A Hybrid Eulerian–Lagrangian Model for Spectral Wave Evolution with Application to Bottom Friction on the Continental Shelf

A hybrid Eulerian–Lagrangian wave model is presented that solves the spectral energy balance equation for surface gravity waves in varying depth. The energy of each spectral component is advected along (Lagrangian) ray trajectories. The source terms in the energy balance equation (e.g., interactions between wave components and nonconservative processes) are computed on a fixed Eulerian grid and interpolated onto the ray trajectories. The source terms are integrated in time along the rays. This integration is performed in parallel over the entire model domain. The main advantage of this new model, named CREST (Coupled Rays with Eulerian Source Terms), is that refraction of waves by subgrid-scale depth variations is evaluated accurately using precomputed rays, and thus the model can be applied with relatively coarse source term grids to large coastal areas. Hindcasts of swell evolution across the North Carolina continental shelf are presented for a source term restricted to energy dissipation in the bottom boundary layer over a movable sandy seabed. The results show that the hybrid Eulerian–Lagrangian method is a viable approach for accurate wave predictions in large coastal regions with nonstationary boundary conditions. Good agreement between model predictions and field observations of swell decay supports the hypothesis that, in the absence of strong local wind forcing, the evolution of waves across a wide, sandy continental shelf is dominated by refraction and bottom friction, which is well represented by a moveable bed parameterization.