Internal Rossby radius

Kelvin waves require a flat-bottomed ocean, so the coastal boundary needs to be a vertical cliff. In a real ocean, there is a topographic transition from the coastline to the central plain areas of the basin. We denote this transition region as shelf. If the horizontal scale of the shelf is small compared with the internal Rossby radius, the Kelvin wave is the most important... 

When the shelf scale is comparable with the internal Rossby radius, wave motions normal to the shelf induce vertical motions due to the inclined bottom that generate internal pressure gradients. Therefore, a separation between barotropic and baroclinic modes is not possible anymore and these modes are denoted as mixed or hybrid modes that have been called coastally trapped waves. To evaluate their dispersion relations with respect to frequency and longshore wave number and their modal structure in the vertical plain normal to the coast, a two-dimensional eigenvalue problem must be solved numerically (Brink, 1991). The nodal lines of the velocity modes of these hybrid modes are inclined with respect to the sea surface in contrast to the baroclinic modes in case of a flat-bottomed ocean. 

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