Based on linear shallow water theory for a uniformly rotating, homogeneous ocean, the properties of freely propagating shelf waves are investigated, applying the rigid lid approximation. Applied to the Norwegian shelf, the ocean depth is allowed to vary in the direction normal to the coast, in two different models of the bottom topography. The stream function solutions of the resulting vorticity equations are found, the dispersion diagrams are plotted, and the kinematic properties of the waves are discussed.
The linear theory derived for the shelf waves is applied in an attempt to find the wave-induced mean currents along the western coast of Norway. First, the friction is neglected, and the second-order Stokes drift inherent in the wave motion is found. Secondly, to take the effect of dissipation into account, the linear analysis is redone, including friction in the momentum equation. The waves are in this case assumed to be long, which simplifies the analysis considerably. The resulting, damped solutions are used tocalculate the wave-induced, non-linear forcing terms in the vertically integrated momentum and continuity equations. This yields a set of equations that are solved for the total mean Lagrangian volume flux.