Shallow flow modelling using curvilinear depth‐averaged stream function and vorticity transport equations

<jats:title>Abstract</jats:title><jats:p>Most receiving water, such as lakes and open reservoirs, have large plan dimensions with respect to their depth. In such cases, the flow may be nearly two‐dimensional and the depth‐averaged Reynolds equations are appropriate. This paper presents a new version of the governing equations in curvilinear depth‐averaged stream function and vorticity transport (ψ, ω) form appropriate for non‐orthogonal computational meshes. The equations are discretized using finite differences and solved using successive over‐relaxation for the depth‐averaged stream function equation and an alternating direction implicit scheme for the vorticity transport equation. Results from the numerical model are validated against data from flow past a backward facing step and jet‐forced flow in a circular reservoir. The results indicate that the (ψ, ω) form of the shallow water equations may be useful for applications where the free surface can either be assumed horizontal, or is know <jats:italic>a priori</jats:italic>.</jats:p>