In the interstellar medium the turbulence is believed to be forced mostly through supernova explosions. In a first approximation these flows can be written as a gradient of a potential being thus devoid of vorticity. There are several mechanisms that could lead to vorticity generation, like viscosity and baroclinic terms, rotation, shear and magnetic fields, but it is not clear how effective they are, neither is it clear whether the vorticity is essential in determining the turbulent diffusion acting in the ISM. Here we present a study of the role of rotation, shear and baroclinicity in the generation of vorticity in the ISM.