Swell across the continental shelf

Abstract

The transformation of surface gravity waves propagating through shallow regions is investigated with extensive field data from the North Carolina continental shelf. A spectral energy balance equation is derived for a bidimensional bottom topography with random small-scale irregularities, in which bottom friction is introduced heuristically whith a parameterized source term, and solved numerically using a hybrid Eulerian-Lagrangian scheme. This new model named CREST (Coupled Rays with Eulerian Source Terms) determines accurately refraction of waves by sub grid-scale depths variations using precomputed rays, allowing applications to large coastal areas with relatively coarse grids. Hindcasts of swell events during field experiments show large variations in wave heights caused by refraction and bottom friction. Widespread observations of sand ripples confirm that the bottom roughness is enhanced by wave-generated vortex ripples, thus sheltering the shore from offshore swells by dissipating wave energy in the bottoni boundary layer. Resulting wave height attenuation up to 70 % (84 % 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.