A new mathematical model has been constructed for tidal motion and level in the Tay Estuary. The model is based upon the two-dimensional vertically integrated equations of motion and gives two-dimensional vector velocities and levels from the rail bridge to the Bar, about 5 km east of Buddon Ness. The extent of the model outside the mouth of the Tay is 3 km north of Buddon Ness and 7 km south. The equations of motion are expressed in the form of central differences in space and solved explicitly in time using the Local Integral Method. The emergence and submergence of drying zones in the estuary are calculated during the tidal cycle. A representation of the hydrodynamic resistance of the road bridge was included in the model.
The boundary conditions for the model were based upon estimates of river flows at the western entrance and tidal levels at the eastern, northern and southern boundaries. Boundary conditions at the eastern end of the model presented considerable complexities because of the presence of an amphidromic system to the south of the Norwegian coast. The final solution adopted was to choose tidal levels along the easterly boundaries to give velocities in the outer estuary that agreed with available tidal atlases of the region.
Velocities and levels at intervals of 250 m for the period of a tide show the prevalent shoaling conditions over the estuary combined during certain periods with conditions of high velocity, giving very difficult approaches to the River Tay.