Sheared salt fingers: Instability in a truncated system

We derive a model for fingering doubly diffusive convection from a truncated expansion in horizontal planform functions with the inclusion of a large-scale shearing mode. This produces nonlinear partial differential equations in time and in vertical coordinate. At a high enough Rayleigh number, both convection and shear modes are sustained and their interaction produces rich cyclic dynamics with the fingering layer dividing into two distinct finger layers that engender steps in the mean salinity before being disrupted by the beginning of a new cycle.