arXiv subjects

Rudy Magne

Publications and source records attributed to Rudy Magne.

4 recordsLinked to original sources

arXiv2010

Semi-empirical dissipation source functions for ocean waves: Part I, definition, calibration and validation

New parameterizations for the spectra dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observation of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is non-zero only when a non-dimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short wave dissipation due to long wave breaking is introduced to represent the dissipation of short waves due to longer breaking waves. Several degrees of freedom are introduced in the wave breaking and the wind-wave generation term of Janssen (J. Phys. Oceanogr. 1991). These parameterizations are combined and calibrated with the Discrete Interaction Approximation of Hasselmann et al. (J. Phys. Oceangr. 1985) for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height. The wave energy balance is verified in a wide range of conditions and scales, from gentle swells to major hurricanes, from the global ocean to coastal settings. Wave height, peak and mean periods, and spectral data are validated using in situ and remote sensing data. Some systematic defects are still present, but the parameterizations yield the best overall results to date. Perspectives for further improvement are also given.

physics.ao-ph↗

arXiv2006

Evolution of surface gravity waves over a submarine canyon

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.

physics.ao-ph↗

arXiv2006

Current effects on scattering of surface gravity waves by bottom topography

Scattering of random surface gravity waves by small amplitude topography in the presence of a uniform current is investigated theoretically. This problem is relevant to ocean waves propagation on shallow continental shelves where tidal currents are often significant. A perturbation expansion of the wave action to second order in powers of the bottom amplitude yields an evolution equation for the wave action spectrum. A scattering source term gives the rate of exchange of the wave action spectrum between wave components, with conservation of the total action at each absolute frequency. With and without current, the scattering term yields reflection coefficients for the amplitudes of waves that converge, to the results of previous theories for monochromatic waves propagating in one dimension over sinusoidal bars. Over sandy continental shelves, tidal currents are known to generate sandwaves with scales comparable to those of surface waves. Application of the theory to such a real topography suggests that scattering mainly results in a broadening of the directional wave spectrum, due to forward scattering, while the back-scattering is generally weaker. The current may strongly influence surface gravity wave scattering by selecting different bottom scales with widely different spectral densities due the sharp bottom spectrum roll-off.

physics.ao-ph↗

arXiv2005

Topographical scattering of waves: a spectral approach

The topographical scattering of gravity waves is investigated using a spectral energy balance equation that accounts for first order wave-bottom Bragg scattering. This model represents the bottom topography and surface waves with spectra, and evaluates a Bragg scattering source term that is theoretically valid for small bottom and surface slopes and slowly varying spectral properties. The robustness of the model is tested for a variety of topographies uniform along one horizontal dimension including nearly sinusoidal, linear ramp and step profiles. Results are compared with reflections computed using an accurate method that applies integral matching along vertical boundaries of a series of steps. For small bottom amplitudes, the source term representation yields accurate reflection estimates even for a localized scatterer. This result is proved for small bottom amplitudes $h$ relative to the mean water depth $H$. Wave reflection by small amplitude bottom topography thus depends primarily on the bottom elevation variance at the Bragg resonance scales, and is insensitive to the detailed shape of the bottom profile. Relative errors in the energy reflection coefficient are found to be typically $2h/H$.

physics.ao-ph↗