| The goal of this research is to explore barotropic instability effects in shallow water. We will begin by performing instability analysis on the non-rotating shallow-water system with a specific mean velocity profile (the “broken” profile) and compare it to the instability results of the quasi-geostrophic model. Next, we will look at the special case of subcritical disturbances for general mean velocity profiles. For the special case of the subcritical disturbances, we found that the instability regions for both the non-rotating shallow water and the case of zero potential vorticity are an improvement of the previous semicircle results. These regions depend on the Froude number, wave number, and depth of the fluid layer. |
