New omega vortex identification method

A new vortex identification criterion called Omega-method is proposed based on the ideas that vorticity overtakes deformation in vortex. The comparison with other vortex identification methods like Q-criterion and lambda(2)-method is conducted and the advantages of the new method can be summarized as follows: (1) the method is able to capture vortex well and very easy to perform; (2) the physical meaning of Omega is clear while the interpretations of iso-surface values of Q and lambda(2) chosen to visualize vortices are obscure; (3) being different from Q and lambda(2) iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, Omega is pretty universal and does not need much adjustment in different cases and the iso-surfaces of Omega=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated; (4) both strong and weak vortices can be captured well simultaneously while improper Q and lambda(2) threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared; (5) Omega=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate Omega, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow, the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity.