Meanders and eddies are routinely observed in the Gulf Stream along the South Atlantic Bight. We analyze here the instability processes that lead to the formation of submesoscale eddies on the cyclonic side of the Gulf Stream at the exit of the Florida Straits using very high resolution realistic simulations. The positive relative vorticity and potential vorticity on the cyclonic side of the Gulf Stream are strongly intensified in the Straits due to topographic drag along the continental slope. The bottom drag amplifies the cyclonic shear by generating large positive vertical vorticity values within the sloped turbulent bottom boundary layer. Downstream from the Straits the current becomes unstable to horizontal shear instability, rolls up, and forms a street of submesoscale vortices. The vortices expand as they propagate northward along the shelf, where they can generate large vertical displacements and enhance cross‐shelf exchanges.