The pressure gradient and the gradient of mass density are misaligned in a baroclinic fluid. Their cross product contributes a source to the vorticity equation.
Vorticity is generated when density and pressure gradients are not parallel. Under the Boussinesq approximation, the source is .
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Baroclinity refers to a condition in fluid dynamics, particularly in the context of atmospheric and oceanic sciences, where surfaces of constant density (isopycnals) and surfaces of constant pressure (isobars) do not align. In simpler terms, it describes a scenario where the density of a fluid varies with temperature and/or salinity in such a way that the pressure gradient at a particular level does not point in the same direction as the density gradient.