The Bragg scattering of random, non-stationary surface gravity waves by random
topography on a gently sloping bottom is investigated. A correction is given of
previously published expressions for the triad wave–wave–bottom interaction source
term in the spectral energy balance equation, and the result is reconciled with
deterministic theories for the reflection of waves from sinusoidal seabed undulations.
For both normal and oblique incidence, the stochastic and deterministic theories are
equivalent in the limit of long propagation distances. Even for relatively short distances
(for example two bottom undulations), the reflected energy predicted by the stochastic
source term formulation is generally within 15% of values predicted by deterministic
theories. The detuning of Bragg resonance by refraction and shoaling is discussed,
suggesting practical validity conditions for the stochastic theory. The effect of bottom
scattering on swell propagation is illustrated with numerical model computations for
the North Carolina continental shelf using high-resolution bathymetry and an efficient
semi-implicit scheme to evaluate the bottom scattering source term and integrate
the energy balance equation. Model results demonstrate the importance of forward
scattering of waves that propagate at large oblique angles over bottom features
with typical scales of one to several surface wavelengths. This process contributes
significantly to the directional spread of swell on the continental shelf by diffusing
energy, in the spectrum, around the mean wave direction. Back-scattering, caused by
bottom features with crests parallel to those of the surface waves and wavelengths
close to half the surface wavelength, is weak, owing to the sharp roll-off of the bottom
elevation spectrum at high wavenumbers. Model predictions are consistent with field
measurements.
Experimental Assessment of the Performance of High-Frequency CODAR and WERA Radars to Measure Ocean Currents in Partially Ice-Covered Waters
