Effect of stratification on long period trapped waves on the shelf

The effect of stratification on very long-period waves trapped on a straight continental shelf of constant depth is examined for a two-layer model. There are 4 modes in this system. The characteristics of the mode with the largest phase velocity can be approximated by the barotropic mode. The mode corresponding to the barotropic shelf-wave mode is modified by the baroclinic motions significantly, and in the limit of very narrow shelf width, the mode characteristics are transformed from those of the barotropic shelf-wave to the baroclinic Kelvin wave if the long-shore wave length is larger than the internal deformation radius. In this case, the stratification has an apparent effect of increasing phase velocity of barotropic shelf-waves. The remaining two modes are dominated by baroclinic motions with significant contribution from barotropic motions: among which the one has a shelf-wave characteristics for small values of the shelf width and approaches the mode corresponding to the baroclinic Kelvin wave in shallower water for large shelf width and the other is a stationary mode. If the long-shore wave length is much shorter than the internal deformation radius, the motions in the upper and lower layers are decoupled: the surface and bottom modes analogous to those discussed byRhines (1970) appears.If the interface is deeper than the shelf depth, the stationary mode is absent and the characteristics of the third mode approaches those of the baroclinic double Kelvin wave mode as the shelf width increases.