Dynamic Coupling of Wave and Surge Models by Eulerian-Lagrangian Method

Abstract

An Eulerian-Lagrangian method is employed in a third-generation ocean wave model and a two­ dimensional storm surge model that are dynamically coupled. The stability, accuracy, and consistency of the synchronously coupled models are first verified using an idealized case of waves on a Gulf Stream Ring by comparing the computed results with that by others. Application of the coupled models to two hindcastings of storms occurred in the northern South China Sea under different forcing conditions, taking into account the mutual influences of waves and currents, gives satisfactory results in comparison with observations. Calculations show that the surface wave-dependent drag has significant effects on the surges, but the wave radiation stress has only slight effects. For prediction of wave heights, the inclusion of both the wave-dependent drag and the wave radiation stress in the storm surge model has a very small effect on the computed results. The coupled models can be easily applied to prediction or hindcasting of ocean waves and storm surges without the need for further treatment. ABSTRACT: An Eulerian-Lagrangian method is employed in a third-generation ocean wave model and a two­ dimensional storm surge model that are dynamically coupled. The stability, accuracy, and consistency of the synchronously coupled models are first verified using an idealized case of waves on a Gulf Stream Ring by comparing the computed results with that by others. Application of the coupled models to two hindcastings of storms occurred in the northern South China Sea under different forcing conditions, taking into account the mutual influences of waves and currents, gives satisfactory results in comparison with observations. Calculations show that the surface wave-dependent drag has significant effects on the surges, but the wave radiation stress has only slight effects. For prediction of wave heights, the inclusion of both the wave-dependent drag and the wave radiation stress in the storm surge model has a very small effect on the computed results. The coupled models can be easily applied to prediction or hindcasting of ocean waves and storm surges without the need for further treatment. numerically been proved useful and successful by many au­ thors, but physically, a process usually needs to be split into several steps, and thus noninherently conservative errors are raised (Leonard et al. 1995). Compared with the piecewise ray method, the full ray method requires the computation to be conducted separately and independently at each position, and, hence, is less advantageous for the evaluation of horizontal distribution of wave characteristics (Yamaguchi and Hatada 1990). Casulli (1990) developed a semiimplicit finite difference scheme for the solution of the two-dimensional shallow water equations with a Eulerian-Lagrangian method for the approx­ imation of the convective terms, which was proved to be sta­ ble, accurate, and conservative. The Eulerian-Lagrangian method has advantages over other commonly used numerical methods, such as upwind method, ADI method, time-splitting or operator-splitting techniques, and the mode-splitting tech­ nique. The scheme was subsequently extended to three di­