Abstract Coastal currents are strongly affected by the topography of the ocean bed close to the shore. In some locations, notably off the southern coast of Africa, the ocean depth drops off very sharply, forming a shelf break. Several authors have analysed the role of such sharply-varying topography in steering and stabilising coastal currents. The present work aims to resolve an apparent conflict between theoretical and experimental results for currents flowing along discontinuous topography in a rotating annulus. The existing analytical theory, based on a long-wave scaling, fails to explain the short-wavelength instabilities and wave breaking that arise in the laboratory experiments. We integrate the rigid-lid quasigeostrophic (QG) equations numerically in an annular domain using a combined finite-difference/pseudo-spectral approach. To replicate the inviscid theoretical conditions as closely as possible, we employ an additional piecewise-linear source term that sharpens fronts of potential vorticity. We find that initial configurations that vary slowly in azimuth rapidly develops features with large azimuthal variations. The numerical results also produce the same qualitative features as the experiments, suggesting that the experiments are well described by QG theory.