This renewal request focuses on the dynamics of oceanic double-diffusive convection, an important small-scale mixing process driven by the two order of magnitude difference in the diffusivities of heat and salt in seawater. One of the most distinctive features of double-diffusive convection is its tendency to form stacks of convective layers known as staircases, which are prominent in the Arctic at the transition between the cool water beneath the sea ice and the warm water of Atlantic origin. The reservoir of warm water in the Arctic would be sufficient to melt the sea ice in only a few years if not for the slow heat transport through these staircases; thus, it is critical to our understanding of global climate to know the thermal properties of staircases and how such properties depend on any external forces. Recently, our work has identified that shear can play an important role in the formation of staircases via double-diffusive instabilities, but little work has been completed to date on how the heat-transfer characteristics of staircases depend on steady or time-dependent shear. This renewal seeks to address that problem using numerical simulations performed on a finite-volume, MPI-based general circulation model (MITgcm).