 Three-layer stratified piecewise-linear shear flow

This three-layer shear flow has $U=\Delta Uz/h$ and density ${\rho }_0$ between $z=\pm h/2$. Above and below, the velocity is the corresponding constant $\pm \Delta U/2$, and the mass density is ${\rho }_0\mp \Delta \rho /2$. The density drops and vorticity jumps coincide at both interfaces. Its hydrodynamic stability involves coupled gravity-vorticity interface waves, unlike a profile with uniform shear extending through all three layers.