The passing of long internal and external gravity wave over a step. Laboratory and in-situ measurements compared with analytical modelling

Within the MORSE project of the CEC-MASTIII, LEGI investigates the interaction of long gravity waves with the continental shelf. It is well known that internal tides are primarily generated at these dramatic topographic features. Propagating onshelf they desintegrate to “shed” solitary waves and highly nonlinear waves that very often give signatures on SAR images of the ocean surface. Moreover off-shore operators have shown recent concern in predicting internal wave fields that they regard as hazards. The present authors analyze the generation and the refraction of these long waves. They extend the shallow water model for linear long waves devised by Rattray (1960), which accounts for the stratification of the ocean water column (2-layer), for the earth rotation (f-plane approximation), for free surface boundary conditions, to take into account the oblicity of the wave crest with respect to the shelf break (modelled as a step shelf). The long wave assumption implies that the pressure on the vertical is hydrostatic. The horizontal component of the velocity is much larger than the vertical one due to the shallow water assumption. The equations reduce to vertically integrated (in each layer) 2D equations for the 2 horizontal velocity components, the interface displacement and free surface one. This system of equation yields for instance Poincare waves, Kelvin waves and standing waves for the 2 modes sustained by the two layer stratification. Long wave models of this type have been shown to be limited to the description of wave propagation on short time scales. The results of the model are used to describe how an internal solitary waves is refracted by a step and how internal tides are generated at the shelf break by an incoming surface tide modelled as a free Poincare wave