A parabolic approximation to the reduced wave equation is investigated for the propagation of periodic surface waves in shoaling water. The approximation is derived from splitting the wave field into transmitted and reflected components. In the case of an area with straight and parallel bottom contourlines, the asymptotic form of the solution fer high frequencies is compared with the geometrical optics approximation. Two numerical solution techniques are applied to the propagation of an incident plane wave ever a circular shoal.

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On the parabolic equation method for water wave propagation

A 1.6-yr time series of radial current velocity from a 25-MHz high-frequency radar system located near a coastal river plume is analyzed to determine how the working range varies in response to changing near-surface conductivity, sea state, and tides. Working range is defined as the distance to the farthest radial velocity solution along a fixed bearing. A comparison to spatially resolved near-surface conductivity measurements from an instrumented ferry shows that fluctuations in conductivity had the largest impact of the three factors considered. The working range increases nearly linearly with increasing conductivity, almost doubling from 19.4 km at 0.9 S m−1 to 37.4 km at 3.5 S m−1, which yields a slope of 7.0 km per S m−1. The next largest factor was sea state, which was investigated using measured winds. The working range increases linearly at a rate of 1 km per m s−1 of wind speed over the range of 0.5–6.5 m s−1, but it decreases weakly for wind speeds higher than 7.5 m s−1. Finally, a power...

Dependence of 25-MHz HF Radar Working Range on Near-Surface Conductivity, Sea State, and Tides

Between 1 March and 26 March 2002, a wave and current measurement station was deployed on the upper delta slope of Roberts Bank in approximately 12 m of water. The field data were analyzed and used in a parabolic wave model to determine wave characteristics for fair-weather, moderate, and storm conditions. The model shows that storm waves act nonuniformly along the beach depending on the local morphology and tidal elevation. Waves propagating during high tide are characterized by smooth dissipation and progressive refraction, whereas waves propagating during low tide show intense refraction and breaking in front of or over a low-tide bar. Sediment transport divergence in the nearshore is strongly controlled by the temporal relationship between storm waves and tidal height. Resume : Entre le 1er et le 26 mars 2002, une station instrumentee a ete deployee sur la partie superieure de la pente deltaique du banc Roberts, dans approximativement 12 m d’eau, afin de mesurer la houle et les courants. Les donnees de terrain ont ete ensuite analysees et utilisees dans un modele parabolique de houle afin de determiner les caracteristiques des houles pendant les conditions de beau temps, moderees et de tempete. Le modele montre que les houles de tempete agissent non uniformement le long de la plage selon la morphologie locale et le marnage. La propagation de la houle a maree haute est caracterisee par une legere dissipation et une refraction progressive tandis que les houles se propageant a maree basse montrent une intense refraction et deferlent sur le front ou au-dessus d’une barre de maree basse. La divergence du transport sedimentaire dans la zone littorale est fortement controlee par la relation temporelle entre les houles de tempete et le niveau de la maree. Current Research 2007-A11 1 S. Meule et al.

http://publications.gc.ca/collections/collection_2007/nrcan-rncan/M44-2007-A11E.pdf

C. Pinazo

Papers

Wave dynamics over Roberts Bank, British Columbia: processes and modelling