Rotating shallow water - beyond the textbook

Rotating shallow water is traditionally the first model encountered in the study of geophysical fluid dynamics. Its simplicity and applicability at large scales make it a favourable starting point for understanding midlatitude atmospheric behaviour. The linearized model reveals two principal dynamical features - fast time-scale wave disturbances, and slow time-scale balanced flow. Textbook analysis typically includes linear wave properties, and the leading order balanced dynamics of quasigeostrophy. We seek to further understand the successes and limitations of rotating shallow water in modelling geophysical fluid dynamics. In this study, nonlinear wave dynamics are restricted to uniform potential vorticity. This reduced set of equations enables the computational analysis of nonlinear waves, devoid of balanced dynamics. Additionally, balanced dynamics are investigated beyond quasigeostrophy to include small Rossby number corrections. As anticipated, an asymmetry between cyclone and anticyclone vortices emerges; the biases are consistent with similar models, and contradict atmospheric behaviour.