The vorticity conservation laws can be viewed as constraints on the motion of the vorticity. These conservation laws can be used to monitor the accuracy of numerical computations or even to construct accurate numerical schemes.
The conservation laws can be derived from the vorticity equation.
Poincaré [174] derived the conservation laws for two-dimensional
flow of a homogenous incompressible viscous fluid in free space;
they are,
The above conservation laws have the following interpretation [14,122]: The first equation (2.19) states that the total circulation is conserved. Equation (2.20) implies that the average position of the vorticity (center of vorticity) does not change in time. Equation (2.21) is a measure of how fast a vortical region expands. For flows in which the linear and angular momenta are bounded, the equations (2.20) and (2.21) can also be interpreted as conservation of those two momenta respectively [122].