Numerical solution of two‐layer, two‐dimensional tidal flow in a boundary‐fitted orthogonal curvilinear co‐ordinate system

A new two‐layer, two‐dimensional mathematical model employing a finite difference method based on numerically generated boundary‐fitted orthogonal co‐ordinates and a grid ‘block’ technique for unsteady boundary problems is developed which can be used to simulate flows with density stratification in a natural water‐body with complicated topography. In the model the turbulent exchange across the interface is treated empirically and a time‐splitting finite difference method with two fractional steps is employed to solve the governing equations. The model is calibrated and verified by comparing the computational results with data measured in Tolo Harbour, Hong Kong. The simulation results mimie the field measurements very closely. The computation shows that the model reproduces the two‐layer, two‐dimensional tidal flow with density stratification in Tolo Harbour very well. The computed velocity hodographs show that the tidal circulations at various positions in each layer have different patterns and that the features of the patterns are independent of the tidal type except for their scales. The computed Lagrangian pathlines show that the tidal excursion is dependent on the tidal type, especially in the inner harbour and side‐coves.