The linear stability and numerical analysis of geophysical flow patterns is carried out on the beta-plane in a quasigeostrophic approximation. We consider initial steady state dipoles in a one-and-a-half-layer model that are capable of zonal drift in either direction. Despite previous numerical works suggesting that eastward propagating dipoles are stable, our high resolution simulations identify the spontaneous symmetry breaking of weak dipoles over time. The evolution is associated with a growing critical mode with even symmetry about the zonal axis. On carrying out a linear stability analysis, the critical modes obtained share consistency with the numerical fields. In addition, both methods of analysis show that the linear growth rate is inversely proportional to the dipole intensity. Furthermore, the partner separation becomes more pronounced after the linear growth stage, suggesting that nonlinear effects play a pivotal role in the underlying dynamics. Beyond this, the dynamics of initially tilted dipoles and dipole-rider solutions are considered, while stronger dipoles are further analysed using the method of distillation.

Flows over sinusoidal bottom relief are considered in a two-layer model on the quasigeostrophic beta-plane. Fourier mode solutions are assumed for the layer-wise perturbation field in order to carry out a linear stability analysis, from which a coupled eigenproblem is derived between fluid columns for both zonal and meridional bottom irregularities. The presence of zonally oriented multiple ridges stabilises an otherwise unstable homogeneous zonal current with respect to increases in the number of ridges and ridge amplitude. Moreover, a bifurcation occurs in the unstable mode spectra and is dependent on the number of ridges. The critical eigenmodes in this case are found to be eddy chains of alternating sign, and these share remarkable resemblance with those obtained numerically. Meridionally oriented multiple ridges are also considered, but are found not to affect the maximum growth rate directly.