Equilibrium stability analysis of hyperbolic shallow water moment equations

In this paper, we analyze the stability of equilibrium manifolds hyperbolic shallow water moment equations. Shallow equations describe flows for complex velocity profiles which vary in vertical direction and models can be seen as extensions standard Equilibrium is an important property balance laws that determines linear solutions vicinity manifolds, it a necessary condition stable numerical solutions. After analysis structure models, identify three different based on limits right-hand side friction term, physically correspond to water-at-rest, constant-velocity, bottom-at-rest profiles. The then shows structural conditions are fulfilled water-at-rest constant-velocity equilibrium. However, lead instable modes depending profile. Relaxation toward respective investigated numerically models.