text: * In case of conservative body forces, .
  * For a barotropic fluid, . This is also true for a constant density fluid (including incompressible fluid) where . Note that this is not the same as an incompressible flow, for which the barotropic term cannot be neglected.
  * For inviscid fluids, the viscosity tensor  is zero.
  Thus for an inviscid, barotropic fluid with conservative body forces, the vorticity equation simplifies to
  Alternately, in case of incompressible, inviscid fluid with conservative body forces, 
  For a brief review of additional cases and simplifications, see also. For the vorticity equation in turbulence theory, in context of the flows in oceans and atmosphere, refer to.