Stream function finite elements for nearshore current

This paper presents a finite element method for the analysis of nearshore current, which is mainly induced by surface waves. The analysis is divided into two parts, i.e., the analysis of wave and the analysis of currents. The basic equations are conservation of wave number, wave energy, momentum and continuity. The first two are for wave analysis and the last two for the current analysis. The wave angle is determined from the conservation law of wave number. Using the resulting wave angle and the conservation of wave energy, the distribution of wave height is derived. The radiation stress is derived from the wave angle and height. The nearshore current flow is obtained from the conservations of momentum and continuity including the radiation stress. All the numerical procedures are based on the finite element method. For the analysis of the wave angle and wave height, the incremental iteration method and logarithmic function formulation are employed. For the analysis of the current flow, the stream function formulation is used. From the numerical computations, it is seen that the finite element method presented in this paper is very valuable in practical applications. The method is applied to the analysis of the nearshore current flow of Twan Bay in Japan.