Vorticity and viscous dissipation in an incompressible flow

The relation between the vorticity and viscous dissipation in an incompressible flow has been investigated. It is shown that the square of relative vorticity with respect to the coordinate system fixed to the container or to the flow at infinity gives the global rate of viscous dissipation, that is, the viscous dissipation is proportional to the volume integral of the square of relative vorticity. Thus, the total rate of viscous dissipation in the flow produced by the motion of a rigid body is proportional to the integral of the square of vorticity taken over the whole space including the region occupied by the volume of the rigid body in which the vorticity is assumed to be the twice of the angular velocity of the body.