Energy transfer from sub-inertial Kelvin waves to continental shelf waves at a transverse bottom escarpment

We consider barotropic coastally-trapped Kelvin waves of tidal origin along a straight coast that propagate from deeper water across a transverse bottom escarpment into a more shallow region. The M2 component, which has a frequency above the inertial frequency f, is modified by crossing the escarpment, but continues basically as a Kelvin wave into the shallow region. For tidal components that have frequencies smaller than f, like K1, some of the energy in the Kelvin wave is converted into a continental shelf wave (CSW) that follows the escarpment with shallow water to the right (in the northern hemisphere). The theory is applied to the shelf north-west of Norway where the deep Norwegian Sea is separated from the much shallower Barents Sea by an escarpment reaching from the north-Norwegian coast towards Spitsbergen. By introducing an idealized bottom topography and coastal geometry, analytical calculations and numerical modeling are used to investigate the energy flux in CSWs towards Spitsbergen caused by sub-inertial Kelvin wave motion along the west coast of Norway. Both analytical and numerical calculations indicate that the CSW energy flux towards Spitsbergen is about eighty percent of the incident sub-inertial Kelvin wave energy flux, and that only twenty percent of the energy flux is transmitted into the Barents Sea in the form of sub-inertial Kelvin waves.