The instability of vertically curved fronts in a two-layer shallow water model

This paper investigates frontal instabilities in the context of a two-layer shallow water model with both linear and curved interfaces. First, we generalize the model previously established to allow for curved interfaces. Second, we revisit the linear interface case but with higher spatial resolution and study the impact of no-normal flow or radiation boundary conditions. The results show that the former prevents a baroclinic mode from occurring. Third, we investigate the novel problem of curved interfaces and deduce that it does not have a significant impact on a baroclinic instability; however, it does alter the regions of Kelvin–Helmholtz and Rossby–Kelvin instabilities. Furthermore, it introduces a new type of baroclinic instability that we refer to as the vertically curved-interface baroclinic instability.