Diurnal continental shelf waves with a permeable coastal boundary: Application to the shelf northwest of Norway

Spatially damped continental shelf waves (CSWs) with diurnal tidal frequency outside Lofoten–Vesterålen in north-west Norway are studied theoretically for an idealized shelf topography. Wave damping is caused by the exchange of fluid on the shelf with an inner archipelago through a permeable coastline. This exchange is modelled by the application of a Robin condition at the coastal boundary. It is shown that CSWs with diurnal frequencies are possible in a small wave number range centred around zero group velocity. By calculating the nonlinear radiation stress components in the spatially damped CSWs, we find the time- and depth averaged Lagrangian mean drift current to second order along the coast. We show that the Lagrangian mean drift current is independent of the value of the damping coefficient, however small, as long as it is nonzero. This illustrates the singular behaviour of the Lagrangian wave drift problem for CSWs.