Abstract
This paper incorporates the Bingham rheology model with the Navier–Stokes solver to simulate the tsunamis excited by a slump-type landslide. The slump is modeled as the Bingham material, in which the rheological properties changing from the un-yield phase to yield phase is taken into account. The volume of fluid method is used to track the interfaces between three materials: air, water, and slump. The developed model is validated by the laboratory data of the benchmark landslide tsunami problem. A series of rheological properties analyses is performed to identify the parameter sensitivity to the tsunami generation. The results show that the yield stress plays a more important role than the yield viscosity in terms of the slump kinematics and tsunami generation. Moreover, the scale effect is investigated under the criterion of Froude number similarity and Bingham number similarity. With the same Froude number and Bingham number, the result from the laboratory scale can be applied to the field scale. If the slump material collected in the field is used in the laboratory experiments, only the result of the maximum wave height can be used, and significant errors in slump shape and moving speed are expected.
Highlights
In the tsunami generation, “landslide” is a general term that describes several types of mass movement, including rock falls, slope failures, debris flows, slides, and slumps [1]
The Bingham model is integrated into the Navier–Stokes equations solver, Splash3D, for a better description of the vertical acceleration of water waves and slumps
The Bingham model is integrated into the Navier–Stokes equations and the large eddy simulation (LES) turbulent model to have a detailed description of the vertical acceleration of the landslides and the induced waves
Summary
“landslide” is a general term that describes several types of mass movement, including rock falls, slope failures, debris flows, slides, and slumps [1]. The difficulty and cost of the experiments make researchers adopt mathematical and numerical models to study the landslide tsunamis [17]. Several studies have investigated the effect of deformable slumps on wave generation [34,36,37,38] These studies described the slumps as high viscosity materials, while some studies consider the slumps as the Bingham fluids [16,39,40,41]. Many of the studies [23,24,25] adopted shallow water equations as fundamental governing equations They are not applicable in the case of strong vertical accelerations. This study aims to develop a numerical model to simulate the tsunamis generated by slumps. The Bingham model is integrated into the Navier–Stokes equations solver, Splash3D, for a better description of the vertical acceleration of water waves and slumps.
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