text: Since the vorticity vector  and the velocity vector  are parallel to each other, we can write
  where  is some scalar function. One immediate consequence of Beltrami flow is that it can never be a planar or axisymmetric  flow because in those flows, vorticity is always perpendicular to the velocity field. The other important consequence will be realized by looking at the incompressible vorticity equation
  where  is an external body forces such as gravitational field, electric field etc., and  is the kinematic viscosity. Since  and  are parallel, the non-linear terms in the above equation are identically zero . Thus Beltrami flows satisfies the linear equation
  When , the components of vorticity satisfies a simple heat equation.