Vorticity

Vorticity Definition: The vorticity Ω in its simplest form is defined as a vector which is equal to two times the rotation vector (8.6) For an irrotational flow, vorticity components are zero.         Vortex line: If tangent to an imaginary line at a point lying on it is in the direction of the Vorticity vector at that point , the line is a vortex line.         The general equation of the vortex line can be written as, (8.6b) In a rectangular cartesian cartesian coordinate system, it becomes (8.6c)  where, Vorticity components as vectors:          The vorticity is actually an anti symmetric tensor and its three distinct elements transform like the components of a vector in cartesian coordinates. This is the reason for which the vorticity components can be treated as vectors. Existence of Flow  A fluid  must obey the law of conservation of mass in course of its flow as it is a material body.  For a Velocity field to exist in a fluid continuum, the velocity components must obey the mass conservation principle. Velocity components which follow the mass conservation principle are said to constitute a possible fluid flow Velocity components violating this principle, are said to describe an impossible flow. The existence of a physically possible flow field is verified from the principle of conservation of mass.       The detailed discussion on this is deferred to the next chapter along with the discussion on principles of conservation of momentum and energy.