500 with a water and sand re-circulating system. A series of 120-degree meanders was constructed, with a sinuosity of 1.37 and a crossover length of 750mm. Details of the channel dimensions are given in Table 1 and a plan of the test section is shown in Figure 1. The flow rate was measured by a calibrated orifice plate in the delivery pipe and the water surface slope was measured by means of a point gauge along the channel. The main channel bed consisted of uniform sand with a mean sand diameter of 0.85mm, chosen to allow comparison with work conducted in straight compound channels. Velocity measurements were taken at various cross-sections using a three-component Laser Doppler Anemometer system. The data at each point was collected over 3 minutes with a sampling rate of more than 200Hz.

Both flat bed and natural bed cases were examined, where natural bed refers to bedforms in the main channel formed by the flow. For each experimental depth the water was run initially at bankfull level until the bedforms became fully developed. The water depth was then raised to the overbank condition and run until bedforms were re-established, which normally took 72 hours. The sediment transport rate was manually determined by collecting sediment from the sand re-circulation pipe system for 6 hours after the bedforms were established. The water was then drained and the bedforms were measured using automated digital photogrammetry (Chandler et. al., 2001), the accuracy of which was 2.4mm. The bedforms were then fixed with a thin layer of cement so that they were undisturbed while the velocity measurements were taken.

3 FLOW STRUCTURES

3.1 Layer averaged velocity

The meandering channel was divided at the bankfull level to calculate the layer-averaged velocities below and above the bankfull level. Figures 1 and 2 show the layer-averaged velocities for both the flat and mobile bed cases. In the flat bed case, the upper layer velocity along the crossover reach (e5-e9), adjacent to the upstream floodplain side, is smaller than the lower layer velocity. There is a sharp velocity change across each cross section, the location of which progressively moves from the inner side to the outer side further downstream. For the mobile bed case, the difference of the velocities is less pronounced, except section e3. These differences of flow pattern suggest that there is stronger interaction between the main channel flow and the floodplain flow for the flat bed than for the mobile bed. This implies that more turbulence is generated by the interaction for the flat bed than for the mobile bed.

3.2 Velocity and secondary flow

Figures 3(a) and 3(b) show the mean longitudinal velocity and secondary flow results in the main channel at each measured cross section along the meandering channel for the flat bed case, Dr =0.3. It can be seen from the figures that there are dense contour lines in the vicinity of the bankfull level, adjacent to the upstream floodplain along the crossover reach (e5-e9). This again indicates that there is a strong interaction between main channel flow and floodplain flow. This interaction starts at section e3 and ends at the end of the crossover section, e9. The interaction layer extends laterally as the flow goes downstream. It can also be seen from the secondary flow figures that there are strong lateral velocities, i.e. floodplain flow crossing over the main channel, which correspond to the dense contour lines of the longitudinal velocity. As the floodplain flow starts to plunge into the main channel at section e3, it can be identified from the figures that the secondary flow cell also starts to occur below the bankfull level. This cell develops and occupies in the whole cross section as the flow goes downstream to section e11. In previous work by Knight and Shiono (1996) and Shiono and Muto (1998), they observed more than two secondary flow cells of the same circulation direction at the apex section. This data also shows this but is not clear.

For the mobile bed case, the maximum velocity occurs on the outer bank side after the bend apex and before the crossover reach as shown in Figure 4. It is interesting to notice that the bed level decreases along the crossover section even though the velocity increases. When velocity increases bed scour normally becomes deeper, but this does not appear to happen in this location. There is very small velocity at section e3 just after the bend apex with shallow depth. This is caused by the flow separation behind the bend, and sediment deposits in this area, as it is a dead zone. There are also small velocities along the inner bend region adjacent to the floodplain. Here the bed does not change from the initial level, which indicates that no sediment transport has taken place. This area increases as the section goes downstream.

The secondary flow caused by the floodplain flow appears from section e3 and occupies the whole area where sediment transport has not taken place as mentioned before. There exist many secondary flow cells across section e9, for example, of which are a pair of cells counteracting to maintain the bedforms. More detailed observations of the secondary flow are given in the next section.

The secondary flow structures for the flat and mobile beds are totally different. When secondary flow for the flat bed case is compared with that of Shiono and Muto (1998) who used a smaller aspect ratio of 2.88, it is evident that the flow pattern is the same and the only difference is the size of the secondary flow. The secondary flow occupies the whole cross section for the narrow aspect ratio, but extends only partially across the wide aspect ratio. This indicates that energy loss due to secondary flow for a wide channel may be smaller than that for a narrow channel. For the mobile bed cases, a number of secondary flow cells has been observed in the wavy bedform region. This suggests that energy loss due to secondary flow in the main channel may be larger than that for the flat bed case.

