The Red Sea Water enters the Gulf of Aden through the Strait of Bab El Mandeb as a density current. The Red Sea Water subsequently spreads into the Gulf of Aden under the influence of surface mesoscale eddies, which dominate the surface flow, of topographic features such as rift and capes, and of the monsoon regimes. The dynamics of a bottom density current overflowing in a semi-enclosed basin, as the Red Sea Water outflows in the Gulf of Aden, is investigated by performing idealised numerical simulations, at submesoscale resolution, in which we progressively add topographic and dynamical elements. The rift and cape play an important role, respectively, on the vertical and the horizontal mixing as well as baroclinic and barotropic instabilities undergone by the bottom density current. Mesoscale and submesoscale eddies are generated depending on the model configuration. In the presence of surface mesoscale eddies, the bottom density current water is mainly advected at their periphery. In winter, both mesoscale and submesoscale eddies are generated, while in summer only submesoscale eddies are present. Finally, to put our results based on idealised numerical simulations and Lagrangian experiments in perspective, we analyse the trajectories of three Argo floats, deployed in the Rift of Tadjurah. Clues of submesoscale eddies generation at capes are observed which is in agreement with our idealised numerical simulations.