The current study provides a new test case for the coastal numerical solutions dedicated to the plume spreading in the estuary and on the shelf. The suggested estuary-shelf system represents a mixture between pronounced nonlinear flow dynamics with sharp frontal boundaries and linear dynamics and across-shore geostrophic balance. The major aspects of the plume dynamics are analytically predicted, but are difficult to reproduce numerically. The test case manifests the level of numerical diffusion, ability of the model to reproduce the nonlinear processes and frontal zone dynamics. Numerical solutions were obtained with three unstructured mesh models SCHISM, THETIS and FESOM-C. The current study also suggests the plume spreading analysis based on numerical results, which can be useful for any intercomparison studies with focus on the plume behavior.