We present a test case of river plume spreading to evaluate numerical methods used in coastal ocean modeling. It includes an estuary–shelf system whose dynamics combine nonlinear flow regimes with sharp frontal boundaries and linear regimes with cross-shore geostrophic balance. This system is highly sensitive to physical or numerical dissipation and mixing. The main characteristics of the plume dynamics are predicted analytically but are difficult to reproduce numerically because of numerical mixing present in the models. Our test case reveals the level of numerical mixing as well as the ability of models to reproduce nonlinear processes and frontal zone dynamics. We document numerical solutions for the Thetis and FESOM-C models on an unstructured triangular mesh, as well as ones for the GETM and FESOM-C models on a quadrilateral mesh. We propose an analysis of simulated plume spreading which may be useful in more general studies of plume dynamics. The major result of our comparative study is that accuracy in reproducing the analytical solution depends less on the type of model discretization or computational grid than it does on the type of advection scheme.