A note on the decay of vorticity in shallow flow calculations

Vorticity dynamics is studied within the viscous formulation of the nonlinear shallow water equations framework with a major emphasis on the description of decay of vortical structures. Suitable transport equations for vorticity and enstrophy are derived and the nature of one specific contribution which leads to localized vorticity/enstrophy dissipation is clarified showing that steep gradients of the flow depth act as sinks of vorticity/enstrophy and not only as sources. One simple example of importance for natural water flows is, finally, discussed.