Conveyance Estimation System (CES) Launch

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Berenice Mathews
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1 (CES) Launch Conveyance Principles Caroline McGahey 10 June 2004

2 Why is there a new approach? Existing 1D software still based on historic hand-calculation methods - not based in rigorous physics - as SCM poor predictions for overbank flow - as DCM ignores lateral shearing - all physical processes lumped into one catch-all parameter - Manning n

3 Why is there a new approach? Research advances over past 20 years understanding flow mechanisms quantifying associated energy losses Quality data sets from: - experimental set-ups e.g. FCF - purpose-made river measurements - large scale rivers - EA gauging sites Advent of computing power enabled coding & testing of methods against extensive database

4 Energy transfer mechanisms 2. Momentum Transfer 2. Shear layer Direction of flow 1. Boundary shear stresses 3. Secondary flows

5 Meandering mechanisms

6 Observed flow features Ikeda et al 2001 Shiono & Muto 1998 Sellin 1964 Shiono & Muto 1998 Ikeda et al 2001

7 Meandering velocity profiles U d AA A A AA BB B B C BB C CC Distance across section

8 Conveyance calculation Depth integration of Reynolds-Averaged Navier-Stokes equations dy Integrate unit flow rate q (m 2 /s) Q = qdy 2 K = Q / S f 1

9 Conveyance calculation ghs o β f q 2 8H 2 + y λ H f q y q H = α Γ+ (1 α) y C uvq H 2 I II III IV V I II III IV V hydrostatic pressure boundary friction turbulence due to lateral shear straight secondary flow losses meandering secondary flow losses

10 Calibration coefficients Terms to cover all energy losses - coefficients for: - skin friction f based on RA unit roughness n l - lateral shearing - dimensionless eddy viscosity λ - straight secondary flow losses Γ - meandering secondary flow losses C uv Form loss is not accounted for

11 Calibration parameters f - complete Colebrook-White equation 1 k s 3.09ν = 2.03log + f 12.27H 4q f λ function of relative depth λ ( ) = λ mc Dr

12 Secondary flow model Γ = khρ gs o straight C uv = f ( σ, Dr ) Secondary flow term straight transitional fully meandering Key: C uv Γ total Relative depth Sinuosity

13 Typical distributions f λ Γ C uv Colebrook-White λ = f (λ mc, D r ) Γ fp (-ve) Γ mc (+ve) Γ fp (-ve) Varies with σ, D r Top of bank

14 CES Outputs Cross-section: total flow Q area A conveyance K ave velocity U Re number Fr number α, β Across section: unit flow q unit conveyance k depth-ave U d bed shear stress τ shear velocity U * Fr number f,n l with depth

FCF Straight: Large Scale Bed level (m) 0.35 0.30 0.25 0.20 0.15 0.10 0.05 Depth = 0.249m 0.00 0 1 2 3 4 5 6 7 Lateral distance across channel (m) Bed shear stress (N/m 2 ) 2.4 2.2 2.0 1.8 1.6 1.

15 FCF Straight: Large Scale Bed level (m) Depth = 0.249m Lateral distance across channel (m) Bed shear stress (N/m 2 ) Lateral distance across channel (m) Depth-averaged velocity (m/s) Lateral distance cross channel (m)

River Blackwater Model 0.40 0.35 Sinuosity = 1.1800 Bed level (m) 0.30 0.25 0.20 0.15 0.10 0.05 0.

16 River Blackwater Model Sinuosity = Bed level (m) Lateral distance across channel (m) Depth-averaged velocity (m/s) Lateral distance across channel (m)

17 River Severn, Shrewsbury 1.2 Sinuosity = Depth-averaged velocity (m/s) Elevation (m) Lateral distance across channel (m)

Comparison to isis method 0.16 isis 0.14 CES prediction data Stage (m) 0.12 0.

18 Comparison to isis method 0.16 isis 0.14 CES prediction data Stage (m) Glasgow Flume Discharge (m 3 /s)

4 isis CES Prediction 7.2 data Stage (m) 7.

8 150 200 250 300 Discharge (m 3 /s) Bed

19 Comparison to isis method River 7.8 Severn at Montford Bridge isis CES Prediction 7.2 data Stage (m) Discharge (m 3 /s) Bed level (m) Lateral distance across channel (m)

CES stage-discharge River 2 Main 1.8 1.6 1.

/ lower bands Stage m 1.2 1 0.8 0.6 0.4 0.

20 CES stage-discharge River 2 Main CES central estimate Measured data Credible upper / lower bands Stage m Bed elevation (m) Lateral distance across channel - offset (m) Discharge m 3 /s

This is a repository copy of An analytical model for lateral depth-averaged velocity distributions along a meander in curved compound channels.

This is a repository copy of An analytical model for lateral depth-averaged velocity distributions along a meander in curved compound channels. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/80340/