How Much of a Baroclinic Coastal Kelvin Wave Gets over a Ridge?

Abstract

Abstract This paper considers the interaction between a bottom-trapped low-frequency, reduced-gravity maid Kelvin wave propagating along a coastal wall, and a smooth ridge extending away from the coastline. Although the full problem appears intractable, it is shown that simple bounds may be placed on the amplitude of the Kelvin wave after it has passed the region of topography. The upper bound is found to be a good estimate for cases examined here. For a ridge of width one or two deformation radii, the reduction in amplitude of the Kelvin wave, induced by scattering along the ridge, is roughly equal to the fractional depth remaining in the undisturbed fluid layer at the highest point of the ridge; the reduction in energy is of course given by the square of this quantity. The bounds are found by considering the (approximate) conservation of mass between the incoming and transmitted Kelvin waves and the range of topographic waves on the rider, and also the (exact) conservation of energy. The full, and very ...