A two-layer non-hydrostatic landslide model for tsunami generation on irregular bathymetry. 1. Theoretical basis

We describe a two-layer, coupled model for landslide motion over irregular bathymetry and resulting water column motion and tsunami generation. The three-dimensional non-hydrostatic wave model NHWAVE (Ma et al., 2012) is applied as the upper-layer model to simulate landslide-generated tsunami waves. Here, we focus on the derivation of governing equations for the lower-layer model, where the landslide is described as either a viscous mud flow or a saturated granular debris flow. The governing equations are depth-integrated in a Cartesian coordinate system referenced to the still water surface. Vertical acceleration of the slide is taken into account by including non-hydrostatic pressure effects within the slide. The model is validated in comparison to analytic results of Mangeney et al. (2000) and the slope-oriented numerical approach of Ma et al. (2015). The numerical approach and further examples are described in the companion paper Zhang et al. (2021)