On group velocity and spatial damping of diurnal continental shelf waves

Diurnal continental shelf waves (CSWs) are studied theoretically for an idealized shelf topography. Wave attenuation is caused by the exchange of fluid on the sloping shelf with an inner region through a permeable coastline. As an example, we consider the region outside Lofoten-Vesteralen in north Norway. Here CSWs with diurnal tidal frequencies are possible in a small wave number range centered around zero group velocity. A previous investigation with a Robin condition (a weighted combination of Dirichlet and Neumann conditions) at the permeable boundary has shown that the spatial damping coefficient becomes infinitely large when the group velocity of the CSWs approaches zero. Here we demonstrate that this is not a result of the mathematical formulation, but reflects a physical reality. We show this by modelling the highly convoluted inner archipelagic region as a series of densely packed vertical Hele Shaw cells. By comparing the two ways of describing a permeable coastal boundary (Robin/Hele Shaw), we may express the Robin parameter in terms of the physical parameters (permeability, eddy viscosity) that characterize the flow on the inner porous shelf. The radiation stresses that drive the Lagrangian mean currents are the same in the two cases. This means that the spatial mean current distribution over the sloping shelf becomes unaltered when we compare the Robin case and the porous inner shelf case.