Finite element analysis of long-period water waves

The finite element representation of the nonlinear equations governing the unsteady flow of the two-dimensional long-period shallow water wave is considered. The approximate solution assumes, that the flow is only a slight perturbation of an existing flow. With this assumption a finite element formulation in terms of discrete nodal values of velocity and water height is generated using Galerkin's method. The resulting matrix equation for an arbitrary triangular-based space-time element constitutes a set of linear algebraic equations solvable for nodal values of the flow variables. The topological properties of estuaries are treated and with the solution thus obtained, numerical results are shown for the North Sea.