How can I use Qcriterion to visualize vortex?
I am simulating incompressible boundary layer transition flow. I separate the flow velocity (u, v, w) into a base flow part (U, V, W) and a disturbance part (u’ ,v’ ,w’,). I use the below equations to calculate Q (second invariant of velocity gradient tensor):
Ω= (0.5*{dudy}0.5*{dvdx})**2+(0.5*{dudz}0.5*{dwdx})**2+ (0.5*{dvdx}0.5*{dudy})**2+(0.5*{dvdz}0.5*{dwdy})**2+ (0.5*{dwdx}0.5*{dudz})**2+(0.5*{dwdy}0.5*{dvdz})**2 S={dudx}**2+(0.5*{dvdx}+0.5*{dudy})**2+(0.5*{dwdx} +0.5*{dudz})**2+ (0.5*{dvdx}+0.5*{dudy})**2+{dvdy}**2+(0.5*{dwdy}+0 .5*{dvdz})**2 + (0.5*{dwdx}+0.5*{dudz})**2+(0.5*{dwdy}+0.5*{dvdz}) **2+{dwdz}**2 Q=0.5*(ΩS) My questions are: (1) In the calculation of velocity gradient tensor, should I use the total flow or disturbance flow quantities? (2) I have tried both in (1), but the values of dudx is around 1.0e2 pre second in the transition region and the final Q is around 1.0e5 or larger. Are these values normal? In the papers I read, Q are usually closed to zero about 1.0e2. (3) I am using very coarse grid in my simulation (820*80*16 for streamwise, wallnormal and spanwise direction) and I cannot see vortical structures, for example, a ring at the tip and two long legs at the tail as the papers. Is that because of my resolution? Thank you in advance. 
Hi,
I can't understand your notation very well, sorry, but i usually write Q=0.5*(Ω^2S^2) where Ω is the vorticity magnitude and S the mean strain rate (absolute quantities) I use the normalized Qcriterion, so the range is 1<Q<1 Hope be helpful 
Thanks a lot. After normalization the result looks better.

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