Vorticity and bathymetry effects on spiral streamlines

Analytical solutions for a shallow water vorticity transport equation are found to describe horizontal spiral streamline patterns. The mechanical model is water flow in an annular domain around a hydraulic outlet. The variable water depth, i.e. the bathymetry is included in the solutions. We discuss the effects of the vorticity and the bathymetry on the polar slope of the spirals, by using four different bathymetrical shapes and vorticities. We examine the qualitative picture of the solutions by setting up categories for the spirals. A duality between the vorticity and the bathymetry is defined as they both effect the polar slope. •Analytical solutions of the shallow water vorticity transport equation.•Spiral streamline pattern description with polar slope function.•Vorticity and bathymetry effects on the spiral streamlines.•Spiral streamline categories such as compressing spiral, logarithmic spiral, expanding spiral.