Derivation of The Wave Speed-Discharge Relationship from Cross Section Survey For Use In Approximate Flood Routing Methods
PhD thesis by Tang X., 1999

The PhD work of Tang was related to a theoretical understanding of how two key flood routing parameters, wave speed and attenuation, are linked to the geometry of the channel cross-section. The aim, described further in Paper 83, was to tackle the practical problem in flood routing of how to estimate the speed of propagation of the flood wave. It is well known that this propagation speed varies with the discharge in quite a complex manner for natural rivers.

Introduction

The principal innovative step in this thesis is the identification of a relatively simple conceptual model of river geometry to obtain two methods for generating realistic wave speeds from standard river cross-section survey. These are verified against data from two rivers in the UK, showing good agreement with wave speeds deduced from long term records. This work has particular value in building forecasting models of un-gauged or partially gauged river systems, as it removes the need for long term concurrent records to estimate wave speeds. The two methods were incorporated into the Variable Parameter Muskingum-Cunge (VPMC) method of analysis for rapid assessment of flooding problems at river basin scale.

The post-doctoral work was aimed at obtaining very detailed sediment transport data, together with some velocity and boundary shear stress data, for overbank flows in channels with roughened floodplains. It thus continued, at a smaller scale, the work of Brown who used the large-scale Flood Channel Facility (FCF) at HR Wallingford. The experimental work at Birmingham used the same flume as Ayyoubzadeh and Atabay (see files), with an 18m long compound section built within it. The main channel was of fixed rectangular size, with a mobile bed of sand (d 35 = 0.8 mm) of the same size as used in the FCF..

The two symmetric floodplains had their roughness varied by the insertion of wire meshes at varying longitudinal distances, thus altering the floodplain roughness in a systematic way. Quasi-equilibrium conditions were obtained for each floodplain roughness, and measurements made of sediment transport rates, velocity and boundary shear stress distributions. A later series of experiments was undertaken with non-equilibrium conditions, altering the sediment feed or re-circulation rate, thereby causing either deposition or erosion along the channel bed. See listed papers and reports.

Abstract

Approximate flood routing methods are reviewed, particularly the Muskingum-Cunge method and Price's diffusion wave model. Some technical issues in both methods are examined through a number of numerical experiments, for both inbank flows and overbank flows. Some new issues, arising from the tests for overbank flows, are highlighted in this thesis, such as an unrealistic oscillation in the recession stage and some volume loss of outflow in very mild slope channels.

A thorough discussion of the governing equations for flood routing is also carried out, and based on the general equations of 1-D unsteady gradually-varied open channel flow, a generalized diffusion wave equation with inertial terms is derived. This leads to four inertial models for flood routing: non-inertial, local-inertial, convective-inertial and full-inertial models. An analysis of these four models shows that only the momentum correction coefficient, p, has an effect on the selection of the inertial models, and that the non-inertial model is the best approximation to the full inertial model when 1 < P < 3/2. Other forms of generalized diffusion wave equations are discussed, and a new analytical solution of the constant parameter convection-diffusion equation is derived.

A completion comparison of several variable parameter Muskingum-Cunge (VPMC) schemes suggests that VPMC4-4 & VPMC4 are the two best schemes. Numerical tests and mathematical analysis demonstrate that the constant parameter Muskingum-Cunge (CPMC) always conserves volume of outflows, but VPMC does not. A robust and accurate variable parameter method for flood routing (VPMC4-H) is developed.

Two key routing parameters (wave speed and wave attenuation) were examined. Their variation with discharge was explored based on the geometry of the river cross-section and by considering storage effects. Two approaches, the vertical moving boundary (VMB) or RIBAMAN approach and the width-modified approach, are proposed and studied in order to produce reasonable c~Q relationships for compound rivers/channels. Field data confirm that the VMB method and modified RIBAMAN approach are appropriate to predict the c~Q curves based on the hydraulic features and the geometry of the cross-sections alone. Finally the simulated results by the VPMC method agree reasonably well with the recorded data of three flood events in the river Wye, although further field data are required for precise comparisons.

Some suggestions for future studies are included at the end of the thesis.

Data files

Experiments were carried out by X. Tang on the flume of Birmingham University, which is a non-tilting 22m long flume with a test length of 18m. The flume was 1213mm wide, and configured into a two-stage channel with a 398mm wide, 50mm deep mobile bed main channel composed of sand, and two rigid 407.3 mm wide floodplains, as shown in Fig.1. The flume had water supplied through a circulation system comprising of three pipelines, 50mm, 100mm and 150mm in diameter, and discharges were measured by an electro-magnetic flow meter, a Venturi meter and a Dall tube respectively. Sand, with a d35 = 0.80mm, was re-circulated in the flume via a Linatek slurry pump and the 50mm pipeline. Water surface profiles were measured directly using pointer gauges, and uniform flow was set up through adjustments to three tailgates until the mean water surface slope was equal to the valley slope of the floodplain, fixed at 2.024 x 10^-3. The floodplains were made of smooth PVC material and left in this state when studying flows with smooth floodplains. For the study of roughened floodplains, four different floodplain roughnesses were created using metal meshes. These meshes had a width of 355 mm, a height of 145mm and an angle of 30 degrees, and were placed at 4 different interval spacings (l =3.0m, 1.0m, 1/2m and 1/4m) on each floodplain in order to provide a particular roughness. A separate series of experiments was undertaken to ascertain their precise resistance properties.

