Two-layer shallow water system and its applications

The multi-layer shallow water system is derived by depth averaging the incompressible Navier-Stokes equations with the hydrostatic assumption within layers. While the single layer shallow water system is hyperbolic, the two-layer system is conditionally hyperbolic because of the coupling terms between the layers. The eigenstructure of the system cannot be found in closed form and the eigenvalues may become imaginary number. In this work, we assume that the system conserves hyperbolicity. The eigenvalues are computed numerically, and the f-wave approach is used to balance the source term. As an application, we consider a tsunami generated by an underwater landslide.