Spectral Evolution of Swell across the Continental Shelf

The spectral evolution of swell propagating across a wide, shallow continental shelf is investigated with extensive data from the North Carolina shelf, on the East coast of the United States. A spectral energy balance equation is proposed for the evolution of swell that includes refraction and shoaling, bottom friction over a movable bed, and Bragg scattering of waves by wavelength-scale bottom topography. This equation is solved numerically using a hybrid Eulerian-Lagrangian model. Hindcasts of swell events during recent field experiments show large variations in wave heights that can be attributed to refraction and bottom friction, and are consistent with a variable bottom roughness. Wave height attenuation up to 73 % (93 % of the wave energy) was observed in moderately energetic conditions. Bragg scattering of waves by wavelength-scale bottom features significantly increases (up to a factor two) the directional spread of waves.