The application of the method of characteristics for the simulation of nearly horizontal flow in two and three spatial dimensions

Certain free surface flows exhibit in nature negligible vertical accelerations and as a result the pressure within the fluid remains hydrostatic. The method of characteristics is developed as a solution technique for the integration of the partial differential equations describing this kind of flow. The equations are integrated over the depth to provide a two‐dimensional model which is then tested and validated by comparing its results with tide‐induced flows occurring in a number of cases where either analytical or observational data are available for comparison. On the basis of the results of the 2D model, a finite difference 3D model is developed which provides the values of the unknown velocities u , v and w along the three axes x , y and z . This combined 2D–3D model is verified by applying it in cases of wind‐induced flow inside closed or open basins for which the classical Ekman solution may be used as a testing means.