River confluences, longshore currents along the coast and flows in compound and composite channels are examples of shallow turbulent flows that are characterized by having horizontal lengthscales far exceeding vertical length-scales. A striking feature of shallow turbulent flows is vortical two-dimensional coherent structures (2DCSs). The onset of 2DCSs is believed to be a result of the linear instability of horizontal shear layers. Such 2DCSs govern mass, momentum and constituent transport and the understanding of 2DCSs is important for water quality modeling and flow conveyance capacity in compound and composite channels. Previous work suggested that such stabilization is due to wave radiation through which energy is radiated from the shear layer and become unavailable for 2DCSs to develop. However, the relationship between wave radiation and shear layer stabilization has not been established; wave radiation may not be as critical in explaining the shear layer stabilization as it was suggested. This work proposes a two-step mechanism for shear layer stabilization under higher Frc (yet Frc<1) from the linearized vorticity and potential vorticity equations. First, the water depth variation causes the transverse velocity perturbation v’ to decrease in a way the potential vorticity is conserved; such decrease in v’is greater under larger Frc. Second, the decreased v’ leads to a decrease in the magnitude of the potential vorticity production term. The growth of potential vorticity is reduced, and the shear layer is stabilized as a result. The explanation is verified by solving a linear initial value problem (IVP) for the linearized inviscid and frictionless shallow water equations for Frc[removed]