Data for mobile main channel with rough floodplains and experimental data of roughness on metal meshes are presented here. Other data are given respectively by Ayyoubzadeh (mobile, inbank flow and asymmetric compound channel) and Atabay (rigid/mobile smooth channels -inbank and overbank flows)

Details on the notation and programme are given in Notes on Birmingham data. Data files are in Microsoft Excel format (raw data + analysis), which are regrouped and listed in the following manner. All files need to be unzipped using WINZIP and then opened with MS Excel.

Fig. 1

Fig 1: Schematic cross-section of the flume at the University of Birmingham

Data file links

Rigid channels

Rough - simple channels (inbank flow)

Rough - compound channels (overbank flow) - large wire meshes

Smooth - simple channels (inbank flow) - see Atabay's data

Smooth - compound channels (overbank flow)

Mobile channels (mobile main channel bed and rigid floodplain)

Inbank flows and asymmetric compound channels, see Ayyoubzadeh's data

Overbank flows (smooth floodplain) - both symmetric and asymmetric

Overbank flows (rough floodplain) - symmetric channels

Overbank flows (smooth floodplain) - symmetric channels, non-equilibrium

Notes on Tang's Birmingham data

The flume of Birmingham University is a non-tilting 22m long flume with a test length of 18m. The flume was 1213mm wide, and configured into a two-stage channel with a 398mm wide, 50mm deep mobile bed main channel composed of sand, and two rigid 407.3 mm wide floodplains, as shown in Fig.1. The flume had water supplied through a circulation system comprising of three pipelines, 50mm, 100mm and 150mm in diameter, and discharges were measured by an electro-magnetic flow meter, a Venturi meter and a Dall tube respectively.

The flume can be configured into different channels, such as rigid simple rectangual channel, rigid rectangual compound channels (symmetric and asymmetric) and mobile main channel bed with rigid floodplains (symmetric and asymmetric). Their cross-sections are illustrated in Fig.2.

For the experiments of mobile bed, sand, with a d35 = 0.80mm, was re-circulated in the flume via a Linatek slurry pump and the 50mm pipeline. Water surface profiles were measured directly using pointer gauges, and uniform flow was set up through adjustments to three tailgates until the mean water surface slope was equal to the valley slope of the floodplain, fixed at 2.024 x 10^-3. The floodplains were made of smooth PVC material and left in this state when studying flows with smooth floodplains. For the study of roughened floodplains, four different floodplain roughnesses were created using metal meshes. These meshes had a width of 355 mm, a height of 145mm and an angle of 30 degrees, as shown in Fig. 3, and were placed at 4 different interval spacings (l = 3.0m, 1.0m, 1/2m and 1/4m) on each floodplain in order to provide a particular roughness. A separate series of experiments was undertaken to ascertain their precise resistance properties.

Fig 1: Schematic cross-section of the flume at the University of Birmingham

Fig 2: Cross-section of Birmingham Flume (different configuration)


Summary list of Birmingham experimental data

Notes

In the above tables, TGL, Vel, BSS, Sed,Cs, BF mean the measurement of H-Q, Velocity, Boundary Shear Stress, Sediment Transport Rate, Dune Migration Rate, Bed Profile respectively.

Publications and reports

Publications

  • Tang, X., Knight, D.W., and Samuels, P.G., 1999, Volume conservation in variable parameter Muskingum-Cunge method, Journal of Hydraulic Engineering, ASCE, Vol. 125, No. 6, June, 610-620. [J]
  • Tang, X., Knight, D.W., and Samuels, P.G., 1999, "Variable parameter Muskingum-Cunge method for flood routing in a compound channel", Journal of Hydraulic Research, IAHR, Vol. 37, No. 5, 591-614. [J]
  • Tang, X., Knight, D.W., and Samuels, P.G., 2001, Wave speed-discharge relationship from cross-section survey, Proc. Instn. of Civil Engineers, Water and Maritime Engineering, London, 148, June, Issue 2, 81-96. [J]
  • Tang, X., and Knight, D.W., 2001, Migration rate of bed forms in a compound channel with overbank flow, Proc. 2 nd IAHR Symposium on River, Coastal and Estuarine Morphodynamics, September, Obihiro, Japan, 545-553. [C]
  • Tang, X., and Knight, D.W., 2001, Analysis of bed form dimensions in a compound channel, Proc. 2 nd IAHR Symposium on River, Coastal and Estuarine Morphodynamics, September, Obihiro, Japan, 555-563. [C]
  • Tang, X., and Knight, D.W., 2001, Experimental study of stage-discharge relationships and sediment transport rates in a compound channel, Proc. 29th IAHR Congress, Hydraulics of Rivers, Theme D, Vol II, September, Beijing, China,Tsinghua University Press, 69-76. [C]
  • Tang, X. and Knight, D.W., 2003, Study of sediment transport in a compound channel with non-uniform flow, Proc. 3 rd Int Conf. on River, Coastal and Estuarine Morphodynamics, Barcelona, 857-864. [C]
  • Tang, X. and Knight, D.W., 2005, Sediment transport in river models with overbank flows, Journal of Hydraulic Engineering, ASCE, (in press) [J]
  • Knight, D.W., Omran, M. & Tang, X., 2005, Modelling depth-averaged velocity and boundary shear in trapezoidal channels with secondary flows, Journal of Hydraulic Engineering, ASCE, (submitted) [J]

Reports

  • Knight, D.W., 2002, Sediment transport in river models with overbank flows, Final report to EPSRC on grant GR/M41797, 1-6
  • Knight, D.W., 2002, A scheme for enabling the adoption and application of alternative conveyance formulations in river models, Final report to EPSRC on grant GR/M13202, 1-6