In order to study the role of a sloping bottom on the mesoscale variability of the Northern Current, a series of barotropic laboratory experiments was performed on a rotating table setup. The present work is devoted to a numerical model which aims to simulate these laboratory conditions in order to further investigate aspects which are difficult to treat in the laboratory. The onset of instabilities, the influence of the velocity profile, the relative position of the jet over the slope, and the influence of the jet width on the resulting instabilities are discussed. The robustness and the origin of a shelf-break topographic Rossby wave detected in our westward laboratory flows is also discussed. The barotropic model for westward currents (such as the Northern Current) with Rossby numbers in the range Ro = 0.1--0.2 predicts wavelengths of 50--75 km, similar to those observed in SST images. The periods associated with the model instabilities (3.3--3.8 days) would be close to a 3.5-day band of mesoscale activity recorded from current meter devices in the Gulf of Lions which lies out of the traditionally considered baroclinic instability theory. Other particularities such as the up-slope migration of the Northern Current and the increasing mesoscale activity for increasing jet velocities can also be explained through the present model. These results would point out barotropic instability as a factor to consider, apart from the traditional idea of baroclinic instability, in order to partially explain the Northern Current mesoscale variability.