Hydraulic influences on dispersion and reaeration in rivers

Abstract

An important application of environmental hydraulics is the prediction of the fate and transport of dissolved oxygen within fluvial systems. For rivers this requires knowledge of the principle hydrological processes such as advection and dispersion and the physico-chemical process of re-aeration. Currently, in the absence of appropriate field measurements quantifying the mixing or aeration processes in a river, we rely on semi-empirical predictive equations that attempt to relate these processes to global flow and channel parameters. Although there is some theoretical justification for the form of these equations, they are not particularly successful even for channels of simple shape. As more complex channel shapes (e.g. two-stage flood relief channels) are tackled the equations become increasingly inappropriate. To help address this concern, the chapter proposes a theoretical approach for evaluating both the longitudinal dispersion coefficient and the re-aeration coefficient in channels of arbitrary shape that is based on integral formulations and which uses theoretical predictions of the transverse flow structure that are based on Shiono and Knight’s (J Fluid Mech 222:617–646, 1991) momentum balance equation. The results for a simple channel (trapezoidal) are consistent with current knowledge, but they reveal unexpected patterns for a complex channel (two-stage, trapezoidal with active floodplains) that contains zones of distinctly different velocity and depth. The results also explore the role of the transverse turbulent transfer of momentum. For the simple channel, the dispersion coefficient was very small (being in the range 0–1 m2/s for flow rates between 0 and 35 m3/s and channel widths of approximately 15 m), and increased approximately linearly with flow rate. The influence of the transverse turbulent momentum exchange was relatively significant. For the complex channel, the dispersion coefficient was very large (being in the range 27,000–500 m2/s for flow rates between 35 and 175 m3/s and widths of approximately 55 m), and decreased with flow rate according to a power law with an exponent of about −4.7. The influence of the transverse turbulent momentum exchange was less than for the simple channel case. The predictions for both flow conditions are consistent with observed trends reported in Rutherford (River mixing. Wiley, Chichester, 1994). The very large dispersion coefficients found in the complex channel case could not be predicted using the existing semi-empirical equations proposed by Liu (J Environ Eng Div, Am Soc Civil Eng 103(EE1):59–69, 1977) and Deng et al. (J Hydraul Eng, Am Soc Civil Eng 127(11):919–927, 2001); neither could the rapid decrease with increasing flow rate. This is not surprising because the equations cannot represent the extremely strong transverse velocity shear that exists in these flows that contain zones of quite different velocity and depth. For the re-aeration coefficient in the simple channel we identified a power law decrease (exponent of about −0.5) with flow rate from about 40 to 10 per day up to the bank full condition. Once flows went over-bank the re-aeration coefficient jumped considerably (to about 100 per day) due to the small depths on the floodplains. It then reduced as a power law as flow rate increased (exponent of about −0.9). The influence of the transverse turbulent momentum exchange was not very significant for either channel case. Results from a semi-empirical equation proposed by Bennett and Rathbun (Reaeration in open-channel flow. United Sates Geological Survey, Washington, 74 pp, 1972) mirrored the computational results, but underpredicted the coefficient by about 50 % for both the simple and complex channel cases. Clearly, existing semi-empirical equations for the dispersion coefficient and the re-aeration coefficient should not be used for predicting non-conservative chemical transport for the over-bank case of a complex channel. A sensitivity analysis for the case of a steady oxygen demanding waste water discharge showed that the maximum dissolved oxygen sag and its location were insensitive to dispersion but were significantly sensitive to re-aeration for both channel cases. Hence, for this waste water scenario future work should focus on improving the prediction of re-aeration coefficients in both types of channel.