Vortices like eddies are created by instabilities in a flow. When there are instabilities within the mean flow, energy can be transferred from the mean flow to the small perturbations which can then grow. In a barotropic fluid the density is a function of only the pressure and not the temperature (in contrast to a baroclinic fluid, where the density is a function of both the pressure and temperature). This means that surfaces of constant density (isopycnals) are also surfaces of constant pressure (isobars). Barotropic instability can form in different ways. Two examples are; when there is an interaction between the fluid flow and the bathymetry or topography of the domain; when there are frontal instabilities (may also lead to baroclinic instabilities). These instabilities are not dependent on the density and might even occur when the density of the fluid is constant. Instead, most of the instabilities are caused by a shear on the flow as can be seen in Figure 1. This shear in the velocity field induces a vertical and horizontal vorticity within the flow. As a result, there is upwelling on the right of the flow and downwelling on the left. This situation might lead to a barotropic unstable flow. The eddies that form alternatingly on both sides of the flow are part of this instability.
Another way to achieve this instability is to displace the Rossby waves in the horizontal direction (see Figure 2). This leads to a transfer of kinetic energy (not potential energy) from the mean flow towards the small perturbations (the eddies). The Rayleigh–Kuo criterion states that the gradient of the absolute vorticity should change sign within the domain. In the example of the shear induced eddies on the right, this means that the second derivative of the flow in the cross-flow direction, should be zero somewhere. This happens in the centre of the eddies, where the acceleration of the flow perpendicular to the flow changes direction.