# Assessment of a Lagrangian 1DV Modelling Approach for Turbidity Currents Generated by Water Injection Dredging

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## Abstract

Siltation affects navigation in harbors and waterways by reducing the water depth. To regain depth and safeguard navigation, dredging is required. Water Injection Dredging (WID) is one of the available hydrodynamic dredging techniques, in which pumps on a vessel inject water at high flow velocities and low pressure into the bed and fluidize the bed material into a mixture of water and suspended sediment. The fluidized material travels as a turbidity current to deeper areas, driven by natural processes. Sediment transport is then less controlled and the final destination of the dredged material is more difficult to estimate than for other dredging techniques. The passage of a WID-induced turbidity current produces an increase in suspended sediment concentration (SSC) in the water column that increases turbidity. Turbidity increase may have a negative environmental impact. Therefore, to evaluate and mitigate the environmental impact of WID, the increase in SSC should be estimated. Additionally, from an operational perspective, the sedimentation footprint of the turbidity current should be determined. Deltares developed with Boskalis a numerical tool named “Lagrangian 1DV model” (Deltares, 2019). The Lagrangian 1DV model can calculate the thickness and density of the WID-induced turbidity current at a distance from the dredger, as well as the deposition rate. It provides the information to estimate the increase in SSC in the water column and the sedimentation footprint. The tool was defined to be a rapid assessment tool, as it is necessary at the early stages of WID projects when there is usually a limitation of time and available data. Such a tool is useful to analyze different dredging strategies and different solutions to mitigate environmental impact.

As its name indicates, it follows a Lagrangian 1DV (1-Dimensional Vertical) approach. This approach follows the turbidity current in space as it moves away from the dredger. It is an innovative approach that requires less computational effort than a 3D or a 2DV (2-Dimensions in the Vertical plane) approach.

Three main steps were followed by Deltares (2019) for conceptual and mathematical modelling: - Step 1: assume that the turbidity current is a 2DV process, thus neglecting lateral gradients - Step 2: schematize the 2DV process as a Lagrangian 1DV approach. - Step 3: select the 1DV Point Model (Uittenbogaard and Winterwerp, 1997) as the basis to solve velocity and concentration profiles over the vertical. In order to schematize the 2DV process as a Lagrangian 1DV approach (Step 2), two main points were assumed:

- Uniformity of the 1DV Point Model (in the Eulerian frame of reference) was assumed as stationarity in the Lagrangian frame of reference - The Lagrangian velocity was defined as a concentration-weighted velocity over the water column, expressed as the ratio between the mass flux and sediment load.

The validity of these assumptions to estimate sediment transport was analyzed in this report. For that purpose, the Lagrangian 1DV model (Lagrangian 1DV approach) was compared to a 2DV computation in Delft3D-FLOW (called Delft3D model) in four sets of numerical experiments. The validity of the Lagrangian 1DV approach for uniform flow was confirmed with the first set of numerical experiments. Experiment Set 2 showed that the Lagrangian 1DV approach is as valid as the Eulerian 2DV approach to represent sediment transport in non-uniform flow when density differences are negligible. Differences between the Lagrangian 1DV model and the Delft3D model in velocity, concentration and, consequently, in the concentration-weighted velocity (calculated in the Delft3D model as the ratio between mass flux and sediment load), arose in non-uniform flow for the cases in which density differences became significant. The results suggest that the origin of the differences between the Lagrangian 1DV model and the Delft3D model in the concentration-weighted velocity relies on the expression of the advective transport term of the sediment transport equation.

In Experiments Set 3 and Set 4, the numerical models were based on laboratory experiments on turbidity currents by Parker et al. (1987) and van Kessel and Kranenburg (1996), respectively. The baroclinic pressure gradient was higher for these sets experiments. Thus, differences in the baroclinic pressure gradient between the models produced important differences in velocity.

In the case of Experiments Set 3, based on Run 13 of Parker et al. (1987), the concentration-weighted velocity was lower for the Lagrangian 1DV model along the analyzed reach. Experiments Set 4, based on Run 2 of van Kessel and Kranenburg (1996), presented the opposite behavior: a higher value for the concentration-weighted velocity for the Lagrangian 1DV model. A possible explanation for these results was found, based on the variation of the sediment load along the channel in the Delft3D model and the magnitude of the baroclinic pressure gradient. In order to analyze possible implications of the observed differences when the model parameters are in the range of the WID application, the variation of the concentration-weighted velocity was calculated in the Lagrangian 1DV model for a typical case of WID. The trend of the variation along the reach was similar to the case of Experiments Set 3. Then, the results suggest that the estimated concentration-weighted velocity in the Lagrangian 1DV model may be lower than the result for the 2DV approach. As a consequence, the travelling distance of the turbidity current may be shorter. More specific cases can be addressed by comparing the Lagrangian 1DV model and the Delft3D model, following the methodology presented in this report.