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 $2h/H$.Comment: Second revision for Journal of Waterways Ports and Coastal Engineerin

Tidal modulation of infragravity waves via nonlinear energy losses in the surfzone

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 33 (2006): L05601, doi:10.1029/2005GL025514.The strong tidal modulation of infragravity (200 to 20 s period) waves observed on the southern California shelf is shown to be the result of nonlinear transfers of energy from these low-frequency long waves to higher-frequency motions. The energy loss occurs in the surfzone, and is stronger as waves propagate over the convex low-tide beach profile than over the concave high-tide profile, resulting in a tidal modulation of seaward-radiated infragravity energy. Although previous studies have attributed infragravity energy losses in the surfzone to bottom drag and turbulence, theoretical estimates using both observations and numerical simulations suggest nonlinear transfers dominate. The observed beach profiles and energy transfers are similar along several km of the southern California coast, providing a mechanism for the tidal modulation of infragravity waves observed in bottom-pressure and seismic records on the continental shelf and in the deep ocean.Support was provided by ONR and NSF

Data-Enhanced Modeling of Sea and Swell on the Continental Shelf

LONG-TERM GOAL: Our long-term goal is to contribute to the accurate prediction of surface gravity wave generation, propagation, and dissipation in coastal regions through the combined use of measurements and models.Award #s: N00014-98-1-0019; N0001499WX30036; N0001499WR3000

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

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

Refraction and reflection of infragravity waves near submarine canyons

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 112 (2007): C10009, doi:10.1029/2007JC004227.The propagation of infragravity waves (ocean surface waves with periods from 20 to 200 s) over complex inner shelf (water depths from about 3 to 50 m) bathymetry is investigated with field observations from the southern California coast. A wave-ray-path-based model is used to describe radiation from adjacent beaches, refraction over slopes (smooth changes in bathymetry), and partial reflection from submarine canyons (sharp changes in bathymetry). In both the field observations and the model simulations the importance of the canyons depends on the directional spectrum of the infragravity wave field radiating from the shoreline and on the distance from the canyons. Averaged over the wide range of conditions observed, a refraction-only model has reduced skill near the abrupt bathymetry, whereas a combined refraction and reflection model accurately describes the distribution of infragravity wave energy on the inner shelf, including the localized effects of steep-walled submarine canyons.Funding was provided by the Office of Naval Research and the National Science Foundation

Measurement of Directional Wave Spectra Using Aircraft Laser Altimeters

A remote sensing method to measure directional oceanic surface waves by three laser altimeters on the NOAA LongEZ aircraft is investigated. To examine feasibility and sensitivity of the wavelet analysis method to various waves, aircraft motions, and aircraft flight directions relative to wave propagation directions, idealized surface waves are simulated from various idealized aircraft flights. In addition, the wavelet analysis method is also applied to two cases from field measurements, and the results are compared with traditional wave spectra from buoys. Since the wavelet analysis method relies on the “wave slopes” measured through phase differences between the time series of the laser distances between the aircraft and sea surface at spatially separated locations, the resolved directional wavenumber and wave propagation direction are not affected by aircraft motions if the resolved frequencies of the aircraft motion and the wave are not the same. However, the encounter wave frequency, which is directly resolved using the laser measurement from the moving aircraft, is affected by the Doppler shift due to aircraft motion relative to wave propagations. The wavelet analysis method could fail if the aircraft flies in the direction such that the aircraft speed along the wave propagation direction is the same as the wave phase speed (i.e., the aircraft flies along wave crests or troughs) or if two waves with different wavelengths and phase speed have the same encountered wavelength from the aircraft. In addition, the data noise due to laser measurement uncertainty or natural isotropic surface elevation perturbations can also affect the relative phase difference between the laser distance measurements, which in turn affects the accuracy of the resolved wavenumber and wave propagation direction. The smallest waves measured by the lasers depend on laser sampling rate and horizontal distances between the lasers (for the LongEZ this is 2 m). The resolved wave direction and wavenumber at the peak wave from the two field experiments compared well with on-site buoy observations. Overall, the study demonstrates that three spatially separated laser altimeters on moving platforms can be utilized to resolve two-dimensional wave spectra

Experimental study of particle trajectories below deep-water surface gravity wave groups

Due to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of Particle Tracking Velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement