  Analysing the impact of bottom friction on shallow water waves over bottom
terrains is important in areas including environmental and coastal engineering
as well as the oceanic and atmospheric sciences. However, current theoretical
developments rely on making certain limiting assumptions about these flows and
thus more development is needed to be able to further generalise this
behaviour. This work uses Adomian decomposition method (ADM) to not only
develop semi-analytical formulations describing this behaviour, for flat
terrains, but also as reverse-engineering mechanisms to develop new closed-form
solutions describing this type of phenomena. Specifically, we respectively
focus on inertial geostrophic oscillations and anticyclonic vortices with
finite escape times in which our results directly demonstrate the direct
correlation between the constant Coriolis force, the constant bottom friction,
and the overall dynamics. Additionally, we illustrate elements of
dissipation-induced instability with respect to constant bottom friction in
these types of flows where we also demonstrate the connection to the initial
dynamics for certain cases.
