Finite element modeling of nonlinear coastal currents

A numerical model describing wave-induced mean sea level variations and coastal currents in the nearshore region is developed by the finite element method. The model includes nonlinear convective accelerations, lateral mixing and bottom friction. To specify the wave refraction field, a wave model is also developed with a semi-discrete Galerkin method. The numerical accuracy of the model is verified with the analytic solutions for one-dimenional longshore currents and two-dimensional rip currents The numerical model is also applied to predict realistic meandering currents occurring on a periodic rip channel. Due to the nonlinear inertial effect, the unaccelerated longshore current profile is stretched and causes a decrease in the magnitude of maximum velocity. A comparison with the analytic solution of a one-dimensional longshore current velocity distribution indicates that the linear analytic solution significantly overestimates the maximum velocity. The numerical results quantitatively demonstrate the relative importance of the nonlinear convective terms in the nearshore current problem.