Baroclinic pressure gradient

They are driven by baroclinic pressure gradients, especially horizontal salinity differences ... 

Alternatively, the vertical grid cell size may vary horizontally following the depth variations. This is the so-called ct-coordinate approach, which is expected to give a better representation of dense inflowing water masses over varying bottom topography. However, the accurate calculation of baroclinic pressure gradients creates problems for this type of coordinates. Moreover, the vertical acceleration is also excluded by the hydrostatic approximation. 

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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