The behaviour of turbulence in unsteady open channel flow: a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Civil Engineering at the University of Canterbury / by Alan Ernest Hunt.

Typescript (photocopy).

Thesis (Ph. D.)--University of Canterbury, 1997.

Includes bibliographical references.

1 Introduction -- 1.1 Project Scenario -- 1.2 Experimental Objectives -- 1.3 Thesis Structure -- 1.4 References -- 2 Literature Review -- 2.1 Introduction -- 2.2 Turbulence -- 2.2.1 The History of Turbulence Research -- 2.2.2 Flow Structure -- 2.2.3 Reynolds Number Effects -- 2.2.4 The Spectrum of Turbulence -- 2.2.5 Numerical Modelling -- 2.3 Open Channel Flow -- 2.3.1 Steady Flow -- 2.3.1.1 The Effect of Channel Characteristics -- 2.3.1.2 Sediment Transport Effects -- 2.3.1.3 Pressure Gradient Effects -- 2.3.2 Unsteady Flow -- 2.3.2.1 Mean Flow Unsteadiness -- 2.3.2.2 Unsteadiness and Sediment Transport -- 2.3.2.3 Turbulence Behaviour -- 2.4 References -- 3 Experimental Programme -- 3.1 Introduction -- 3.2 Laboratory Configuration -- 3.2.1 Water Supply -- 3.2.2 The Flume -- 3.3 Experimental Methodology -- 3.4 Flow Measurement -- 3.4 .1 Depth Probe -- 3.4.2 Flow Meter -- 3.4.3 Laser Doppler Anemometer -- 3.4.3.1 LDA Configuration -- 3.4.3.2 Velocity Determination -- 3.4 .4 Flow Visualisation -- 3.5 Data Acquisition -- 3.6 Flows to be Examined -- 3.6.1 Steady Flow -- 3.6.2 Unsteady Flow Hydrographs -- 3.7 Control Systems -- 3.7.1 Inflow Control -- 3.7.2 Downstream Control -- 3.8 References -- 4 Flow Data Presentation -- 4.1 Introduction -- 4.2 Analytical Procedure -- 4.2.1 Friction Slope -- 4.2.2 Unsteady Flow Duration -- 4.2.3 Velocity Decomposition -- 4.3 Flow Structure -- 4.3.1 Mean Flow Structure -- 4.3.2 Turbulence Structure -- 4.4 Temporal Turbulence Behaviour -- 4.4.1 Steady Flow Turbulence -- 4.4.2 Unsteady Flow Turbulence -- 4.5 Flow Visualisation -- 4.6 References -- 5 Theoretical Analysis -- 5.1 Introduction -- 5.2 Spectral Analysis -- 5.2.1 The Turbulent Energy Spectrum -- 5.2.2 Calculation of the 1-D Spectrum -- 5.2.3 Turbulent Kinetic Energy Calculation -- 5.3 Turbulent Kinetic Energy Budget -- 5.4 Quantifying Unsteadiness -- 5.4.1 Mean Flow Unsteadiness -- 5.4.1.1 Flood Routing -- 5.4.1.2 Hydrograph Unsteadiness Parameters -- 5.4.2 Unsteadiness in Turbulence -- 5.5 Pressure Gradients -- 5.5.1 1996 Study by Song and Graf -- 5.5.2 Boundary Layer Theory -- 5.5.3 Mean Flow Divergence -- 5.6 Flow Resistance -- 5.7 Secondary Flow Patterns -- 5.8 Time Scales -- 5.9 References -- 6 Interpretation of Results -- 6.1 Introduction -- 6.2 A Scenario for Turbulence -- 6.2.1 Evidence Obtained -- 6.2.2 The Postulation of Mechanisms -- 6.2.2.1 Additional Source of Turbulence -- 6.2.2.2 Mean Flow and Turbulence Coupling -- 6.2.2.3 Unsteadiness and Hazard -- 6.3 Methodology Review -- 6.4 References -- 7 Conclusion -- 7.1 Findings from this Study -- 7.1.1 Experimental Conclusions -- 7.1.2 Turbulence Conjecture -- 7.2 Recommendations for Future Research -- Appendix -- A Calibrations for the LDA -- A.1 Calibration of the Doppler Signal Processor -- A.2 LDA Velocity Calibration -- B Point Velocity Acquisition Parameters -- B.1 Steady Flows -- B.2 Unsteady Flow Hydrographs -- C Boundary Layer Theory -- D Inflow Control System -- D.1 Proportional Integral Derivative Control -- D.1.1 Proportional Control -- D.1.2 Integral Control -- D.1.3 Derivative Control -- D.1.4 Three Mode Control -- D.2 Experimental Control Variables -- D.3 References -- E Flow Data -- E.1 Hydrograph Repeatibility -- E.1.1 Flow Rate -- E.1.2 Flow Depth -- E.2 Unsteady Flow 1 (HI} Data -- E.3 Unsteady Flow 2 (H2} Data -- E.4 Unsteady Flow 3 (H3} Data -- E.5 Steady Flow Data -- E.6 Wave Shape Assessment -- E.7 Rotta Flow Equilibrium -- F Downstream Control System -- F.1 System Methodology -- F.2 Sluice Gate Control -- F.2.1 Sluice Gate Calibration -- F.2.2 Depth Probe Calibration -- F.2.3 Feedback Relation -- F.2.4 Software Development -- F.2.5 SUGAR (Control program for H1) -- F.3 References

An investigation into the behaviour of the turbulence during laboratory simulations of floods in rivers with mild bed slopes was undertaken. Computer control of the flow rate into the flume enabled reproducible flood waves to be generated. To rigorously model the energy gradients in a long channel, an interactive sluice gate control was developed for the downstream end of the flume. Mean flow unsteadiness effects on the turbulence were evaluated by considering different duration hydrographs with similar shapes and magnitudes. The investigation was limited to the longitudinal component of turbulence, as a one-component laser Doppler anemometer was employed for the determination of point velocities. Flow visualisation using a dye plume supplemented velocity data. It was observed that for events having a shorter duration the peak turbulent intensity had a greater magnitude, and occurred relatively earlier on the rising limb of the flood. The turbulent energy peak coincided with the maximum flow rate divergence. For increasing flow divergence magnitude, which only occurs on the rising limb, the production of turbulence was larger than dissipation, with the transport of turbulence providing an additional sink for turbulent energy. After the depth had peaked the flow experienced pseudo-equilibrium conditions, where the transport mechanism was insignificant and the rate of production approximated dissipation. A feature of the falling limb was a period of inactivity, in which the magnitudes of production and dissipation were at minimum. A second -5/3 slope region was observed in the energy spectra. The length scale associated with an energy source for this double structure was two orders of magnitude larger than the Kolmogorov dissipation length scale. Decay times for flow structures of this size are similar to the duration of these hydrographs. It is possible that the unsteady flow created vortex structures that persisted for some time after the flow which generated them had moved downstream. These vortex structures, which provide a turbulence memory mechanism, and the state of pseudo-equilibrium on the falling limb are responsible for residual turbulent energy in the flow throughout the falling limb and immediately following the passing of the flood wave. In addition, it is suggested that mean flow controls both the production and dissipation of turbulence, with the dissipation of turbulent kinetic energy being controlled by the diffusion of momentum during low speed streaks. The Kolmogorov scale may be interpreted as defining the critical damping condition along these streaks where Reynolds stresses balance viscous forces.

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