vorticity depends on noninertia frame of referenc
I find that, vorticity depends on noninertia frame of reference: the vorticity expression under cylindrical coordinate in stationary frame of reference is different from that under cylindrical coordinate in a rotating frame of reference. For turbomachinery flow field simulation, the NS under cylindrical coordinate is usually adopted. When rotor is concerned, a rotating frame of reference is used. When implementing BaldwinLomax or SpalartAllmaras turbulence models, vorticity is needed. According to the above, vorticity in stationary frame is different from that in stationary one, then which one is to be chosen?

Re: vorticity depends on noninertia frame of refe
>vorticity depends on noninertia frame of reference
Yes. >vorticity in stationary frame is different from that in stationary one Huh? Don't confuse the distinction between Cartesian and cylindrical coordinates with the distinction between an absolute and a relative reference frame. Those two issues are independent of each other. Of course, in cylindrical coordinates the mathematical expression for vorticity looks different than on Cartesian coordinates, but they should be equivalent. What you should pay attention to is the reference frame, i.e. relative (rotating with the blade row in turbomachinery) or absolute. You simply have to be consistent within your reference frame, e.g. if your NS equations are expressed in the relative frame than you have to do the same with vorticity. 
Re: vorticity depends on noninertia frame of refe
Thanks! vorticity in stationary frame is different from that in stationary one
this is a typing error, it should be vorticity in stationary frame is different from that in a rotating one We can find the quivalent vorticity expression in cylindrical coordinate for the vorticity in cartesian coordinate, however it seems impossible to find an equivalent one in a roating reference frame? 
Re: vorticity depends on noninertia frame of refe
You need to properly account for the transformation from an inertial system to a noninertial coordinate frame.

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