  The effects of a submarine canyon on the propagation of ocean surface waves
are examined with a three-dimensional coupled-mode model for wave propagation
over steep topography. Whereas the classical geometrical optics approximation
predicts an abrupt transition from complete transmission at small incidence
angles to no transmission at large angles, the full model predicts a more
gradual transition with partial reflection/transmission that is sensitive to
the canyon geometry and controlled by evanescent modes for small incidence
angles and relatively short waves. Model results for large incidence angles are
compared with data from directional wave buoys deployed around the rim and over
Scripps Canyon, near San Diego, California, during the Nearshore Canyon
Experiment (NCEX). Wave heights are observed to decay across the canyon by
about a factor 5 over a distance shorter than a wavelength. Yet, a spectral
refraction model predicts an even larger reduction by about a factor 10,
because low frequency components cannot cross the canyon in the geometrical
optics approximation. The coupled-mode model yields accurate results over and
behind the canyon. These results show that although most of the wave energy is
refractively trapped on the offshore rim of the canyon, a small fraction of the
wave energy 'tunnels' across the canyon. Simplifications of the model that
reduce it to the standard and modified mild slope equations also yield good
results, indicating that evanescent modes and high order bottom slope effects
are of minor importance for the energy transformation of waves propagating
across depth contours at large oblique angles.