3.3 Evolution of secondary flow

To understand where secondary flow comes from, the measurements of secondary flow along the sand bar were undertaken (Figure 5). It is clearly seen from Figure 5 that the anti-clockwise secondary flow cell is generated at the edge of the floodplain, at section A. This cell grows in size and strength between sections A and D, where the bed also deepens, which suggests that bed erosion is occurring. The cell then decreases in size and strength after section D, where the bed is shallower before finally dissipating. It was also observed that there is a clockwise secondary flow cell on the right side of the ridge generated by flow crossing over the ridge (see sections B-D). This cell increases in size after there is no cross-flow over the ridge at section E, however the strength of the cell is weak as if it is a residual flow. The evidence of the cell weakening can be seen from the reducing bed level after section D. These two cells work together as a counter flow to maintain a regular wavy bed-form. A number of secondary flow cells are initiated by the flood plain flow plunging into the main channel flow. As flood depth increases the strength of secondary flow cells increases, which generates a sand bar in the main channel. Most literature only illustrates a number of secondary flow cells induced by floodplain flow in the main channel but the pair of the secondary flow cells has not been identified before. The secondary flows and bedforms are closely related. This experimental result clearly shows a new secondary flow behaviour in a meandering channel for overbank flow.

4 MEAN ENERGY LOSS

The energy loss coefficients over a half meander for the flat and mobile bed cases were estimated using the method proposed by Shiono et. al., (1999) and are shown in Figure 6. Kts is the energy loss coefficient due to turbulence at the bankfull level as mentioned above. The Reynolds shear stresses (i.e. turbulence) on the horizontal plane at the bankfull level were measured using the LDA. Kbf is the energy loss coefficient due to boundary friction, which was determined by the bed materials. Ksf is the energy loss coefficient due to secondary flow, which was obtained from secondary flow data. Figure 6 shows that for the flat bed, the boundary friction loss, Kbf, is dominant and the turbulence loss, Kts, is relatively significant but the secondary loss, Ksf, is small. For the mobile bed, Kbf and Ksf are equally significant but Kts is small. This suggests that the turbulence at the bankfull for the mobile bed represents a minor component of energy loss. In this calculation of Ksf, it should have included the losses due to both secondary flow and form drag due to bed irregularity. The difference of Ksf between the flat bed and mobile bed also shown in Figure 6 is relatively large until the sediment transport rate rapidly increases at Dr =0.4. At the large relative depth the bedforms become sandbars almost aligned in the floodplain flow direction, hence the form drag becomes small and Ksf also becomes smaller. This comparison reveals a distinct difference of energy loss mechanisms between flat and mobile beds.

5 CONCLUSIONS

Flow and bedform measurements in meandering channels with flat and mobile beds for overbank flow were carried using Laser Doppler Anemometer and automated digital photogrammetry. Differences of flow structures between the flat bed and mobile bed cases were identified. The interaction between the main channel flow and the floodplain flow is larger for the flat bed than for the mobile bed case. Secondary flow cells were generated more for the mobile bed case than for the flat bed case. The mechanisms of energy loss in the main channels with flat bed and mobile bed were found to be totally different.

Acknowledgements

The authors gratefully acknowledge the financial support of Engineering and Physical and Sciences Research Council (EPSRC), UK. We are also grateful to Professor R.A Falconer of Cardiff University, UK for the loan of the Laser Doppler Anemometer system.

References

Chandler, J.H., Rameshwaran, P., Shiono, K., and Lane, S.N. (2001) Measuring Flume Surfaces for Hydraulics research using a Kodak DCS460. Photogrammetric Record (In Press).

Knight, D.W. and Brown, F.A., (2001) Resistance studies of overbank flow in rivers with sediment using the Flood Channel Facility, Journal of Hydraulic Research, IAHR (in press).

Knight, D.W. and Shiono, K. (1996), River channel and floodplain hydraulics, in Floodplain Processes, (Eds. Anderson, Walling & Bates), Chapter 5, J. Wily, pp.139-181.

Nezu, I. (1994), Compound open-channel turbulence and its role in river environment-Significant of secondary flow, Congress of APD-IAHR, Keynote Lecture, Singapore, pp. 1-24.

Rameshwaran, P., Spooner, J., Shiono, K., and Chandler, J.H. (1999), “ Flow Mechanisms in two-stage meandering channel with mobile bed, Proceedings of IAHR Congress in Graz, Austria, 22-27 August, D6.

Shiono, K. and Muto, Y. (1998), “Complex flow mechanisms in compound meandering channel for overbank flow”, Journal of Fluid Mechanics, Vol. 376, pp. 221-261.

Shiono, K. & Knight, D.W. (1991), Turbulent open-channel flows with variable depth across the channel., J. Fluid Mech., Vol.222, pp.617-646.

Shiono, K., Muto, Y., Knight, D.W. and Hyde, A.F.L. (1999) Energy losses due to secondary flow and turbulence in meandering channels with overbank flows.. J. Hydr. Res., 37, 641-664.

Willetts, B.B. & Hardwick, R.I. (1990), Model studies of overbank flow from a meandering channel, Int. Conf. on River Flood Hydraulics, Wallingford, UK, pp. 197-205.

Table 1 Configuration of meandering channel

Main channel sinuosity:		1.3837 (60^o)
Main channel width:		0.4 m
Main channel initial depth:		0.04m
Main channel bank side slope:		90^o
Sediment:		Uniform sand (d₅₀=0.855 mm)
Floodplain longitudinal slope:		1/500
Meander belt width/floodplain width:		1.815m/2.400m
Aspect ratio:		10