Hydraulic roughness in sediment-laden flow

Abstract

Most estuarine, and some coastal, areas are characterised by large amounts of fine-grained cohesive and non-cohesive sediments. At sufficiently high concentrations, sediment transport in suspension may significantly influence the hydrodynamics. In sediment-laden flow with concentrations of approximately, stratification may occur due to a vertical gradient of sediment concentration. In a stratified flow, turbulence is damped due to buoyancy destruction. According to many reports in literature buoyancy destruction results in a decrease of effective hydraulic roughness. Furthermore, the sediment induced stratification causes an appreciable modification of the vertical profiles of velocity, vertical eddy viscosity and shear stresses (e.g. Winterwerp [2001])). Considering the propagation of a tidal wave in estuaries, the decrease of roughness results in an increase of the depth-averaged velocity and an increase of tidal amplitudes of the water level. When modelling flow behaviour in estuarine and coastal environments, vertical gradients of horizontal velocity and sediment and salt concentration in stratified systems can only be simulated with three dimensional numerical modelling. However a full three dimensional model is not always practical. The wide shallow domains that occur in civil engineering practice make depth-averaged simulation often necessary in view of the computational demands. However no theoretically accepted, justifiable parameterisation for effective hydraulic roughness in turbulent sediment-laden flow exists to date. Therefore the effect of suspended sediment on tidal propagation in estuaries is not accounted for in 2Dh modelling. This makes 2Dh modelling intrinsically less accurate than 3D. In case the flow contains an appreciable amount of suspended sediment it is difficult to reliably predict flow behaviour in estuaries through 2Dh modelling. In depth-averaged equations solved in 2Dh models, the bottom shear stress is explicitly prescribed using a friction coefficient. The reduction of hydraulic roughness due to stratification can in this case effectively be accounted for by alteration of the friction coefficient. By applying theories commonly used for stratified flow in the earth's atmosphere and taking into account the free surface effects, a depth-averaged friction law was derived This friction law is validated by numerical experiments with the 1DV POINT MODEL. These numerical experiments show that the buoyancy effect is small compared to the integral effect of sediment in nature that is reported in literature. To further evaluate the depth-averaged roughness parameterisation it is applied to a numerical model of the Yangtze Estuary (China). Calibration shows that the bottom of the Yangtze Estuary is very smooth even without the buoyancy effect, and that the buoyancy effect decreases the effective roughness further. For the Yangtze Estuary the buoyancy effect is properly simulated by the depth-averaged roughness parameterisation. Through the parameterisation the effective Chézy coefficient is increased from for clear water to for flow conditions commonly found in the Yangtze Estuary. Thereby the sediment-induced error in 2Dh modelling is reduced by approximately 75%. From this it is concluded that 2Dh modelling becomes more accurate through application of the roughness parameterisation. Several other issues can be done that might increase the reliability of 2Dh models even more. For example it is recommended to implement the roughness parameterisation in the numerical code of DELFT3D-FLOW, so that the effective hydraulic roughness is continuously updated with feedback to hydrodynamics and sediment transport.